(%i1) batch("diffeq.max") read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load("stringproc") (%o2) /usr/share/maxima/5.31.3/share/stringproc/stringproc.mac (%i3) alias(convfloat,float) (%o3) [convfloat] (%i4) alias(int_trunc,truncate) (%o4) [truncate] (%i5) alias(elapsed_time_seconds,elapsed_real_time) (%o5) [elapsed_time_seconds] (%i6) alias(ln,log) (%o6) [log] (%i7) alias(arcsin,asin) (%o7) [asin] (%i8) alias(arccos,acos) (%o8) [acos] (%i9) alias(arctan,atan) (%o9) [atan] (%i10) alias(float_abs,abs) (%o10) [mabs] (%i11) keepfloat:true (%o11) true (%i12) mode_declare(display_poles(),fixnum) (%o12) [display_poles()] (%i13) mode_declare(est_size_answer(),convfloat) (%o13) [est_size_answer()] (%i14) mode_declare(test_suggested_h(),convfloat) (%o14) [test_suggested_h()] (%i15) mode_declare(reached_interval(),boolean) (%o15) [reached_interval()] (%i16) mode_declare(display_alot([iter],fixnum),fixnum) (%o16) [display_alot([iter], fixnum)] (%i17) mode_declare(adjust_for_pole([h_param],convfloat),convfloat) (%o17) [adjust_for_pole([h_param], convfloat)] (%i18) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum) (%o18) [prog_report([x_start], convfloat, [x_end], convfloat)] (%i19) mode_declare(check_for_pole(),fixnum) (%o19) [check_for_pole()] (%i20) mode_declare(atomall(),fixnum) (%o20) [atomall()] (%i21) mode_declare(log10([x],convfloat),convfloat) (%o21) [log10([x], convfloat)] (%i22) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum) (%o22) [logitem_timestr([fd], fixnum, [secs_in], number)] (%i23) mode_declare(omniout_timestr(secs_in,number),fixnum) (%o23) [omniout_timestr(secs_in, number)] (%i24) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum) (%o24) [zero_ats_ar(ar, array([MAX_TERMS], convfloat))] (%i25) mode_declare(ats([mmm_ats],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_ats], fixnum),convfloat) (%o25) [ats([mmm_ats], fixnum, [arr_a], completearray([MAX_TERMS], convfloat), [arr_b], completearray([MAX_TERMS], convfloat), [jjj_ats], fixnum)] (%i26) mode_declare(att([mmm_att],fixnum,[arr_a], completearray([MAX_TERMS],convfloat),[arr_b], completearray([MAX_TERMS],convfloat),[jjj_att], fixnum),convfloat) (%o26) [att([mmm_att], fixnum, [arr_a], completearray([MAX_TERMS], convfloat), [arr_b], completearray([MAX_TERMS], convfloat), [jjj_att], fixnum)] (%i27) mode_declare(logitem_ditto([file],fixnum),fixnum) (%o27) [logitem_ditto([file], fixnum)] (%i28) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum) (%o28) [logitem_integer([file], fixnum, [n], fixnum)] (%i29) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum) (%o29) [logitem_good_digits([file], fixnum, [relerror], convfloat)] (%i30) mode_declare(logitem_number([file],fixnum,[x],number),fixnum) (%o30) [logitem_number([file], fixnum, [x], number)] (%i31) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum) (%o31) [logitem_pole([file], fixnum, [pole], fixnum)] (%i32) mode_declare(logstart([file],fixnum),fixnum) (%o32) [logstart([file], fixnum)] (%i33) mode_declare(logend([file],fixnum),fixnum) (%o33) [logend([file], fixnum)] (%i34) mode_declare(chk_data(),fixnum) (%o34) [chk_data()] (%i35) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat, [t2],convfloat,[clock_sec2],convfloat), convfloat) (%o35) [comp_expect_sec([t_end2], convfloat, [t_start2], convfloat, [t2], convfloat, [clock_sec2], convfloat)] (%i36) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2], convfloat),convfloat) (%o36) [comp_percent([t_end2], convfloat, [start2], convfloat, [t2], convfloat)] (%i37) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%o37) [comp_rad_from_ratio([term1], convfloat, [term2], convfloat, [last_no], fixnum)] (%i38) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat, [last_no],fixnum),convfloat) (%o38) [comp_ord_from_ratio([term1], convfloat, [term2], convfloat, [last_no], fixnum)] (%i39) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%o39) [comp_rad_from_three_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [last_no], fixnum)] (%i40) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [last_no],fixnum),convfloat) (%o40) [comp_ord_from_three_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [last_no], fixnum)] (%i41) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%o41) [comp_rad_from_six_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [term4], convfloat, [term5], convfloat, [term6], convfloat, [last_no], fixnum)] (%i42) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2], convfloat,[term3],convfloat, [term4],convfloat,[term5], convfloat,[term6],convfloat, [last_no],fixnum),convfloat) (%o42) [comp_ord_from_six_terms([term1], convfloat, [term2], convfloat, [term3], convfloat, [term4], convfloat, [term5], convfloat, [term6], convfloat, [last_no], fixnum)] (%i43) mode_declare(factorial_2([nnn],fixnum),fixnum) (%o43) [factorial_2([nnn], fixnum)] (%i44) mode_declare(factorial_1([nnn],fixnum),fixnum) (%o44) [factorial_1([nnn], fixnum)] (%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum) (%o45) [factorial_3([mmm], fixnum, [nnn], fixnum)] (%i46) mode_declare(convfloat([mmm],fixnum),convfloat) (%o46) [convfloat([mmm], fixnum)] (%i47) mode_declare(elaped_time_seconds(),convfloat) (%o47) [elaped_time_seconds()] (%i48) mode_declare(Si([x],convfloat),convfloat) (%o48) [Si([x], convfloat)] (%i49) mode_declare(Ci([x],convfloat),convfloat) (%o49) [Ci([x], convfloat)] (%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end], convfloat,[estimated_h], convfloat,[estimated_answer], convfloat),convfloat) (%o50) [estimated_needed_step_error([x_start], convfloat, [x_end], convfloat, [estimated_h], convfloat, [estimated_answer], convfloat)] (%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat) (%o51) [my_check_sign([x0], convfloat, [xf], convfloat)] (%i52) mode_declare(main_prog(),fixnum) (%o52) [main_prog()] (%i53) define_variable(MAX_TERMS,30,fixnum) (%o53) 30 (%i54) define_variable(glob_iolevel,5,fixnum) (%o54) 5 (%i55) define_variable(glob_yes_pole,4,fixnum) (%o55) 4 (%i56) define_variable(glob_no_pole,3,fixnum) (%o56) 3 (%i57) define_variable(glob_not_given,0,fixnum) (%o57) 0 (%i58) define_variable(glob_no_sing_tests,4,fixnum) (%o58) 4 (%i59) define_variable(glob_ratio_test,1,fixnum) (%o59) 1 (%i60) define_variable(glob_three_term_test,2,fixnum) (%o60) 2 (%i61) define_variable(glob_six_term_test,3,fixnum) (%o61) 3 (%i62) define_variable(glob_log_10,log(10.0),convfloat) (%o62) 2.302585092994046 (%i63) define_variable(ALWAYS,1,fixnum) (%o63) 1 (%i64) define_variable(INFO,2,fixnum) (%o64) 2 (%i65) define_variable(DEBUGL,3,fixnum) (%o65) 3 (%i66) define_variable(DEBUGMASSIVE,4,fixnum) (%o66) 4 (%i67) define_variable(MAX_UNCHANGED,10,fixnum) (%o67) 10 (%i68) define_variable(glob_check_sign,1.0,convfloat) (%o68) 1.0 (%i69) define_variable(glob_desired_digits_correct,8.0,convfloat) (%o69) 8.0 (%i70) define_variable(glob_max_estimated_step_error,0.0,convfloat) (%o70) 0.0 (%i71) define_variable(glob_ratio_of_radius,0.1,convfloat) (%o71) 0.1 (%i72) define_variable(glob_percent_done,0.0,convfloat) (%o72) 0.0 (%i73) define_variable(glob_subiter_method,3,fixnum) (%o73) 3 (%i74) define_variable(glob_total_exp_sec,0.1,convfloat) (%o74) 0.1 (%i75) define_variable(glob_optimal_expect_sec,0.1,convfloat) (%o75) 0.1 (%i76) define_variable(glob_estimated_size_answer,100.0,convfloat) (%o76) 100.0 (%i77) define_variable(glob_html_log,true,boolean) (%o77) true (%i78) define_variable(glob_good_digits,0,fixnum) (%o78) 0 (%i79) define_variable(glob_max_opt_iter,10,fixnum) (%o79) 10 (%i80) define_variable(glob_dump,false,boolean) (%o80) false (%i81) define_variable(glob_djd_debug,true,boolean) (%o81) true (%i82) define_variable(glob_display_flag,true,boolean) (%o82) true (%i83) define_variable(glob_djd_debug2,true,boolean) (%o83) true (%i84) define_variable(glob_sec_in_minute,60,fixnum) (%o84) 60 (%i85) define_variable(glob_min_in_hour,60.0,convfloat) (%o85) 60.0 (%i86) define_variable(glob_hours_in_day,24.0,convfloat) (%o86) 24.0 (%i87) define_variable(glob_days_in_year,365,fixnum) (%o87) 365 (%i88) define_variable(glob_sec_in_hour,3600,fixnum) (%o88) 3600 (%i89) define_variable(glob_sec_in_day,86400,fixnum) (%o89) 86400 (%i90) define_variable(glob_sec_in_year,31536000,fixnum) (%o90) 31536000 (%i91) define_variable(glob_almost_1,0.999,convfloat) (%o91) 0.999 (%i92) define_variable(glob_clock_sec,0.0,convfloat) (%o92) 0.0 (%i93) define_variable(glob_clock_start_sec,0.0,convfloat) (%o93) 0.0 (%i94) define_variable(glob_not_yet_finished,true,boolean) (%o94) true (%i95) define_variable(glob_initial_pass,true,boolean) (%o95) true (%i96) define_variable(glob_not_yet_start_msg,true,boolean) (%o96) true (%i97) define_variable(glob_reached_optimal_h,false,boolean) (%o97) false (%i98) define_variable(glob_optimal_done,false,boolean) (%o98) false (%i99) define_variable(glob_disp_incr,0.1,convfloat) (%o99) 0.1 (%i100) define_variable(glob_h,0.1,convfloat) (%o100) 0.1 (%i101) define_variable(glob_diff_rc_fm,0.1,convfloat) (%o101) 0.1 (%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat) (%o102) 0.1 (%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat) (%o103) 0.1 (%i104) define_variable(glob_diff_ord_fm,0.1,convfloat) (%o104) 0.1 (%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat) (%o105) 0.1 (%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat) (%o106) 0.1 (%i107) define_variable(glob_six_term_ord_save,0.1,convfloat) (%o107) 0.1 (%i108) define_variable(glob_guess_error_rc,0.1,convfloat) (%o108) 0.1 (%i109) define_variable(glob_guess_error_ord,0.1,convfloat) (%o109) 0.1 (%i110) define_variable(glob_max_h,0.1,convfloat) (%o110) 0.1 (%i111) define_variable(glob_min_h,1.0E-6,convfloat) (%o111) 1.0E-6 (%i112) define_variable(glob_type_given_pole,0,fixnum) (%o112) 0 (%i113) define_variable(glob_large_float,1.0E+100,convfloat) (%o113) 1.0E+100 (%i114) define_variable(glob_larger_float,1.1E+100,convfloat) (%o114) 1.1E+100 (%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat) (%o115) 9.9E+100 (%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat) (%o116) 9.9E+100 (%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat) (%o117) 9.9E+100 (%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat) (%o118) 9.9E+100 (%i119) define_variable(glob_last_good_h,0.1,convfloat) (%o119) 0.1 (%i120) define_variable(glob_look_poles,false,boolean) (%o120) false (%i121) define_variable(glob_neg_h,false,boolean) (%o121) false (%i122) define_variable(glob_display_interval,0.0,convfloat) (%o122) 0.0 (%i123) define_variable(glob_next_display,0.0,convfloat) (%o123) 0.0 (%i124) define_variable(glob_dump_analytic,false,boolean) (%o124) false (%i125) define_variable(glob_abserr,1.0E-11,convfloat) (%o125) 1.0E-11 (%i126) define_variable(glob_relerr,1.0E-11,convfloat) (%o126) 1.0E-11 (%i127) define_variable(glob_min_pole_est,1.0E+9,convfloat) (%o127) 1.0E+9 (%i128) define_variable(glob_max_hours,0.0,convfloat) (%o128) 0.0 (%i129) define_variable(glob_max_iter,1000,fixnum) (%o129) 1000 (%i130) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat) (%o130) 1.0E-11 (%i131) define_variable(glob_max_trunc_err,1.0E-11,convfloat) (%o131) 1.0E-11 (%i132) define_variable(glob_no_eqs,0,fixnum) (%o132) 0 (%i133) define_variable(glob_optimal_clock_start_sec,0.0,convfloat) (%o133) 0.0 (%i134) define_variable(glob_optimal_start,0.0,convfloat) (%o134) 0.0 (%i135) define_variable(glob_upper_ratio_limit,1.0001,convfloat) (%o135) 1.0001 (%i136) define_variable(glob_lower_ratio_limit,0.9999,convfloat) (%o136) 0.9999 (%i137) define_variable(glob_small_float,0.0,convfloat) (%o137) 0.0 (%i138) define_variable(glob_smallish_float,0.0,convfloat) (%o138) 0.0 (%i139) define_variable(glob_unchanged_h_cnt,0,fixnum) (%o139) 0 (%i140) define_variable(glob_warned,false,boolean) (%o140) false (%i141) define_variable(glob_warned2,false,boolean) (%o141) false (%i142) define_variable(glob_max_sec,10000.0,convfloat) (%o142) 10000.0 (%i143) define_variable(glob_orig_start_sec,0.0,convfloat) (%o143) 0.0 (%i144) define_variable(glob_start,0,fixnum) (%o144) 0 (%i145) define_variable(glob_curr_iter_when_opt,0,fixnum) (%o145) 0 (%i146) define_variable(glob_current_iter,0,fixnum) (%o146) 0 (%i147) define_variable(glob_iter,0,fixnum) (%o147) 0 (%i148) define_variable(glob_normmax,0.0,convfloat) (%o148) 0.0 (%i149) define_variable(glob_max_minutes,0.0,convfloat) (%o149) 0.0 (%i150) array(array_y1_init,MAX_TERMS) (%o150) array_y1_init (%i151) array(array_y2_init,MAX_TERMS) (%o151) array_y2_init (%i152) array(array_norms,MAX_TERMS) (%o152) array_norms (%i153) array(array_fact_1,MAX_TERMS) (%o153) array_fact_1 (%i154) array(array_1st_rel_error,3) (%o154) array_1st_rel_error (%i155) array(array_last_rel_error,3) (%o155) array_last_rel_error (%i156) array(array_type_pole,3) (%o156) array_type_pole (%i157) array(array_type_real_pole,3) (%o157) array_type_real_pole (%i158) array(array_type_complex_pole,3) (%o158) array_type_complex_pole (%i159) array(array_y1,MAX_TERMS) (%o159) array_y1 (%i160) array(array_x,MAX_TERMS) (%o160) array_x (%i161) array(array_y2,MAX_TERMS) (%o161) array_y2 (%i162) array(array_tmp0,MAX_TERMS) (%o162) array_tmp0 (%i163) array(array_tmp1,MAX_TERMS) (%o163) array_tmp1 (%i164) array(array_tmp2,MAX_TERMS) (%o164) array_tmp2 (%i165) array(array_tmp3,MAX_TERMS) (%o165) array_tmp3 (%i166) array(array_tmp4,MAX_TERMS) (%o166) array_tmp4 (%i167) array(array_tmp5,MAX_TERMS) (%o167) array_tmp5 (%i168) array(array_m1,MAX_TERMS) (%o168) array_m1 (%i169) array(array_y1_higher,2,MAX_TERMS) (%o169) array_y1_higher (%i170) array(array_y1_higher_work,2,MAX_TERMS) (%o170) array_y1_higher_work (%i171) array(array_y1_higher_work2,2,MAX_TERMS) (%o171) array_y1_higher_work2 (%i172) array(array_y1_set_initial,3,MAX_TERMS) (%o172) array_y1_set_initial (%i173) array(array_y2_higher,2,MAX_TERMS) (%o173) array_y2_higher (%i174) array(array_y2_higher_work,2,MAX_TERMS) (%o174) array_y2_higher_work (%i175) array(array_y2_higher_work2,2,MAX_TERMS) (%o175) array_y2_higher_work2 (%i176) array(array_y2_set_initial,3,MAX_TERMS) (%o176) array_y2_set_initial (%i177) array(array_given_rad_poles,3,3) (%o177) array_given_rad_poles (%i178) array(array_given_ord_poles,3,3) (%o178) array_given_ord_poles (%i179) array(array_rad_test_poles,3,3) (%o179) array_rad_test_poles (%i180) array(array_ord_test_poles,3,3) (%o180) array_ord_test_poles (%i181) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o181) array_fact_2 (%i182) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o182) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i183) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o183) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i184) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o184) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i185) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%o185) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i186) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o186) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i187) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o187) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i188) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%o188) logitem_time(fd, secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs : secs_in, printf(fd, "~%"), secs if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "~d Seconds~%", sec_int)) else printf(fd, " 0.0 Seconds~%"), printf(fd, "~%")), 0) (%i189) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%o189) omniout_timestr(secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs secs : secs_in, if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, "= 0.0 Seconds~%")), 0) (%i190) zero_ats_ar(arr_a):=( block(modedcclare([iii],fixnum),iii:1, while iii <= MAX_TERMS do (arr_a[iii]:0.0,iii:1+iii)),0) (%o190) zero_ats_ar(arr_a) := (block(modedcclare([iii], fixnum), iii : 1, while iii <= MAX_TERMS do (arr_a : 0.0, iii : 1 + iii)), 0) iii (%i191) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:0.0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= MAX_TERMS and iii_ats <= MAX_TERMS then ret_ats :arr_a[iii_ats]*arr_b[lll_ats]+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%o191) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block(mode_declare([[iii_ats, lll_ats, ma_ats], fixnum, [ret_ats], convfloat]), ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, if (lll_ats <= MAX_TERMS) and (iii_ats <= MAX_TERMS) then ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i192) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:0.0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= MAX_TERMS do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS then ret_att :arr_aa[iii_att]*arr_bb[lll_att]*al_att +ret_att,iii_att:1+iii_att), ret_att:ret_att/mmm_att),ret_att) (%o192) att(mmm_att, arr_aa, arr_bb, jjj_att) := block(mode_declare([[al_att, iii_att, lll_att, ma_att], convfloat, [ret_att], fixnum]), ret_att : 0.0, if jjj_att < mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while (iii_att < mmm_att) and (iii_att <= MAX_TERMS) do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if (lll_att <= MAX_TERMS) and (iii_att <= MAX_TERMS) then ret_att : arr_aa arr_bb al_att + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : -------), ret_att) mmm_att (%i193) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o193) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i194) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o194) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i195) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o195) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i196) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), if rel_error # -1.0 then (if rel_error > +1.0E-34 then ( good_digits :3-floor(log10(rel_error)), printf(file,"~d",good_digits)) else (good_digits:16, printf(file,"~d", good_digits))) else printf(file,"Unknown"), printf(file,"")),0) (%o196) logitem_good_digits(file, rel_error) := (block(mode_declare([[good_digits], fixnum]), printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 3 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")), 0) (%i197) log_revs(file,revs):=printf(file,revs) (%o197) log_revs(file, revs) := printf(file, revs) (%i198) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o198) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i199) logitem_pole(file,pole):=(printf(file,""), if pole = 0 then printf(file,"NA") elseif pole = 1 then printf(file,"Real") elseif pole = 2 then printf(file,"Complex") elseif pole = 4 then printf(file,"Yes") else printf(file,"No"), printf(file,""),0) (%o199) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, ""), 0) (%i200) logstart(file):=(printf(file,""),0) (%o200) logstart(file) := (printf(file, ""), 0) (%i201) logend(file):=(printf(file,"~%"),0) (%o201) logend(file) := (printf(file, "~%"), 0) (%i202) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(ALWAYS,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%o202) chk_data() := (block(mode_declare([[errflag], boolean]), errflag : false, if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()), 0) (%i203) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:clock_sec2, sub1:t_end2-t_start2,sub2:t2-t_start2, if sub1 = 0.0 then sec_left:0.0 else (if sub2 > 0.0 then (rrr:sub1/sub2, sec_left:rrr*ms2-ms2) else sec_left:0.0),sec_left) (%o203) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block(mode_declare([[ms2, rrr, sec_left, sub1, sub2], convfloat]), ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i204) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:100.0*sub2/sub1 else rrr:0.0,rrr) (%o204) comp_percent(t_end2, t_start2, t2) := block(mode_declare([[rrr, sub1, sub2], convfloat]), sub1 : t_end2 - t_start2, 100.0 sub2 sub2 : t2 - t_start2, if sub2 > glob_small_float then rrr : ---------- sub1 else rrr : 0.0, rrr) (%i205) comp_rad_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%o205) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i206) comp_ord_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret :abs(term2)*convfloat(last_no) *log(abs(term1*glob_h/term2)) /log(convfloat(last_no)) +1.0 else ret:glob_larger_float,ret) (%o206) comp_ord_from_ratio(term1, term2, last_no) := !term1 glob_h! mabs(term2) convfloat(last_no) log(!------------!) ! term2 ! (if term2 > 0.0 then ret : -------------------------------------------------- log(convfloat(last_no)) + 1.0 else ret : glob_larger_float, ret) (%i207) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no)), if temp > 0.0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%o207) comp_rad_from_three_terms(term1, term2, term3, last_no) := (temp : mabs(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no)), if temp > 0.0 !term2 glob_h term1! then ret : !------------------! else ret : glob_larger_float, ret) ! temp ! (%i208) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*convfloat(last_no*last_no) +term2*term2*convfloat(last_no*last_no) +4.0*term2*term2 -4.0*term2*term2*convfloat(last_no) -3.0*term1*term3 +4.0*term1*term3*convfloat(last_no)) /(term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no))),ret) (%o208) comp_ord_from_three_terms(term1, term2, term3, last_no) := (ret : mabs((- term1 term3 convfloat(last_no last_no) + term2 term2 convfloat(last_no last_no) + 4.0 term2 term2 - 4.0 term2 term2 convfloat(last_no) - 3.0 term1 term3 + 4.0 term1 term3 convfloat(last_no))/(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no))), ret) (%i209) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # 0.0 and term4 # 0.0 and term3 # 0.0 and term2 # 0.0 and term1 # 0.0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :convfloat(last_no-3)*rm2 -2.0*convfloat(last_no-2)*rm1 +convfloat(last_no-1)*rm0, nr2 :convfloat(last_no-4)*rm3 -2.0*convfloat(last_no-3)*rm2 +convfloat(last_no-2)*rm1, dr1:(-1.0)/rm3+2.0/rm2+(-1.0)/rm1, dr2:(-1.0)/rm4+2.0/rm3+(-1.0)/rm2, ds1:5.0/rm3-8.0/rm2+3.0/rm1, ds2:5.0/rm4-8.0/rm3+3.0/rm2, if abs(nr1*dr2-nr2*dr1) = 0.0 or abs(dr1) = 0.0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) # 0.0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(2.0*dr1) -convfloat(last_no)/2.0, if abs(rcs) # 0.0 then (if rcs > 0.0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%o209) comp_rad_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := (if (term5 # 0.0) and (term4 # 0.0) and (term3 # 0.0) term6 term5 and (term2 # 0.0) and (term1 # 0.0) then (rm0 : -----, rm1 : -----, term5 term4 term4 term3 term2 rm2 : -----, rm3 : -----, rm4 : -----, term3 term2 term1 nr1 : convfloat(last_no - 3) rm2 - 2.0 convfloat(last_no - 2) rm1 + convfloat(last_no - 1) rm0, nr2 : convfloat(last_no - 4) rm3 - 2.0 convfloat(last_no - 3) rm2 + convfloat(last_no - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (mabs(nr1 dr2 - nr2 dr1) = 0.0) or (mabs(dr1) = 0.0) rm4 rm3 rm2 then (rad_c : glob_larger_float, ord_no : glob_larger_float) else (if mabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(last_no) ord_no : ------------- - ------------------, 2.0 dr1 2.0 if mabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) mabs(glob_h) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float))) else (rad_c : glob_larger_float, ord_no : glob_larger_float), glob_six_term_ord_save : ord_no, rad_c) (%i210) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o210) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i211) factorial_2(nnn):=nnn! (%o211) factorial_2(nnn) := nnn! (%i212) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%o212) factorial_1(nnn) := block(mode_declare([[ret], convfloat]), if nnn <= MAX_TERMS then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i213) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS and mmm <= MAX_TERMS then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%o213) factorial_3(mmm, nnn) := block(mode_declare([[ret], convfloat]), if (nnn <= MAX_TERMS) and (mmm <= MAX_TERMS) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i214) log10(x):=log(x)/glob_log_10 log(x) (%o214) log10(x) := ----------- glob_log_10 (%i215) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o215) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i216) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(10.0,-glob_desired_digits_correct) *abs(estimated_answer), omniout_float(ALWAYS,"estimated_h",32, estimated_h,32,""), omniout_float(ALWAYS,"estimated_answer", 32,estimated_answer,32,""), omniout_float(ALWAYS, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(ALWAYS,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(ALWAYS,"estimated_steps",32, estimated_steps,32,""), step_error :abs( desired_abs_gbl_error/estimated_steps), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%o216) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) mabs(estimated_answer), omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""), omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, ""), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h !desired_abs_gbl_error! 32, estimated_steps, 32, ""), step_error : !---------------------!, ! estimated_steps ! omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i217) exact_soln_y1(x):=block(cos(x)+1.0) (%o217) exact_soln_y1(x) := block(cos(x) + 1.0) (%i218) exact_soln_y2(x):=block(sin(x)+1.0) (%o218) exact_soln_y2(x) := block(sin(x) + 1.0) (%i219) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 4 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," ")) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > 0.0 and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > 0.0 and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1"), if glob_type_given_pole = 4 then (rad_given :sqrt( array_given_rad_poles[2,2] *array_given_rad_poles[2,2] +(array_x[1] -array_given_rad_poles[2,1]) *(array_x[1] -array_given_rad_poles[2,1])), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4,rad_given,4," "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[ 2,1],4," ")) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2"), if array_rad_test_poles[2,1] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles[2,1], 4," "), if array_rad_test_poles[2,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[2,1], omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[2,1], 4," ")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2"), if array_rad_test_poles[2,2] > 0.0 and array_rad_test_poles[2,2] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles[2,2], 4," "), if array_rad_test_poles[2,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[2,2], omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[2,2], 4," ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2"), if array_rad_test_poles[2,3] > 0.0 and array_rad_test_poles[2,3] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles[2,3], 4," "), if array_rad_test_poles[2,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[2,3], omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[2,3], 4," ")) else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2")), 0) (%o219) display_poles() := (block(mode_declare([[rad_given], convfloat]), if glob_type_given_pole = 4 then (rad_given : sqrt(array_given_rad_poles array_given_rad_poles 1, 2 1, 2 + (array_x - array_given_rad_poles ) 1 1, 1 (array_x - array_given_rad_poles )), 1 1, 1 if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\ 1, 1 dius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 1 1, 1 glob_least_ratio_sing then glob_least_ratio_sing : array_rad_test_poles , 1, 1 omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 1 "NO POLE (ratio test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float) 1, 2 1, 2 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 2 1, 2 glob_least_3_sing then glob_least_3_sing : array_rad_test_poles , 1, 2 omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO REAL POLE (three term test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < 1, 3 1, 3 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 3 1, 3 glob_least_6_sing then glob_least_6_sing : array_rad_test_poles , 1, 3 omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 3 "NO COMPLEX POLE (six term test) for Equation 1"), if glob_type_given_pole = 4 then (rad_given : sqrt(array_given_rad_poles array_given_rad_poles 2, 2 2, 2 + (array_x - array_given_rad_poles ) 1 2, 1 (array_x - array_given_rad_poles )), 1 2, 1 if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 2, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2"), if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\ 2, 1 dius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 2, 1 2, 1 glob_least_ratio_sing then glob_least_ratio_sing : array_rad_test_poles , 2, 1 omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 2, 1 "NO POLE (ratio test) for Equation 2"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float) 2, 2 2, 2 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 2, 2 2, 2 glob_least_3_sing then glob_least_3_sing : array_rad_test_poles , 2, 2 omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 2, 2 "NO REAL POLE (three term test) for Equation 2"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < 2, 3 2, 3 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 2, 3 2, 3 glob_least_6_sing then glob_least_6_sing : array_rad_test_poles , 2, 3 omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 2, 3 "NO COMPLEX POLE (six term test) for Equation 2")), 0) (%i220) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o220) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i221) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y1[1]) < min_size then (min_size:abs(array_y1[1]), omniout_float(ALWAYS,"min_size",32,min_size, 32,"")), if abs(array_y2[1]) < min_size then (min_size:abs(array_y2[1]), omniout_float(ALWAYS,"min_size",32,min_size, 32,"")), if min_size < 1.0 then (min_size:1.0, omniout_float(ALWAYS,"min_size",32,min_size, 32,"")),min_size) (%o221) est_size_answer() := block([min_size], min_size : glob_estimated_size_answer, if !array_y1 ! < min_size then (min_size : !array_y1 !, ! 1! ! 1! omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if !array_y2 ! < min_size then (min_size : !array_y2 !, ! 1! ! 1! omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i222) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:0.0,no_terms:MAX_TERMS, hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125, omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y1[no_terms]*hn_div_ho_3 +array_y1[no_terms-1]*hn_div_ho_2 +array_y1[no_terms-2]*hn_div_ho +array_y1[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, est_tmp:abs(array_y2[no_terms]*hn_div_ho_3 +array_y2[no_terms-1]*hn_div_ho_2 +array_y2[no_terms-2]*hn_div_ho +array_y2[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(ALWAYS,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%o222) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0, no_terms : MAX_TERMS, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), est_tmp : mabs(array_y1 hn_div_ho_3 + array_y1 hn_div_ho_2 no_terms no_terms - 1 + array_y1 hn_div_ho + array_y1 ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, est_tmp : mabs(array_y2 hn_div_ho_3 no_terms + array_y2 hn_div_ho_2 + array_y2 hn_div_ho no_terms - 1 no_terms - 2 + array_y2 ), if est_tmp >= max_estimated_step_error no_terms - 3 then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i223) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display then ret:true else ret:false,return(ret)) (%o223) reached_interval() := block(mode_declare([[ret], boolean]), if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i224) display_alot(iter):=( block(mode_declare( [[abserr],convfloat,[analytic_val_y],convfloat, [ind_var],convfloat,[numeric_val],convfloat, [relerr],convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(ALWAYS, "x[1] ", 33,ind_var,20, " "), analytic_val_y :exact_soln_y1(ind_var), omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y1[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y1[1] (numeric) ", 33,numeric_val, 20," "), if abs(analytic_val_y) # 0.0 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-34 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits :16) else (relerr:-1.0, glob_good_digits:-1), if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20," "), analytic_val_y :exact_soln_y2(ind_var), omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y2[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y2[1] (numeric) ", 33,numeric_val, 20," "), if abs(analytic_val_y) # 0.0 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-34 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits :16) else (relerr:-1.0, glob_good_digits:-1), if glob_iter = 1 then array_1st_rel_error[2] :relerr else array_last_rel_error[ 2] :relerr, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%o224) display_alot(iter) := (block(mode_declare([[abserr], convfloat, [analytic_val_y], convfloat, [ind_var], convfloat, [numeric_val], convfloat, [relerr], convfloat, [term_no], fixnum]), if reached_interval() then (if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y1(ind_var), omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y1 , term_no abserr : mabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "), if mabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : --------------------, if relerr > 1.0E-34 mabs(analytic_val_y) then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_y2(ind_var), omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y2 , term_no abserr : mabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "), if mabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : --------------------, if relerr > 1.0E-34 mabs(analytic_val_y) then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))), 0) (%i225) adjust_for_pole(h_param):=( block(mode_declare( [[hnew],convfloat,[sz2],convfloat,[tmp], convfloat]),hnew:h_param, glob_normmax:glob_small_float, if abs(array_y1_higher[1,1]) > glob_small_float then (tmp:abs(array_y1_higher[1,1]), if tmp < glob_normmax then glob_normmax:tmp), if abs(array_y2_higher[1,1]) > glob_small_float then (tmp:abs(array_y2_higher[1,1]), if tmp < glob_normmax then glob_normmax:tmp), if glob_look_poles and glob_min_pole_est > glob_small_float and glob_min_pole_est < glob_large_float then (sz2:glob_min_pole_est/10.0, if sz2 < hnew then ( omniout_float(INFO, "glob_h adjusted to ", 20,h_param,12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h:true, glob_curr_iter_when_opt :glob_current_iter, glob_optimal_clock_start_sec :elapsed_time_seconds(), glob_optimal_start:array_x[1]), hnew:sz2),hnew) (%o225) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat, [sz2], convfloat, [tmp], convfloat]), hnew : h_param, glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (glob_min_pole_est > glob_small_float) and (glob_min_pole_est < glob_large_float) glob_min_pole_est then (sz2 : -----------------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), hnew) 1 (%i226) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :total_clock_sec+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ",33, percent_done,4,"%")),0) (%o226) prog_report(x_start, x_end) := (block(mode_declare([[clock_sec], convfloat, [opt_clock_sec], convfloat, [clock_sec1], convfloat, [expect_sec], convfloat, [left_sec], convfloat, [percent_done], convfloat, [total_clock_sec], convfloat]), clock_sec1 : elapsed_time_seconds(), total_clock_sec : clock_sec1 - glob_orig_start_sec, glob_clock_sec : clock_sec1 - glob_clock_start_sec, left_sec : - clock_sec1 + glob_orig_start_sec + glob_max_sec, expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 clock_sec1 - glob_orig_start_sec), opt_clock_sec : clock_sec1 - glob_optimal_clock_start_sec, glob_optimal_expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 opt_clock_sec), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(x_end, x_start, glob_h + array_x ), 1 glob_percent_done : percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")), 0) (%i227) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y1_higher[1,last_no-1], array_y1_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y1_higher[1,last_no-1], array_y1_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[2,1]:glob_larger_float, array_ord_test_poles[2,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y2_higher[1,last_no-1], array_y2_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[2,1] then ( array_rad_test_poles[2,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y2_higher[1,last_no-1], array_y2_higher[1,last_no], last_no), array_rad_test_poles[2,1]:rad_c, array_ord_test_poles[2,1] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y1_higher[1,last_no-2], array_y1_higher[1,last_no-1], array_y1_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y1_higher[1,last_no-2], array_y1_higher[1,last_no-1], array_y1_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[2,2]:glob_larger_float, array_ord_test_poles[2,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y2_higher[1,last_no-2], array_y2_higher[1,last_no-1], array_y2_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[2,2] then ( array_rad_test_poles[2,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y2_higher[1,last_no-2], array_y2_higher[1,last_no-1], array_y2_higher[1,last_no], last_no), array_rad_test_poles[2,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[2,2] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y1_higher[1,last_no-5], array_y1_higher[1,last_no-4], array_y1_higher[1,last_no-3], array_y1_higher[1,last_no-2], array_y1_higher[1,last_no-1], array_y1_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y1_higher[1,last_no-5], array_y1_higher[1,last_no-4], array_y1_higher[1,last_no-3], array_y1_higher[1,last_no-2], array_y1_higher[1,last_no-1], array_y1_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[2,3]:glob_larger_float, array_ord_test_poles[2,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y2_higher[1,last_no-5], array_y2_higher[1,last_no-4], array_y2_higher[1,last_no-3], array_y2_higher[1,last_no-2], array_y2_higher[1,last_no-1], array_y2_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[2,3] then ( array_rad_test_poles[2,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y2_higher[1,last_no-5], array_y2_higher[1,last_no-4], array_y2_higher[1,last_no-3], array_y2_higher[1,last_no-2], array_y2_higher[1,last_no-1], array_y2_higher[1,last_no], last_no), array_rad_test_poles[2,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[2,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, term:1,ratio:1.0, while term <= MAX_TERMS do ( array_y1[term] :array_y1[term]*ratio, array_y1_higher[1,term] :array_y1_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, array_y2[term] :array_y2[term]*ratio, array_y2_higher[1,term] :array_y2_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%o227) check_for_pole() := (block(mode_declare([cnt], fixnum, [dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat, [ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum, [h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad], convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 1 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 1 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad : comp_rad_from_ratio(array_y1_higher , array_y1_higher , 1, last_no - 1 1, last_no tmp_rad last_no), tmp_ratio : ------------, if (cnt > 0) prev_tmp_rad and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 1 tmp_ord : comp_ord_from_ratio(array_y1_higher , 1, last_no - 1 array_y1_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 1 array_ord_test_poles : tmp_ord)), tmp_rad : glob_larger_float, 1, 1 prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 2, 1 array_ord_test_poles : glob_larger_float, found_sing : 1, 2, 1 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad : comp_rad_from_ratio(array_y2_higher , array_y2_higher , 1, last_no - 1 1, last_no tmp_rad last_no), tmp_ratio : ------------, if (cnt > 0) prev_tmp_rad and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 2, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 2, 1 tmp_ord : comp_ord_from_ratio(array_y2_higher , 1, last_no - 1 array_y2_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 2, 1 array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float, 2, 1 tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 2 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 2 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad : comp_rad_from_three_terms(array_y1_higher , 1, last_no - 2 array_y1_higher , array_y1_higher , last_no), 1, last_no - 1 1, last_no tmp_rad tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) prev_tmp_rad and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 2 tmp_ord : comp_ord_from_three_terms(array_y1_higher , 1, last_no - 2 array_y1_higher , array_y1_higher , last_no), 1, last_no - 1 1, last_no array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est 1, 2 then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), 1, 2 tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 2, 2 array_ord_test_poles : glob_larger_float, found_sing : 1, 2, 2 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad : comp_rad_from_three_terms(array_y2_higher , 1, last_no - 2 array_y2_higher , array_y2_higher , last_no), 1, last_no - 1 1, last_no tmp_rad tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) prev_tmp_rad and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 2, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 2, 2 tmp_ord : comp_ord_from_three_terms(array_y2_higher , 1, last_no - 2 array_y2_higher , array_y2_higher , last_no), 1, last_no - 1 1, last_no array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est 2, 2 then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), 2, 2 glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 3 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 3 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad : comp_rad_from_six_terms(array_y1_higher , 1, last_no - 5 array_y1_higher , array_y1_higher , 1, last_no - 4 1, last_no - 3 array_y1_higher , array_y1_higher , 1, last_no - 2 1, last_no - 1 tmp_rad array_y1_higher , last_no), tmp_ratio : ------------, 1, last_no prev_tmp_rad if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 3 tmp_ord : comp_ord_from_six_terms(array_y1_higher , 1, last_no - 5 array_y1_higher , array_y1_higher , 1, last_no - 4 1, last_no - 3 array_y1_higher , array_y1_higher , 1, last_no - 2 1, last_no - 1 array_y1_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 3 if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), tmp_rad : glob_larger_float, 1, 3 prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 2, 3 array_ord_test_poles : glob_larger_float, found_sing : 1, 2, 3 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad : comp_rad_from_six_terms(array_y2_higher , 1, last_no - 5 array_y2_higher , array_y2_higher , 1, last_no - 4 1, last_no - 3 array_y2_higher , array_y2_higher , 1, last_no - 2 1, last_no - 1 tmp_rad array_y2_higher , last_no), tmp_ratio : ------------, 1, last_no prev_tmp_rad if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 2, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 2, 3 tmp_ord : comp_ord_from_six_terms(array_y2_higher , 1, last_no - 5 array_y2_higher , array_y2_higher , 1, last_no - 4 1, last_no - 3 array_y2_higher , array_y2_higher , 1, last_no - 2 1, last_no - 1 array_y2_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 2, 3 if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est) 2, 3 glob_ratio_of_radius < mabs(glob_h) then (h_new : glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0, while term <= MAX_TERMS do (array_y1 : array_y1 ratio, term term array_y1_higher : array_y1_higher ratio, 1, term 1, term array_x : array_x ratio, array_y2 : array_y2 ratio, term term term term array_y2_higher : array_y2_higher ratio, 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ------------, term : 1 + term), term term mabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()), 0) (%i228) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_m1[1]*array_y2[1], array_tmp2[1]:array_tmp1[1]+array_const_0D0[1], array_tmp3[1]:array_const_1D0[1]+array_tmp2[1], if not array_y1_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp3[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_y1[2]:temporary, array_y1_higher[1,2]:temporary), temporary:temporary*1.0/glob_h, array_y1_higher[2,1]:temporary,0)),kkk:2, array_tmp5[1]:array_y1[1]-array_const_1D0[1], if not array_y2_set_initial[2,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp5[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_y2[2]:temporary, array_y2_higher[1,2]:temporary), temporary:temporary*1.0/glob_h, array_y2_higher[2,1]:temporary,0)),kkk:2, array_tmp1[2]:ats(2,array_m1,array_y2,1), array_tmp2[2]:array_tmp1[2],array_tmp3[2]:array_tmp2[2], if not array_y1_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp3[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y1[3]:temporary, array_y1_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y1_higher[2,2]:temporary,0)),kkk:3, array_tmp5[2]:array_y1[2], if not array_y2_set_initial[2,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp5[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y2[3]:temporary, array_y2_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y2_higher[2,2]:temporary,0)),kkk:3, array_tmp1[3]:ats(3,array_m1,array_y2,1), array_tmp2[3]:array_tmp1[3],array_tmp3[3]:array_tmp2[3], if not array_y1_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp3[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y1[4]:temporary, array_y1_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y1_higher[2,3]:temporary,0)),kkk:4, array_tmp5[3]:array_y1[3], if not array_y2_set_initial[2,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp5[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y2[4]:temporary, array_y2_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y2_higher[2,3]:temporary,0)),kkk:4, array_tmp1[4]:ats(4,array_m1,array_y2,1), array_tmp2[4]:array_tmp1[4],array_tmp3[4]:array_tmp2[4], if not array_y1_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp3[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y1[5]:temporary, array_y1_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y1_higher[2,4]:temporary,0)),kkk:5, array_tmp5[4]:array_y1[4], if not array_y2_set_initial[2,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp5[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y2[5]:temporary, array_y2_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y2_higher[2,4]:temporary,0)),kkk:5, array_tmp1[5]:ats(5,array_m1,array_y2,1), array_tmp2[5]:array_tmp1[5],array_tmp3[5]:array_tmp2[5], if not array_y1_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp3[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y1[6]:temporary, array_y1_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y1_higher[2,5]:temporary,0)),kkk:6, array_tmp5[5]:array_y1[5], if not array_y2_set_initial[2,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp5[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y2[6]:temporary, array_y2_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y2_higher[2,5]:temporary,0)),kkk:6, while kkk <= MAX_TERMS do (array_tmp1[kkk]:ats(kkk,array_m1,array_y2,1), array_tmp2[kkk]:array_tmp1[kkk], array_tmp3[kkk]:array_tmp2[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y1_set_initial[1,order_d+kkk] then ( temporary :array_tmp3[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_y1[order_d+kkk]:temporary, array_y1_higher[1,order_d+kkk]:temporary, term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= MAX_TERMS and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :temporary*adj2/glob_h else temporary:temporary, array_y1_higher[adj3,term] :temporary),term:term-1, adj2:adj2-1,adj3:1+adj3))), array_tmp5[kkk]:array_y1[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y2_set_initial[2,order_d+kkk] then ( temporary :array_tmp5[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_y2[order_d+kkk]:temporary, array_y2_higher[1,order_d+kkk]:temporary, term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= MAX_TERMS and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :temporary*adj2/glob_h else temporary:temporary, array_y2_higher[adj3,term] :temporary),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%o228) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : array_m1 array_y2 , array_tmp2 : 1 1 1 1 array_tmp1 + array_const_0D0 , array_tmp3 : array_const_1D0 + array_tmp2 , 1 1 1 1 1 if not array_y1_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_y1 : temporary, 2 temporary 1.0 array_y1_higher : temporary), temporary : -------------, 1, 2 glob_h array_y1_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp5 : array_y1 - array_const_1D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= MAX_TERMS 2, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_y2 : temporary, 2 temporary 1.0 array_y2_higher : temporary), temporary : -------------, 1, 2 glob_h array_y2_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : ats(2, array_m1, array_y2, 1), array_tmp2 : array_tmp1 , 2 2 2 array_tmp3 : array_tmp2 , if not array_y1_set_initial 2 2 1, 3 then (if 2 <= MAX_TERMS then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(1, 2), 2 if 3 <= MAX_TERMS then (array_y1 : temporary, 3 temporary 2.0 array_y1_higher : temporary), temporary : -------------, 1, 3 glob_h array_y1_higher : temporary, 0)), kkk : 3, array_tmp5 : array_y1 , 2, 2 2 2 if not array_y2_set_initial then (if 2 <= MAX_TERMS 2, 3 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), 2 if 3 <= MAX_TERMS then (array_y2 : temporary, 3 temporary 2.0 array_y2_higher : temporary), temporary : -------------, 1, 3 glob_h array_y2_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp1 : ats(3, array_m1, array_y2, 1), array_tmp2 : array_tmp1 , 3 3 3 array_tmp3 : array_tmp2 , if not array_y1_set_initial 3 3 1, 4 then (if 3 <= MAX_TERMS then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(2, 3), 3 if 4 <= MAX_TERMS then (array_y1 : temporary, 4 temporary 3.0 array_y1_higher : temporary), temporary : -------------, 1, 4 glob_h array_y1_higher : temporary, 0)), kkk : 4, array_tmp5 : array_y1 , 2, 3 3 3 if not array_y2_set_initial then (if 3 <= MAX_TERMS 2, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 if 4 <= MAX_TERMS then (array_y2 : temporary, 4 temporary 3.0 array_y2_higher : temporary), temporary : -------------, 1, 4 glob_h array_y2_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp1 : ats(4, array_m1, array_y2, 1), array_tmp2 : array_tmp1 , 4 4 4 array_tmp3 : array_tmp2 , if not array_y1_set_initial 4 4 1, 5 then (if 4 <= MAX_TERMS then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(3, 4), 4 if 5 <= MAX_TERMS then (array_y1 : temporary, 5 temporary 4.0 array_y1_higher : temporary), temporary : -------------, 1, 5 glob_h array_y1_higher : temporary, 0)), kkk : 5, array_tmp5 : array_y1 , 2, 4 4 4 if not array_y2_set_initial then (if 4 <= MAX_TERMS 2, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 if 5 <= MAX_TERMS then (array_y2 : temporary, 5 temporary 4.0 array_y2_higher : temporary), temporary : -------------, 1, 5 glob_h array_y2_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : ats(5, array_m1, array_y2, 1), array_tmp2 : array_tmp1 , 5 5 5 array_tmp3 : array_tmp2 , if not array_y1_set_initial 5 5 1, 6 then (if 5 <= MAX_TERMS then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(4, 5), 5 if 6 <= MAX_TERMS then (array_y1 : temporary, 6 temporary 5.0 array_y1_higher : temporary), temporary : -------------, 1, 6 glob_h array_y1_higher : temporary, 0)), kkk : 6, array_tmp5 : array_y1 , 2, 5 5 5 if not array_y2_set_initial then (if 5 <= MAX_TERMS 2, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 if 6 <= MAX_TERMS then (array_y2 : temporary, 6 temporary 5.0 array_y2_higher : temporary), temporary : -------------, 1, 6 glob_h array_y2_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= MAX_TERMS do (array_tmp1 : ats(kkk, array_m1, array_y2, 1), kkk array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 , order_d : 1, kkk kkk kkk kkk if order_d + kkk <= MAX_TERMS then (if not array_y1_set_initial 1, order_d + kkk then (temporary : array_tmp3 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y1 : temporary, order_d + kkk array_y1_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while (term >= 1) and (term <= MAX_TERMS) and (adj3 < 1 + order_d) do (if adj3 <= 1 + order_d temporary adj2 then (if adj2 > 0 then temporary : -------------- else temporary : temporary, glob_h array_y1_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), array_tmp5 : array_y1 , order_d : 1, kkk kkk if order_d + kkk <= MAX_TERMS then (if not array_y2_set_initial 2, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y2 : temporary, order_d + kkk array_y2_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while (term >= 1) and (term <= MAX_TERMS) and (adj3 < 1 + order_d) do (if adj3 <= 1 + order_d temporary adj2 then (if adj2 > 0 then temporary : -------------- else temporary : temporary, glob_h array_y2_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)), 0) (%i229) exact_soln_y1(x):=block(cos(x)+1.0) (%o229) exact_soln_y1(x) := block(cos(x) + 1.0) (%i230) exact_soln_y2(x):=block(sin(x)+1.0) (%o230) exact_soln_y2(x) := block(sin(x) + 1.0) (%i231) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,best_h,found_h], convfloat,[repeat_it],fixnum]),Digits:32, max_terms:30,glob_html_log:true,term:1, while term <= MAX_TERMS do (array_y1_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_y2_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_norms[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_fact_1[term]:0.0,term:1+term),term:1, while term <= 3 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 3 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 3 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 3 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 3 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= MAX_TERMS do (array_y1[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_y2[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp4[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp5[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term), ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y1_higher[ord,term]:0.0,term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y1_higher_work[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y1_higher_work2[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= MAX_TERMS do (array_y1_set_initial[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y2_higher[ord,term]:0.0,term:1+term), ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y2_higher_work[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y2_higher_work2[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= MAX_TERMS do (array_y2_set_initial[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= 3 do (array_given_rad_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= 3 do (array_given_ord_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= 3 do (array_rad_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 3 do (term:1, while term <= 3 do (array_ord_test_poles[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= MAX_TERMS do (term:1, while term <= MAX_TERMS do (array_fact_2[ord,term]:0.0,term:1+term), ord:1+ord),zero_ats_ar(array_y1), zero_ats_ar(array_x),zero_ats_ar(array_m1), zero_ats_ar(array_y2),zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),zero_ats_ar(array_const_1), array_const_1[1]:1,zero_ats_ar(array_const_0D0), array_const_0D0[1]:0.0,zero_ats_ar(array_const_1D0), array_const_1D0[1]:1.0,zero_ats_ar(array_m1), array_m1[1]:-1.0,iiif:0, while iiif <= MAX_TERMS do (jjjf:0, while jjjf <= MAX_TERMS do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_y1_set_initial[1,1]:true, array_y1_set_initial[1,2]:false, array_y1_set_initial[1,3]:false, array_y1_set_initial[1,4]:false, array_y1_set_initial[1,5]:false, array_y1_set_initial[1,6]:false, array_y1_set_initial[1,7]:false, array_y1_set_initial[1,8]:false, array_y1_set_initial[1,9]:false, array_y1_set_initial[1,10]:false, array_y1_set_initial[1,11]:false, array_y1_set_initial[1,12]:false, array_y1_set_initial[1,13]:false, array_y1_set_initial[1,14]:false, array_y1_set_initial[1,15]:false, array_y1_set_initial[1,16]:false, array_y1_set_initial[1,17]:false, array_y1_set_initial[1,18]:false, array_y1_set_initial[1,19]:false, array_y1_set_initial[1,20]:false, array_y1_set_initial[1,21]:false, array_y1_set_initial[1,22]:false, array_y1_set_initial[1,23]:false, array_y1_set_initial[1,24]:false, array_y1_set_initial[1,25]:false, array_y1_set_initial[1,26]:false, array_y1_set_initial[1,27]:false, array_y1_set_initial[1,28]:false, array_y1_set_initial[1,29]:false, array_y1_set_initial[1,30]:false, array_y2_set_initial[2,1]:true, array_y2_set_initial[2,2]:false, array_y2_set_initial[2,3]:false, array_y2_set_initial[2,4]:false, array_y2_set_initial[2,5]:false, array_y2_set_initial[2,6]:false, array_y2_set_initial[2,7]:false, array_y2_set_initial[2,8]:false, array_y2_set_initial[2,9]:false, array_y2_set_initial[2,10]:false, array_y2_set_initial[2,11]:false, array_y2_set_initial[2,12]:false, array_y2_set_initial[2,13]:false, array_y2_set_initial[2,14]:false, array_y2_set_initial[2,15]:false, array_y2_set_initial[2,16]:false, array_y2_set_initial[2,17]:false, array_y2_set_initial[2,18]:false, array_y2_set_initial[2,19]:false, array_y2_set_initial[2,20]:false, array_y2_set_initial[2,21]:false, array_y2_set_initial[2,22]:false, array_y2_set_initial[2,23]:false, array_y2_set_initial[2,24]:false, array_y2_set_initial[2,25]:false, array_y2_set_initial[2,26]:false, array_y2_set_initial[2,27]:false, array_y2_set_initial[2,28]:false, array_y2_set_initial[2,29]:false, array_y2_set_initial[2,30]:false,ALWAYS:1,INFO:2,DEBUGL:3, DEBUGMASSIVE:4,MAX_TERMS:30,glob_iolevel:INFO, glob_orig_start_sec:elapsed_time_seconds(), glob_curr_iter_when_opt:0,glob_display_flag:true, glob_no_eqs:2,glob_iter:-1,opt_iter:-1,glob_max_iter:50000, glob_max_hours:0.0,glob_max_minutes:15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest1postode.ode#################"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; "), omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:0.1,"), omniout_str(ALWAYS,"x_end:10.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000,"), omniout_str(ALWAYS,"glob_display_interval:0.1,"), omniout_str(ALWAYS,"glob_max_minutes:10,"), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_desired_digits_correct:10,"), omniout_str(ALWAYS,"glob_display_interval:0.01,"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000000,"), omniout_str(ALWAYS,"glob_max_minutes:10.0,"), omniout_str(ALWAYS,"glob_subiter_method:3,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y1 (x) := (block("), omniout_str(ALWAYS," (1.0 + cos(x)) "), omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"exact_soln_y2 (x) := (block("), omniout_str(ALWAYS," (1.0 + sin(x)) "), omniout_str(ALWAYS,"));"),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""),omniout_str(ALWAYS,""), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:0.0,glob_smallish_float:0.0, glob_large_float:1.0E+100,glob_larger_float:1.1E+100, glob_almost_1:0.99,x_start:0.1,x_end:10.0, array_y1_init[1+0]:exact_soln_y1(x_start), array_y2_init[1+0]:exact_soln_y2(x_start), glob_look_poles:true,glob_max_iter:1000000, glob_display_interval:0.1,glob_max_minutes:10, glob_desired_digits_correct:10,glob_display_interval:0.01, glob_look_poles:true,glob_max_iter:1000000000, glob_max_minutes:10.0,glob_subiter_method:3, glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, omniout_str(ALWAYS,"START of Optimize"), glob_check_sign:my_check_sign(x_start,x_end),found_h:false, glob_h:glob_min_h*glob_check_sign, if abs(glob_max_h) < abs(glob_h) then glob_h:abs(glob_max_h)*glob_check_sign, if abs(glob_display_interval) < abs(glob_h) then glob_h:abs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h:false, glob_display_interval:abs(glob_display_interval)) else (glob_neg_h:true, glob_display_interval :-abs(glob_display_interval)),chk_data(), best_h:glob_h,min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err:estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:0.0, while opt_iter <= 100 and not found_h do (omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y1[term_no] :array_y1_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1),term_no:1+term_no), rows:order_diff,r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y1_higher[ r_order,term_no] :array_y1_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),r_order:1+r_order), order_diff:1,term_no:1, while term_no <= order_diff do (array_y2[term_no] :array_y2_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1),term_no:1+term_no), rows:order_diff,r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y2_higher[ r_order,term_no] :array_y2_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),r_order:1+r_order), if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter:1, while subiter <= 2 do (atomall(),subiter:1+subiter)) else (subiter:1, while subiter <= MAX_TERMS+2 do (atomall(),subiter:1+subiter)), estimated_step_error:test_suggested_h(), omniout_float(ALWAYS,"estimated_step_error",32, estimated_step_error,32,""), if estimated_step_error > est_needed_step_err and opt_iter = 1 or glob_check_sign*glob_h >= glob_check_sign*glob_max_h then (found_h:true, glob_h:glob_check_sign*glob_max_h, best_h:glob_h) elseif estimated_step_error > est_needed_step_err and not found_h then (glob_h:glob_h/2.0,best_h:glob_h, found_h:true) else (glob_h:glob_h*2.0,best_h:glob_h), omniout_float(ALWAYS,"best_h",32,best_h,32,""), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(ALWAYS,"Beginning glob_h too large."), found_h:false), if opt_iter > 100 then (glob_h:glob_check_sign*glob_max_h,found_h:false), if glob_check_sign*glob_display_interval < glob_check_sign*glob_h then glob_h:glob_check_sign*glob_display_interval, if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(ALWAYS,"START of Soultion"), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y1[term_no] :array_y1_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y1_higher[ r_order,term_no] :array_y1_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no), r_order:1+r_order),order_diff:1,term_no:1, while term_no <= order_diff do (array_y2[term_no] :array_y2_init[term_no] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),rows:order_diff, r_order:1, while r_order <= rows do (term_no:1, while term_no <= 1-r_order+rows do (it:-1+r_order+term_no, if term_no < MAX_TERMS then array_y2_higher[ r_order,term_no] :array_y2_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no), r_order:1+r_order),current_iter:1, glob_clock_start_sec:elapsed_time_seconds(), glob_clock_sec:elapsed_time_seconds(), glob_current_iter:0,glob_iter:0, omniout_str(DEBUGL," "), glob_reached_optimal_h:true, glob_optimal_clock_start_sec :elapsed_time_seconds(), while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and glob_clock_sec-glob_orig_start_sec < glob_max_sec do (if reached_interval() then (omniout_str(INFO," "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter:1+glob_iter, glob_clock_sec:elapsed_time_seconds(), glob_current_iter:1+glob_current_iter, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter:1, while subiter <= 2 do (atomall(), subiter:1+subiter)) else (subiter:1, while subiter <= MAX_TERMS+2 do (atomall(), subiter:1+subiter)), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y1_higher_work[2,iii] :array_y1_higher[2,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y1_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y1_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( array_y1_higher_work[1,iii] :array_y1_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y1_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y1_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y1_higher_work[1,iii] :array_y1_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y1_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y1_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1), term_no:MAX_TERMS, while term_no >= 1 do ( array_y1[term_no] :array_y1_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y1_higher[ord,term_no] :array_y1_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1),order_diff:2, ord:2,calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y2_higher_work[2,iii] :array_y2_higher[2,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y2_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y2_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( array_y2_higher_work[1,iii] :array_y2_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y2_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y2_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1),ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y2_higher_work[1,iii] :array_y2_higher[1,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:1, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( temp_sum :array_y2_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y2_higher_work2[ord,calc_term] :temp_sum*expt(glob_h,calc_term-1) /factorial_1(calc_term-1), term_no:MAX_TERMS, while term_no >= 1 do ( array_y2[term_no] :array_y2_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y2_higher[ord,term_no] :array_y2_higher_work2[ ord,term_no],ord:1+ord), term_no:term_no-1)), omniout_str(ALWAYS,"Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds()-glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec:elapsed_time_seconds(), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; "), omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "), omniout_int(INFO, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-08T22:49:28-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "mtest1"), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_str(html_log_file,"16"), logitem_good_digits(html_log_file, array_last_rel_error[ 1]), logitem_integer(html_log_file, MAX_TERMS), if glob_least_given_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_given_sing), 0) else ( logitem_str(html_log_file, "NOT GIVEN"),0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "mtest1 diffeq.max"), logitem_str(html_log_file, "mtest1 maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_good_digits(html_log_file, array_last_rel_error[ 2]), logditto(html_log_file), if glob_least_given_sing < glob_large_float then (logditto(html_log_file),0) else (logditto(html_log_file),0), if glob_least_ratio_sing < glob_large_float then (logditto(html_log_file),0) else (logditto(html_log_file),0), if glob_least_3_sing < glob_large_float then (logditto(html_log_file),0) else (logditto(html_log_file),0), if glob_least_6_sing < glob_large_float then (logditto(html_log_file),0) else (logditto(html_log_file),0), logditto(html_log_file), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file),0) else (logditto(html_log_file),0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o231) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2], convfloat, [niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii], fixnum, [temp_sum], convfloat, [current_iter], fixnum, [x_start, x_end], convfloat, [it, opt_iter], fixnum, [tmp], convfloat, [subiter], fixnum, [est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 30, glob_html_log : true, term : 1, while term <= MAX_TERMS do (array_y1_init : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_y2_init : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 3 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 3 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 3 do (array_type_pole : 0, term term : 1 + term), term : 1, while term <= 3 do (array_type_real_pole : 0, term term : 1 + term), term : 1, while term <= 3 do (array_type_complex_pole : 0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_x : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y1_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y1_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= MAX_TERMS do (array_y1_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y2_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y2_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= MAX_TERMS do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 3 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1, while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), zero_ats_ar(array_y1), zero_ats_ar(array_x), zero_ats_ar(array_m1), zero_ats_ar(array_y2), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5), zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0), array_const_0D0 : 0.0, 1 1 zero_ats_ar(array_const_1D0), array_const_1D0 : 1.0, zero_ats_ar(array_m1), 1 array_m1 : - 1.0, iiif : 0, while iiif <= MAX_TERMS do (jjjf : 0, 1 while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0, iiif iiif, jjjf jjjf : 1 + jjjf), iiif : 1 + iiif), array_y1_set_initial : true, 1, 1 array_y1_set_initial : false, array_y1_set_initial : false, 1, 2 1, 3 array_y1_set_initial : false, array_y1_set_initial : false, 1, 4 1, 5 array_y1_set_initial : false, array_y1_set_initial : false, 1, 6 1, 7 array_y1_set_initial : false, array_y1_set_initial : false, 1, 8 1, 9 array_y1_set_initial : false, array_y1_set_initial : false, 1, 10 1, 11 array_y1_set_initial : false, array_y1_set_initial : false, 1, 12 1, 13 array_y1_set_initial : false, array_y1_set_initial : false, 1, 14 1, 15 array_y1_set_initial : false, array_y1_set_initial : false, 1, 16 1, 17 array_y1_set_initial : false, array_y1_set_initial : false, 1, 18 1, 19 array_y1_set_initial : false, array_y1_set_initial : false, 1, 20 1, 21 array_y1_set_initial : false, array_y1_set_initial : false, 1, 22 1, 23 array_y1_set_initial : false, array_y1_set_initial : false, 1, 24 1, 25 array_y1_set_initial : false, array_y1_set_initial : false, 1, 26 1, 27 array_y1_set_initial : false, array_y1_set_initial : false, 1, 28 1, 29 array_y1_set_initial : false, array_y2_set_initial : true, 1, 30 2, 1 array_y2_set_initial : false, array_y2_set_initial : false, 2, 2 2, 3 array_y2_set_initial : false, array_y2_set_initial : false, 2, 4 2, 5 array_y2_set_initial : false, array_y2_set_initial : false, 2, 6 2, 7 array_y2_set_initial : false, array_y2_set_initial : false, 2, 8 2, 9 array_y2_set_initial : false, array_y2_set_initial : false, 2, 10 2, 11 array_y2_set_initial : false, array_y2_set_initial : false, 2, 12 2, 13 array_y2_set_initial : false, array_y2_set_initial : false, 2, 14 2, 15 array_y2_set_initial : false, array_y2_set_initial : false, 2, 16 2, 17 array_y2_set_initial : false, array_y2_set_initial : false, 2, 18 2, 19 array_y2_set_initial : false, array_y2_set_initial : false, 2, 20 2, 21 array_y2_set_initial : false, array_y2_set_initial : false, 2, 22 2, 23 array_y2_set_initial : false, array_y2_set_initial : false, 2, 24 2, 25 array_y2_set_initial : false, array_y2_set_initial : false, 2, 26 2, 27 array_y2_set_initial : false, array_y2_set_initial : false, 2, 28 2, 29 array_y2_set_initial : false, ALWAYS : 1, INFO : 2, DEBUGL : 3, 2, 30 DEBUGMASSIVE : 4, MAX_TERMS : 30, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest1postode.ode#################"), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; "), omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:10.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000000,"), omniout_str(ALWAYS, "glob_max_minutes:10.0,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y1 (x) := (block("), omniout_str(ALWAYS, " (1.0 + cos(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_y2 (x) := (block("), omniout_str(ALWAYS, " (1.0 + sin(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_larger_float : 1.1E+100, glob_almost_1 : 0.99, x_start : 0.1, x_end : 10.0, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 1000000000, glob_max_minutes : 10.0, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_sec : 3600.0 glob_max_hours + 60.0 glob_max_minutes, omniout_str(ALWAYS, "START of Optimize"), glob_check_sign : my_check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h glob_check_sign, if mabs(glob_max_h) < mabs(glob_h) then glob_h : mabs(glob_max_h) glob_check_sign, if mabs(glob_display_interval) < mabs(glob_h) then glob_h : mabs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : mabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - mabs(glob_display_interval)), chk_data(), best_h : glob_h, min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y1 : term_no array_y1_init expt(glob_h, term_no - 1) term_no ----------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y1_higher : r_order, term_no array_y1_init expt(glob_h, term_no - 1) it -----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y2 : term_no array_y2_init expt(glob_h, term_no - 1) term_no ----------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y2_higher : r_order, term_no array_y2_init expt(glob_h, term_no - 1) it -----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= MAX_TERMS + 2 do (atomall(), subiter : 1 + subiter)), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_check_sign glob_h >= glob_check_sign glob_max_h) then (found_h : true, glob_h : glob_check_sign glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) and (not found_h) glob_h then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_check_sign glob_max_h, found_h : false), if glob_check_sign glob_display_interval < glob_check_sign glob_h then glob_h : glob_check_sign glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y1 : term_no array_y1_init expt(glob_h, term_no - 1) term_no ----------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y1_higher : r_order, term_no array_y1_init expt(glob_h, term_no - 1) it -----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y2 : term_no array_y2_init expt(glob_h, term_no - 1) term_no ----------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, if term_no < MAX_TERMS then array_y2_higher : r_order, term_no array_y2_init expt(glob_h, term_no - 1) it -----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (glob_clock_sec - glob_orig_start_sec < glob_max_sec) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= MAX_TERMS + 2 do (atomall(), subiter : 1 + subiter)), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS, 2 while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii temp_sum expt(glob_h, calc_term - 1) array_y1_higher_work2 : ------------------------------------, ord, calc_term factorial_1(calc_term - 1) ord : 1, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii temp_sum expt(glob_h, calc_term - 1) array_y1_higher_work2 : ------------------------------------, ord, calc_term factorial_1(calc_term - 1) ord : 1, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii temp_sum expt(glob_h, calc_term - 1) array_y1_higher_work2 : ------------------------------------, ord, calc_term factorial_1(calc_term - 1) term_no : MAX_TERMS, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii temp_sum expt(glob_h, calc_term - 1) array_y2_higher_work2 : ------------------------------------, ord, calc_term factorial_1(calc_term - 1) ord : 1, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii temp_sum expt(glob_h, calc_term - 1) array_y2_higher_work2 : ------------------------------------, ord, calc_term factorial_1(calc_term - 1) ord : 1, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii temp_sum expt(glob_h, calc_term - 1) array_y2_higher_work2 : ------------------------------------, ord, calc_term factorial_1(calc_term - 1) term_no : MAX_TERMS, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - glob_orig_start_sec >= glob_max_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; "), omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-08T22:49:28-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest1"), logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; "), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, MAX_TERMS), 1 if glob_least_given_sing < glob_large_float then (logitem_float(html_log_file, glob_least_given_sing), 0) else (logitem_str(html_log_file, "NOT GIVEN"), 0), if glob_least_ratio_sing < glob_large_float then (logitem_float(html_log_file, glob_least_ratio_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_3_sing < glob_large_float then (logitem_float(html_log_file, glob_least_3_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_6_sing < glob_large_float then (logitem_float(html_log_file, glob_least_6_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then (logitem_time(html_log_file, glob_total_exp_sec), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "mtest1 diffeq.max"), logitem_str(html_log_file, "\ mtest1 maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0 ; "), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_good_digits(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 if glob_least_given_sing < glob_large_float then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), if glob_least_ratio_sing < glob_large_float then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), if glob_least_3_sing < glob_large_float then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), if glob_least_6_sing < glob_large_float then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i232) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o232) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i233) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable fixnum in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable good_digits in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable rad_given in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y1 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable array_y2 in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ALWAYS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable analytic_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable array_y1_higher in translation. warning: encountered undefined variable tmp in translation. warning: variable glob_normmax (declared type convfloat) assigned type any. warning: encountered undefined variable glob_normmax in translation. warning: encountered undefined variable array_y2_higher in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable hnew in translation. warning: encountered undefined variable sz2 in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_current_iter in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_optimal_start (declared type convfloat) assigned type any. warning: encountered undefined variable glob_reached_optimal_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable h_new in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_m1 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_const_1D0 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y1_set_initial in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_y2_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y1_init in translation. warning: encountered undefined variable array_y2_init in translation. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable ord in translation. warning: encountered undefined variable array_y1_higher_work in translation. warning: encountered undefined variable array_y1_higher_work2 in translation. warning: encountered undefined variable array_y2_higher_work in translation. warning: encountered undefined variable array_y2_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable jjjf in translation. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable x_start in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable est_answer in translation. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: encountered undefined variable order_diff in translation. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: encountered undefined variable it in translation. warning: encountered undefined variable glob_subiter_method in translation. warning: encountered undefined variable subiter in translation. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable best_h in translation. warning: encountered undefined variable glob_html_log in translation. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable DEBUGL in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_current_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable calc_term in translation. warning: encountered undefined variable temp_sum in translation. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. WARNING: in $ADJUST_FOR_POLE : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $ADJUST_FOR_POLE : $GLOB_OPTIMAL_START is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. Warning: modedcclare has a function or macro call which has not been translated properly. The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################" "##############temp/mtest1postode.ode#################" "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; " "diff ( y2 , x , 1 ) = y1 - 1.0 ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:10.0," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:1000000000," "glob_max_minutes:10.0," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y1 (x) := (block(" " (1.0 + cos(x)) " "));" "exact_soln_y2 (x) := (block(" " (1.0 + sin(x)) " "));" "" "" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 9.9 "" estimated_steps = 9900000. "" step_error = 1.010101010101010100000000000000000E-17 "" est_needed_step_err = 1.010101010101010100000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.4672086055323014000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" estimated_step_error = 2.4672086055323014000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.65571566460656540000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" estimated_step_error = 1.65571566460656540000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.111131969458435300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" estimated_step_error = 1.111131969458435300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.4566803670241850000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" estimated_step_error = 7.4566803670241850000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.004093412037816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" estimated_step_error = 5.004093412037816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" best_h = 3.200000E-5 "" opt_iter = 6 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.3581901424816235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" estimated_step_error = 3.3581901424816235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.25364312158091970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" estimated_step_error = 2.25364312158091970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.512394117654306500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" estimated_step_error = 1.512394117654306500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.0149502701580553000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" estimated_step_error = 1.0149502701580553000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.81121272440810700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" estimated_step_error = 6.81121272440810700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.570923134360027000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" estimated_step_error = 4.570923134360027000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 2.048000E-3 "" opt_iter = 12 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.0674887502340364000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 3.0674887502340364000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.05854901161817100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" estimated_step_error = 2.05854901161817100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.3814583197406785000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" estimated_step_error = 1.3814583197406785000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.27066811845142800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 9.27066811845142800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.22124900214134000000000000000000000000000000000000000000000000000000000000000000E-66 "" estimated_step_error = 6.22124900214134000000000000000000000000000000000000000000000000000000000000000000E-66 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.1747508757515434000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 4.1747508757515434000000000000000000000000000000000000000000000000000000000E-58 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.80127475800900200000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 2.80127475800900200000000000000000000000000000000000000000000000000E-50 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y1[1] (analytic) = 1.9950041652780257 " " y1[1] (numeric) = 1.9950041652780257 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.0998334166468282 " " y2[1] (numeric) = 1.0998334166468282 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.9334665397530600E-2 " " Order of pole (three term test) = 22.00996671107938 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.93346653975305600E-2 " " Order of pole (three term test) = 22.990033288920625 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y1[1] (analytic) = 1.9939560979566968 " " y1[1] (numeric) = 1.9939560979566968 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.1097783008371749 " " y2[1] (numeric) = 1.1097783008371749 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10911481154043479 " " Order of pole (three term test) = 22.0120512753347 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10911481154043479 " " Order of pole (three term test) = 22.9879487246653 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y1[1] (analytic) = 1.9928086358538661 " " y1[1] (numeric) = 1.9928086358538661 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.1197122072889194 " " y2[1] (numeric) = 1.1197122072889194 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11885131321356734 " " Order of pole (three term test) = 22.014331012573983 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11885131321356733 " " Order of pole (three term test) = 22.985668987426013 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y1[1] (analytic) = 1.991561893714788 " " y1[1] (numeric) = 1.9915618937147879 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114926960722569200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.129634142619695 " " y2[1] (numeric) = 1.129634142619695 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12854027594607764 " " Order of pole (three term test) = 22.01680501093274 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.12854027594607764 " " Order of pole (three term test) = 22.983194989067254 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y1[1] (analytic) = 1.9902159962126371 " " y1[1] (numeric) = 1.990215996212637 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115680937886039300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.1395431146442365 " " y2[1] (numeric) = 1.1395431146442365 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13817782428205697 " " Order of pole (three term test) = 22.019472280844614 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13817782428205697 " " Order of pole (three term test) = 22.980527719155383 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y1[1] (analytic) = 1.9887710779360424 " " y1[1] (numeric) = 1.988771077936042 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.232983045544592600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.1494381324735992 " " y2[1] (numeric) = 1.1494381324735992 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14776010333066977 " " Order of pole (three term test) = 22.022331755437193 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14776010333066977 " " Order of pole (three term test) = 22.97766824456281 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y1[1] (analytic) = 1.9872272833756268 " " y1[1] (numeric) = 1.9872272833756266 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117358878788402300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.159318206614246 " " y2[1] (numeric) = 1.159318206614246 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15728328030805885 " " Order of pole (three term test) = 22.025382290958774 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.15728328030805885 " " Order of pole (three term test) = 22.97461770904122 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y1[1] (analytic) = 1.9855847669095605 " " y1[1] (numeric) = 1.9855847669095603 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118283180982648100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.1691823490669961 " " y2[1] (numeric) = 1.1691823490669961 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16674354607040737 " " Order of pole (three term test) = 22.028622667235826 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16674354607040737 " " Order of pole (three term test) = 22.971377332764174 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y1[1] (analytic) = 1.9838436927881213 " " y1[1] (numeric) = 1.9838436927881211 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119264616119865500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.1790295734258243 " " y2[1] (numeric) = 1.1790295734258243 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17613711663754505 " " Order of pole (three term test) = 22.032051588161035 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.176137116637545 " " Order of pole (three term test) = 22.967948411838968 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y1[1] (analytic) = 1.9820042351172704 " " y1[1] (numeric) = 1.98200423511727 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.240606765523823500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.1888588949765007 " " y2[1] (numeric) = 1.1888588949765007 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1854602347064915 " " Order of pole (three term test) = 22.035667682211745 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18546023470649148 " " Order of pole (three term test) = 22.964332317788262 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y1[1] (analytic) = 1.9800665778412416 " " y1[1] (numeric) = 1.9800665778412412 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24279938270676100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.1986693307950613 " " y2[1] (numeric) = 1.1986693307950613 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19470917115432532 " " Order of pole (three term test) = 22.039469502998553 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1947091711543254 " " Order of pole (three term test) = 22.96053049700144 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y1[1] (analytic) = 1.9780309147241484 " " y1[1] (numeric) = 1.9780309147241477 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.367661292937837400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2084598998460996 " " y2[1] (numeric) = 1.2084598998460996 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20388022652978527 " " Order of pole (three term test) = 22.04345552984385 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2038802265297853 " " Order of pole (three term test) = 22.956544470156157 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y1[1] (analytic) = 1.9758974493306054 " " y1[1] (numeric) = 1.975897449330605 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.247531672256124200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2182296230808694 " " y2[1] (numeric) = 1.2182296230808694 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21296973253299992 " " Order of pole (three term test) = 22.04762416839002 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2129697325329999 " " Order of pole (three term test) = 22.952375831609977 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y1[1] (analytic) = 1.9736663950053748 " " y1[1] (numeric) = 1.9736663950053743 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.250072306920204000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2279775235351884 " " y2[1] (numeric) = 1.2279775235351884 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22197405348275995 " " Order of pole (three term test) = 22.051973751237234 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22197405348275995 " " Order of pole (three term test) = 22.948026248762762 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y1[1] (analytic) = 1.9713379748520294 " " y1[1] (numeric) = 1.971337974852029 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.252729950496674400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2377026264271347 " " y2[1] (numeric) = 1.2377026264271347 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23088958777074164 " " Order of pole (three term test) = 22.05650253861036 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2308895877707416 " " Order of pole (three term test) = 22.943497461389644 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y1[1] (analytic) = 1.9689124217106446 " " y1[1] (numeric) = 1.9689124217106442 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.25550514564901700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.247403959254523 " " y2[1] (numeric) = 1.247403959254523 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23971276930210164 " " Order of pole (three term test) = 22.06120871905481 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2397127693021015 " " Order of pole (three term test) = 22.93879128094518 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y1[1] (analytic) = 1.9663899781345133 " " y1[1] (numeric) = 1.9663899781345127 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.387597690093222500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2570805518921553 " " y2[1] (numeric) = 1.257080551892155 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.766351444947662200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24844006892186837 " " Order of pole (three term test) = 22.066090410161173 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24844006892186835 " " Order of pole (three term test) = 22.93390958983882 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y1[1] (analytic) = 1.9637708963658906 " " y1[1] (numeric) = 1.96377089636589 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.39211573003666500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2667314366888314 " " y2[1] (numeric) = 1.2667314366888311 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.752894090206240400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25706799582655676 " " Order of pole (three term test) = 22.071145659318088 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2570679958265567 " " Order of pole (three term test) = 22.92885434068191 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y1[1] (analytic) = 1.9610554383107708 " " y1[1] (numeric) = 1.9610554383107703 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.26454184402148120000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2763556485641139 " " y2[1] (numeric) = 1.2763556485641137 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.739676595428782000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2655930989604419 " " Order of pole (three term test) = 22.0763724444933 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2655930989604418 " " Order of pole (three term test) = 22.923627555506705 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y1[1] (analytic) = 1.958243875512697 " " y1[1] (numeric) = 1.9582438755126965 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.267793176341703400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2859522251048356 " " y2[1] (numeric) = 1.2859522251048354 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.726694045005671700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27401196839593667 " " Order of pole (three term test) = 22.0817686750424 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2740119683959367 " " Order of pole (three term test) = 22.91823132495759 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y1[1] (analytic) = 1.955336489125606 " " y1[1] (numeric) = 1.9553364891256053 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.4067477310413100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.2955202066613398 " " y2[1] (numeric) = 1.2955202066613394 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.42788331333338600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28232123669751763 " " Order of pole (three term test) = 22.087332192545162 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2823212366975175 " " Order of pole (three term test) = 22.912667807454834 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y1[1] (analytic) = 1.9523335698857134 " " y1[1] (numeric) = 1.9523335698857127 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.41198771075830200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3050586364434436 " " y2[1] (numeric) = 1.3050586364434433 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.701414777271227600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29051758026865265 " " Order of pole (three term test) = 22.093060771668735 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2905175802686527 " " Order of pole (three term test) = 22.90693922833127 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y1[1] (analytic) = 1.949235418082441 " " y1[1] (numeric) = 1.9492354180824403 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.417410788843569500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3145665606161179 " " y2[1] (numeric) = 1.3145665606161177 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.689108878754395600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29859772068119633 " " Order of pole (three term test) = 22.098952121057852 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2985977206811963 " " Order of pole (three term test) = 22.901047878942144 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y1[1] (analytic) = 1.946042343528387 " " y1[1] (numeric) = 1.9460423435283865 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.282012060667089300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3240430283948685 " " y2[1] (numeric) = 1.3240430283948683 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.67701955422260700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.306558425986717 " " Order of pole (three term test) = 22.105003884251314 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30655842598671695 " " Order of pole (three term test) = 22.894996115748683 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y1[1] (analytic) = 1.942754665528346 " " y1[1] (numeric) = 1.9427546655283456 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.28587385597290200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3334870921408146 " " y2[1] (numeric) = 1.3334870921408144 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.665142514192283200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31439651200923435 " " Order of pole (three term test) = 22.111213640624534 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.31439651200923435 " " Order of pole (three term test) = 22.888786359375455 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y1[1] (analytic) = 1.939372712847379 " " y1[1] (numeric) = 1.9393727128473783 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.43479007599874430000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3428978074554516 " " y2[1] (numeric) = 1.3428978074554514 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.65347358296582300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32210884361884595 " " Order of pole (three term test) = 22.117578906357757 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3221088436188459 " " Order of pole (three term test) = 22.882421093642243 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y1[1] (analytic) = 1.9358968236779348 " " y1[1] (numeric) = 1.9358968236779344 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.293971478326798400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.35227423327509 " " y2[1] (numeric) = 1.35227423327509 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3296923359857369 " " Order of pole (three term test) = 22.12409713542955 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.32969233598573683 " " Order of pole (three term test) = 22.875902864570442 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y1[1] (analytic) = 1.9323273456060344 " " y1[1] (numeric) = 1.932327345606034 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.298209000974331400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3616154319649623 " " y2[1] (numeric) = 1.361615431964962 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.63074389223538900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3371439558140726 " " Order of pole (three term test) = 22.1307657206352 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3371439558140725 " " Order of pole (three term test) = 22.86923427936479 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y1[1] (analytic) = 1.92866463557651 " " y1[1] (numeric) = 1.9286646355765098 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.151286754727363400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3709204694129828 " " y2[1] (numeric) = 1.3709204694129826 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.619675319459698800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3444607225552756 " " Order of pole (three term test) = 22.137581994629546 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3444607225552755 " " Order of pole (three term test) = 22.86241800537045 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y1[1] (analytic) = 1.9249090598573129 " " y1[1] (numeric) = 1.9249090598573126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.153532961923358200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3801884151231616 " " y2[1] (numeric) = 1.3801884151231614 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.608799222570036500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35163970960020513 " " Order of pole (three term test) = 22.144543230993865 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35163970960020513 " " Order of pole (three term test) = 22.85545676900614 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y1[1] (analytic) = 1.921060994002885 " " y1[1] (numeric) = 1.9210609940028847 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.31168719388092280000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3894183423086508 " " y2[1] (numeric) = 1.3894183423086504 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.196223889718960400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3586780454497614 " " Order of pole (three term test) = 22.151646645326412 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3586780454497614 " " Order of pole (three term test) = 22.848353354673584 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y1[1] (analytic) = 1.917120822816605 " " y1[1] (numeric) = 1.9171208228166048 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.158219149687220600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.3986093279844232 " " y2[1] (numeric) = 1.3986093279844227 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.175219848490876700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36557291486344795 " " Order of pole (three term test) = 22.15888939635619 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36557291486344784 " " Order of pole (three term test) = 22.841110603643802 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y1[1] (analytic) = 1.9130889403123081 " " y1[1] (numeric) = 1.913088940312308 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.160660125340450400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.4077604530595704 " " y2[1] (numeric) = 1.40776045305957 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.154579380923059300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37232155998542965 " " Order of pole (three term test) = 22.166268587079344 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3723215599854297 " " Order of pole (three term test) = 22.83373141292066 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y1[1] (analytic) = 1.908965749674885 " " y1[1] (numeric) = 1.9089657496748849 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.163167044578183900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.416870802429211 " " y2[1] (numeric) = 1.4168708024292105 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.13429572469611300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3789212814476383 " " Order of pole (three term test) = 22.173781265917974 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37892128144763826 " " Order of pole (three term test) = 22.82621873408202 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y1[1] (analytic) = 1.9047516632199633 " " y1[1] (numeric) = 1.9047516632199633 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.4259394650659998 " " y2[1] (numeric) = 1.4259394650659993 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.114362290474287000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38536943944948454 " " Order of pole (three term test) = 22.18142442790071 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.38536943944948454 " " Order of pole (three term test) = 22.81857557209929 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y1[1] (analytic) = 1.9004471023526768 " " y1[1] (numeric) = 1.9004471023526768 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.4349655341112304 " " y2[1] (numeric) = 1.43496553411123 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.094772656857689400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39166345481374165 " " Order of pole (three term test) = 22.189195015864666 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39166345481374165 " " Order of pole (three term test) = 22.810804984135334 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y1[1] (analytic) = 1.896052497525525 " " y1[1] (numeric) = 1.896052497525525 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.44394810696552 " " y2[1] (numeric) = 1.4439481069655196 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.075520565509264000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39780081001818285 " " Order of pole (three term test) = 22.19708992167827 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39780081001818285 " " Order of pole (three term test) = 22.802910078321734 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y1[1] (analytic) = 1.8915682881953289 " " y1[1] (numeric) = 1.8915682881953289 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.4528862853790685 " " y2[1] (numeric) = 1.452886285379068 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.056599916449734300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4037790502025568 " " Order of pole (three term test) = 22.20510598748445 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40377905020255667 " " Order of pole (three term test) = 22.79489401251555 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y1[1] (analytic) = 1.8869949227792842 " " y1[1] (numeric) = 1.8869949227792842 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.461779175541483 " " y2[1] (numeric) = 1.4617791755414826 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.03800476351402200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40959578415049896 " " Order of pole (three term test) = 22.21324000696377 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40959578415049896 " " Order of pole (three term test) = 22.786759993036224 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y1[1] (analytic) = 1.8823328586101213 " " y1[1] (numeric) = 1.8823328586101216 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.179624548917372600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.4706258881711582 " " y2[1] (numeric) = 1.4706258881711578 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.01972930996287100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4152486852459851 " " Order of pole (three term test) = 22.221488726616894 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4152486852459852 " " Order of pole (three term test) = 22.778511273383106 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y1[1] (analytic) = 1.8775825618903725 " " y1[1] (numeric) = 1.8775825618903728 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.182609007091939300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.4794255386042032 " " y2[1] (numeric) = 1.4794255386042028 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.00176790424375400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4207354924039481 " " Order of pole (three term test) = 22.229848847065927 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42073549240394803 " " Order of pole (three term test) = 22.77015115293407 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y1[1] (analytic) = 1.8727445076457512 " " y1[1] (numeric) = 1.8727445076457514 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.185664163042539800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.4881772468829078 " " y2[1] (numeric) = 1.4881772468829073 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.98411503589534600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42605401097468126 " " Order of pole (three term test) = 22.238317024374172 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4260540109746814 " " Order of pole (three term test) = 22.761682975625828 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y1[1] (analytic) = 1.8678191796776498 " " y1[1] (numeric) = 1.86781917967765 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.188790688846829300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.496880137843737 " " y2[1] (numeric) = 1.4968801378437366 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.96676533159011160000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43120211362166927 " " Order of pole (three term test) = 22.24688987138361 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43120211362166916 " " Order of pole (three term test) = 22.753110128616385 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y1[1] (analytic) = 1.8628070705147608 " " y1[1] (numeric) = 1.862807070514761 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.191989274894003900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5055333412048473 " " y2[1] (numeric) = 1.5055333412048468 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.94971355130977830000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4361777411724932 " " Order of pole (three term test) = 22.255563959069736 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43617774117249314 " " Order of pole (three term test) = 22.744436040930257 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y1[1] (analytic) = 1.857708681363824 " " y1[1] (numeric) = 1.8577086813638242 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.195260630219043700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5141359916531134 " " y2[1] (numeric) = 1.514135991653113 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.932954584648714300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4409789034424737 " " Order of pole (three term test) = 22.26433581791313 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44097890344247376 " " Order of pole (three term test) = 22.735664182086868 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y1[1] (analytic) = 1.8525245220595057 " " y1[1] (numeric) = 1.8525245220595057 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.5226872289306594 " " y2[1] (numeric) = 1.522687228930659 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.91648344724040330000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4456036800307175 " " Order of pole (three term test) = 22.27320193928721 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44560368003071765 " " Order of pole (three term test) = 22.72679806071279 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y1[1] (analytic) = 1.8472551110134159 " " y1[1] (numeric) = 1.847255111013416 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.2020245801524200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5311861979208836 " " y2[1] (numeric) = 1.5311861979208832 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.900295277302445400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45005022108825243 " " Order of pole (three term test) = 22.28215877686164 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45005022108825254 " " Order of pole (three term test) = 22.717841223138354 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y1[1] (analytic) = 1.8419009751622686 " " y1[1] (numeric) = 1.8419009751622688 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.205518689219812800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5396320487339694 " " y2[1] (numeric) = 1.539632048733969 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.88438533229569100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4543167480579415 " " Order of pole (three term test) = 22.29120274802082 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4543167480579414 " " Order of pole (three term test) = 22.708797251979178 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y1[1] (analytic) = 1.8364626499151866 " " y1[1] (numeric) = 1.836462649915187 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.41817719445898900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.548023936791874 " " y2[1] (numeric) = 1.5480239367918733 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.30312347853993900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45840155438588354 " " Order of pole (three term test) = 22.300330235296865 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4584015543858835 " " Order of pole (three term test) = 22.69966976470314 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y1[1] (analytic) = 1.8309406791001632 " " y1[1] (numeric) = 1.8309406791001637 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.425470223690236700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.556361022912784 " " y2[1] (numeric) = 1.5563610229127836 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.853381723855652500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46230300620400977 " " Order of pole (three term test) = 22.309537587816553 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46230300620401 " " Order of pole (three term test) = 22.690462412183443 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y1[1] (analytic) = 1.8253356149096782 " " y1[1] (numeric) = 1.8253356149096784 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.216459061617655300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5646424733950357 " " y2[1] (numeric) = 1.564642473395035 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.25741871451108700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4660195429836131 " " Order of pole (three term test) = 22.318821122761666 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.466019542983613 " " Order of pole (three term test) = 22.681178877238334 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y1[1] (analytic) = 1.8196480178454792 " " y1[1] (numeric) = 1.8196480178454797 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.44052259280274600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5728674601004817 " " y2[1] (numeric) = 1.5728674601004808 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.646873892625286000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46954967815953375 " " Order of pole (three term test) = 22.32817712684198 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46954967815953363 " " Order of pole (three term test) = 22.671822873158018 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y1[1] (analytic) = 1.8138784566625337 " " y1[1] (numeric) = 1.8138784566625341 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.448285375565734400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5810351605373054 " " y2[1] (numeric) = 1.5810351605373048 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.21327641156767400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4728919997247693 " " Order of pole (three term test) = 22.337601857780612 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47289199972476936 " " Order of pole (three term test) = 22.662398142219384 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y1[1] (analytic) = 1.8080275083121515 " " y1[1] (numeric) = 1.808027508312152 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.456208259047083800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.58914475794227 " " y2[1] (numeric) = 1.5891447579422693 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.19177555377427200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47604517079525793 " " Order of pole (three term test) = 22.347091545810855 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.476045170795258 " " Order of pole (three term test) = 22.65290845418915 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y1[1] (analytic) = 1.8020957578842922 " " y1[1] (numeric) = 1.8020957578842927 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.464293076031847400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.5971954413623926 " " y2[1] (numeric) = 1.5971954413623919 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.170646857136582300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47900793014461246 " " Order of pole (three term test) = 22.35664239518402 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4790079301446124 " " Order of pole (three term test) = 22.64335760481598 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y1[1] (analytic) = 1.7960837985490556 " " y1[1] (numeric) = 1.7960837985490559 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.236270852754238600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6051864057360399 " " y2[1] (numeric) = 1.6051864057360394 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.766589651289942400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4817790927085964 " " Order of pole (three term test) = 22.36625058568771 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4817790927085965 " " Order of pole (three term test) = 22.63374941431229 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y1[1] (analytic) = 1.7899922314973646 " " y1[1] (numeric) = 1.789992231497365 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.48095607363934200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6131168519734342 " " y2[1] (numeric) = 1.6131168519734336 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.12948270895668600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48435755005913267 " " Order of pole (three term test) = 22.37591227417381 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48435755005913267 " " Order of pole (three term test) = 22.62408772582619 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y1[1] (analytic) = 1.783821665880849 " " y1[1] (numeric) = 1.7838216658808492 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.24476907738075890000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6209859870365602 " " y2[1] (numeric) = 1.6209859870365595 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.10943598588967800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4867422708476597 " " Order of pole (three term test) = 22.38562359609577 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4867422708476596 " " Order of pole (three term test) = 22.614376403904227 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y1[1] (analytic) = 1.7775727187509276 " " y1[1] (numeric) = 1.7775727187509278 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.249144986209388800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.628793024018469 " " y2[1] (numeric) = 1.6287930240184683 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.08973887382968500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48893230121765807 " " Order of pole (three term test) = 22.395380667054287 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48893230121765807 " " Order of pole (three term test) = 22.60461933294571 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y1[1] (analytic) = 1.7712460149971063 " " y1[1] (numeric) = 1.7712460149971065 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.253606800212866400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6365371822219683 " " y2[1] (numeric) = 1.6365371822219676 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.07038606889864300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4909267651861798 " " Order of pole (three term test) = 22.405179584351078 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4909267651861796 " " Order of pole (three term test) = 22.59482041564891 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y1[1] (analytic) = 1.7648421872844882 " " y1[1] (numeric) = 1.7648421872844884 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.258155581982573500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6442176872376915 " " y2[1] (numeric) = 1.6442176872376908 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.05137239396936470000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49272486499423007 " " Order of pole (three term test) = 22.415016428549876 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49272486499423007 " " Order of pole (three term test) = 22.584983571450124 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y1[1] (analytic) = 1.758361875990508 " " y1[1] (numeric) = 1.7583618759905082 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.26279242035972100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6518337710215372 " " y2[1] (numeric) = 1.6518337710215365 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.03269279549321300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49432588142586 " " Order of pole (three term test) = 22.42488726504416 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49432588142585987 " " Order of pole (three term test) = 22.575112734955844 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y1[1] (analytic) = 1.7518057291408946 " " y1[1] (numeric) = 1.751805729140895 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.535036862037487500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6593846719714735 " " y2[1] (numeric) = 1.6593846719714729 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.01434234042717100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4957291740958432 " " Order of pole (three term test) = 22.434788145630925 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4957291740958433 " " Order of pole (three term test) = 22.56521185436908 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y1[1] (analytic) = 1.7451744023448699 " " y1[1] (numeric) = 1.7451744023448705 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.81700427120668300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6668696350036982 " " y2[1] (numeric) = 1.6668696350036976 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.99631621325692900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4969341817058225 " " Order of pole (three term test) = 22.44471511008997 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49693418170582243 " " Order of pole (three term test) = 22.555284889910034 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y1[1] (analytic) = 1.7384685587295876 " " y1[1] (numeric) = 1.738468558729588 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.55448513934924200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6742879116281455 " " y2[1] (numeric) = 1.6742879116281448 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.97860971311271300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49794042226881996 " " Order of pole (three term test) = 22.454664187767843 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49794042226882007 " " Order of pole (three term test) = 22.545335812232157 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y1[1] (analytic) = 1.7316888688738206 " " y1[1] (numeric) = 1.731688868873821 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.564486137390661000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6816387600233345 " " y2[1] (numeric) = 1.681638760023334 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.640812167316483600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4987474933020272 " " Order of pole (three term test) = 22.464631399166148 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49874749330202744 " " Order of pole (three term test) = 22.535368600833852 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y1[1] (analytic) = 1.7248360107409049 " " y1[1] (numeric) = 1.7248360107409053 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.574674966690333500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6889214451105516 " " y2[1] (numeric) = 1.6889214451105512 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.629424897976790400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4993550719877915 " " Order of pole (three term test) = 22.474612757533208 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4993550719877915 " " Order of pole (three term test) = 22.52538724246679 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y1[1] (analytic) = 1.717910669610943 " " y1[1] (numeric) = 1.7179106696109434 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.585054145746914500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.6961352386273572 " " y2[1] (numeric) = 1.6961352386273567 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.6182417518160500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49976291530273964 " " Order of pole (three term test) = 22.48460427045877 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49976291530273953 " " Order of pole (three term test) = 22.515395729541233 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y1[1] (analytic) = 1.710913538012277 " " y1[1] (numeric) = 1.7109135380122773 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.297813127266504400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7032794192004106 " " y2[1] (numeric) = 1.7032794192004101 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.607259882577201400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999708601149831 " " Order of pole (three term test) = 22.49460194147086 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999708601149831 " " Order of pole (three term test) = 22.50539805852913 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y1[1] (analytic) = 1.7038453156522357 " " y1[1] (numeric) = 1.703845315652236 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.303196967971427300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7103532724176083 " " y2[1] (numeric) = 1.7103532724176078 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.59647651167607200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999788232493701 " " Order of pole (three term test) = 22.504601771634405 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49997882324937 " " Order of pole (three term test) = 22.495398228365595 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y1[1] (analytic) = 1.6967067093471648 " " y1[1] (numeric) = 1.6967067093471653 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.617359897285566000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7173560908995231 " " y2[1] (numeric) = 1.7173560908995227 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.585888926608435600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4997868015207525 " " Order of pole (three term test) = 22.514599761150645 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4997868015207526 " " Order of pole (three term test) = 22.48540023884936 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y1[1] (analytic) = 1.6894984329517466 " " y1[1] (numeric) = 1.6894984329517468 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.314263455912735300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.724287174370143 " " y2[1] (numeric) = 1.7242871743701425 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.575494479405856000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49939487173526204 " " Order of pole (three term test) = 22.52459191095709 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4993948717352621 " " Order of pole (three term test) = 22.475408089042915 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y1[1] (analytic) = 1.682221207287613 " " y1[1] (numeric) = 1.6822212072876135 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.6398978203711100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7311458297268962 " " y2[1] (numeric) = 1.7311458297268958 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.565290585138755300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49880319065958695 " " Order of pole (three term test) = 22.534574224327034 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4988031906595868 " " Order of pole (three term test) = 22.46542577567297 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y1[1] (analytic) = 1.6748757600712665 " " y1[1] (numeric) = 1.674875760071267 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.651475532914552000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.737931371109963 " " y2[1] (numeric) = 1.7379313711099627 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.555274720465150500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49801199495826837 " " Order of pole (three term test) = 22.544542708468235 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49801199495826837 " " Order of pole (three term test) = 22.455457291531765 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y1[1] (analytic) = 1.6674628258413078 " " y1[1] (numeric) = 1.667462825841308 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.331631515161365600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7446431199708599 " " y2[1] (numeric) = 1.7446431199708592 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.81816663333541860000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49702160109903804 " " Order of pole (three term test) = 22.554493376119936 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49702160109903804 " " Order of pole (three term test) = 22.445506623880064 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y1[1] (analytic) = 1.6599831458849816 " " y1[1] (numeric) = 1.659983145884982 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.67526336608259200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7512804051402933 " " y2[1] (numeric) = 1.7512804051402926 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.803695929103544400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4958324052262344 " " Order of pole (three term test) = 22.564422247147764 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49583240522623434 " " Order of pole (three term test) = 22.43557775285224 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y1[1] (analytic) = 1.6524374681640515 " " y1[1] (numeric) = 1.6524374681640517 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.34373983405093680000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7578425628952774 " " y2[1] (numeric) = 1.757842562895277 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.526330965149801000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4944448830023508 " " Order of pole (three term test) = 22.574325350135688 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4944448830023506 " " Order of pole (three term test) = 22.425674649864316 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y1[1] (analytic) = 1.6448265472400005 " " y1[1] (numeric) = 1.644826547240001 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.699915140567490400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7643289370255055 " " y2[1] (numeric) = 1.764328937025505 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.517043168825172600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49285958941777674 " " Order of pole (three term test) = 22.584198723974538 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4928595894177767 " " Order of pole (three term test) = 22.41580127602546 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y1[1] (analytic) = 1.6371511441985795 " " y1[1] (numeric) = 1.63715114419858 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.712573065863468400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7707388788989697 " " y2[1] (numeric) = 1.7707388788989693 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.507931661421437500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4910771585688093 " " Order of pole (three term test) = 22.594038419446445 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4910771585688092 " " Order of pole (three term test) = 22.405961580553555 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y1[1] (analytic) = 1.6294120265736964 " " y1[1] (numeric) = 1.6294120265736967 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.36272840327528100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7770717475268243 " " y2[1] (numeric) = 1.7770717475268238 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.498994261025801700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4890983034040223 " " Order of pole (three term test) = 22.60384050080439 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48909830340402227 " " Order of pole (three term test) = 22.396159499195605 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y1[1] (analytic) = 1.621609968270664 " " y1[1] (numeric) = 1.6216099682706642 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.369284903704845200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7833269096274837 " " y2[1] (numeric) = 1.7833269096274833 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.490228838316737600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4869238154390975 " " Order of pole (three term test) = 22.613601047346545 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4869238154390975 " " Order of pole (three term test) = 22.386398952653455 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y1[1] (analytic) = 1.613745749488811 " " y1[1] (numeric) = 1.6137457494888112 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.375957798775728800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.789503739689951 " " y2[1] (numeric) = 1.7895037396899502 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.72244997314455600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48455456444022804 " " Order of pole (three term test) = 22.623316154984416 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.484554564440228 " " Order of pole (three term test) = 22.37668384501558 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y1[1] (analytic) = 1.6058201566434622 " " y1[1] (numeric) = 1.6058201566434624 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.382748896297056000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.7956016200363665 " " y2[1] (numeric) = 1.7956016200363658 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.70980849728573200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4819914980762241 " " Order of pole (three term test) = 22.632981937804498 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48199149807622405 " " Order of pole (three term test) = 22.367018062195513 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y1[1] (analytic) = 1.5978339822872978 " " y1[1] (numeric) = 1.5978339822872978 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8016199408837776 " " y2[1] (numeric) = 1.801619940883777 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.69741586257268330000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.479235641539457 " " Order of pole (three term test) = 22.64259452962251 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47923564153945714 " " Order of pole (three term test) = 22.35740547037749 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y1[1] (analytic) = 1.5897880250310976 " " y1[1] (numeric) = 1.5897880250310978 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.39669315297986300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8075581004051147 " " y2[1] (numeric) = 1.807558100405114 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.685269174063053300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4762880971357977 " " Order of pole (three term test) = 22.652150085529914 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47628809713579773 " " Order of pole (three term test) = 22.347849914470082 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y1[1] (analytic) = 1.581683089463883 " " y1[1] (numeric) = 1.5816830894638831 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.403850154333344500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8134155047893743 " " y2[1] (numeric) = 1.8134155047893734 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.89782081025763600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4731500438437071 " " Order of pole (three term test) = 22.66164478343175 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47315004384370724 " " Order of pole (three term test) = 22.338355216568246 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y1[1] (analytic) = 1.573519986072456 " " y1[1] (numeric) = 1.5735199860724562 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.411133044959028700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8191915683009987 " " y2[1] (numeric) = 1.8191915683009978 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.88226987842530160000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46982273684266257 " " Order of pole (three term test) = 22.67107482557545 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4698227368426626 " " Order of pole (three term test) = 22.32892517442456 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y1[1] (analytic) = 1.5652995311603537 " " y1[1] (numeric) = 1.565299531160354 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.418543866555879400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8248857133384506 " " y2[1] (numeric) = 1.8248857133384495 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.08379481800047500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4663075070111002 " " Order of pole (three term test) = 22.680436440069883 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4663075070111002 " " Order of pole (three term test) = 22.319563559930117 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y1[1] (analytic) = 1.5570225467662167 " " y1[1] (numeric) = 1.5570225467662169 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.42608471140123320000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.830497370491971 " " y2[1] (numeric) = 1.8304973704919698 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.0651440560483790000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4626057603940843 " " Order of pole (three term test) = 22.689725882394075 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4626057603940844 " " Order of pole (three term test) = 22.310274117605925 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y1[1] (analytic) = 1.5486898605815869 " " y1[1] (numeric) = 1.548689860581587 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.433757723716521400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8360259786005209 " " y2[1] (numeric) = 1.8360259786005197 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.04688080433047600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45871897764090475 " " Order of pole (three term test) = 22.698939436894957 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4587189776409048 " " Order of pole (three term test) = 22.30106056310504 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y1[1] (analytic) = 1.5403023058681393 " " y1[1] (numeric) = 1.5403023058681393 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8414709848078967 " " y2[1] (numeric) = 1.8414709848078958 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.82320072934942560000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4546487134128407 " " Order of pole (three term test) = 22.708073418273568 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4546487134128407 " " Order of pole (three term test) = 22.291926581726425 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y1[1] (analytic) = 1.531860721374355 " " y1[1] (numeric) = 1.5318607213743551 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.44950909587796800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8468318446180154 " " y2[1] (numeric) = 1.8468318446180145 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.80920026524574700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4503965957613137 " " Order of pole (three term test) = 22.717124173059155 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45039659576131363 " " Order of pole (three term test) = 22.282875826940845 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y1[1] (analytic) = 1.523365951251649 " " y1[1] (numeric) = 1.5233659512516493 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.457592016826895200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8521080219493633 " " y2[1] (numeric) = 1.8521080219493622 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.99437511995998400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44596432547669 " " Order of pole (three term test) = 22.72608808107046 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4459643254766899 " " Order of pole (three term test) = 22.273911918929542 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y1[1] (analytic) = 1.514818844969955 " " y1[1] (numeric) = 1.5148188449699551 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.46581623051722300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8572989891886036 " " y2[1] (numeric) = 1.8572989891886027 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.782097146825794500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4413536754079871 " " Order of pole (three term test) = 22.734961556863798 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4413536754079873 " " Order of pole (three term test) = 22.2650384431362 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y1[1] (analytic) = 1.5062202572327776 " " y1[1] (numeric) = 1.506220257232778 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.94836832606369060000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8624042272433388 " " y2[1] (numeric) = 1.8624042272433377 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.9612355276301500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4365664897537583 " " Order of pole (three term test) = 22.74374105116718 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4365664897537583 " " Order of pole (three term test) = 22.25625894883282 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y1[1] (analytic) = 1.4975710478917263 " " y1[1] (numeric) = 1.4975710478917266 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.482698301610629600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8674232255940173 " " y2[1] (numeric) = 1.8674232255940162 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.94521375448782300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43160468332443686 " " Order of pole (three term test) = 22.752423052299932 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4316046833244367 " " Order of pole (three term test) = 22.247576947700068 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y1[1] (analytic) = 1.488872081860527 " " y1[1] (numeric) = 1.4888720818605272 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.491361196373294200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8723554823449866 " " y2[1] (numeric) = 1.8723554823449855 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.92955256143285600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4264702407764381 " " Order of pole (three term test) = 22.76100408757735 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42647024077643797 " " Order of pole (three term test) = 22.23899591242264 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y1[1] (analytic) = 1.4801242290285335 " " y1[1] (numeric) = 1.4801242290285337 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.50017546210136900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.877200504274682 " " y2[1] (numeric) = 1.8772005042746809 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.91424848915714300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4211652158183229 " " Order of pole (three term test) = 22.769480724699758 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4211652158183229 " " Order of pole (three term test) = 22.23051927530025 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y1[1] (analytic) = 1.4713283641737394 " " y1[1] (numeric) = 1.4713283641737396 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.50914378008151800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8819578068849478 " " y2[1] (numeric) = 1.8819578068849467 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.89929817004143500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4156917303893416 " " Order of pole (three term test) = 22.77784957312531 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4156917303893416 " " Order of pole (three term test) = 22.222150426874695 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y1[1] (analytic) = 1.4624853668753002 " " y1[1] (numeric) = 1.4624853668753004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.518268900012618700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8866269144494876 " " y2[1] (numeric) = 1.8866269144494865 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.8846983265322300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4100519738106869 " " Order of pole (three term test) = 22.786107285426223 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41005197381068703 " " Order of pole (three term test) = 22.213892714573788 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y1[1] (analytic) = 1.4535961214255768 " " y1[1] (numeric) = 1.4535961214255768 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8912073600614356 " " y2[1] (numeric) = 1.8912073600614345 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.8704457695696100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.404248201909795 " " Order of pole (three term test) = 22.79425055862767 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40424820190979505 " " Order of pole (three term test) = 22.205749441372323 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y1[1] (analytic) = 1.4446615167417063 " " y1[1] (numeric) = 1.4446615167417063 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.895698685680048 " " y2[1] (numeric) = 1.8956986856800468 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.85653739706468100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.398282736118043 " " Order of pole (three term test) = 22.802276135528963 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39828273611804305 " " Order of pole (three term test) = 22.197723864471037 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y1[1] (analytic) = 1.4356824462767115 " " y1[1] (numeric) = 1.4356824462767117 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.54661363660801300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9001004421765053 " " y2[1] (numeric) = 1.9001004421765042 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.84297019242535900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39215796254221 " " Order of pole (three term test) = 22.81018080600634 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3921579625422101 " " Order of pole (three term test) = 22.189819193993664 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y1[1] (analytic) = 1.4266598079301567 " " y1[1] (numeric) = 1.426659807930157 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.556394900107129500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9044121893788262 " " y2[1] (numeric) = 1.904412189378825 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.82974122312924700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38587633101006297 " " Order of pole (three term test) = 22.817961408297 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3858763310100631 " " Order of pole (three term test) = 22.182038591703 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y1[1] (analytic) = 1.4175945039583575 " " y1[1] (numeric) = 1.4175945039583577 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.566347811768561700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9086334961158835 " " y2[1] (numeric) = 1.9086334961158824 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.8168476393424300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37944035409046106 " " Order of pole (three term test) = 22.82561483026377 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3794403540904611 " " Order of pole (three term test) = 22.174385169736222 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y1[1] (analytic) = 1.4084874408841566 " " y1[1] (numeric) = 1.408487440884157 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.152951151423063500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9127639402605214 " " y2[1] (numeric) = 1.91276394026052 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.96514400709964600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3728526060883603 " " Order of pole (three term test) = 22.833138010639914 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3728526060883603 " " Order of pole (three term test) = 22.166861989360086 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y1[1] (analytic) = 1.3993395294062725 " " y1[1] (numeric) = 1.399339529406273 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.173562959652014000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9168031087717674 " " y2[1] (numeric) = 1.9168031087717659 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 8.10887788819988900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3661157220151258 " " Order of pole (three term test) = 22.840527940253573 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3661157220151259 " " Order of pole (three term test) = 22.15947205974642 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y1[1] (analytic) = 1.3901516843082296 " " y1[1] (numeric) = 1.39015168430823 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.19453779657902100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.920750597736136 " " y2[1] (numeric) = 1.9207505977361345 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 8.0922126813714700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35923239653456307 " " Order of pole (three term test) = 22.84778166323145 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35923239653456307 " " Order of pole (three term test) = 22.15221833676855 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y1[1] (analytic) = 1.380924824366881 " " y1[1] (numeric) = 1.3809248243668815 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.215882588349197600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9246060124080206 " " y2[1] (numeric) = 1.9246060124080193 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.92228757969682600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35220538288508807 " " Order of pole (three term test) = 22.85489627818106 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3522053828850881 " " Order of pole (three term test) = 22.145103721818938 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y1[1] (analytic) = 1.3716598722605322 " " y1[1] (numeric) = 1.3716598722605327 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.237604444301426000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9283689672491668 " " y2[1] (numeric) = 1.9283689672491657 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.75731638229429900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34503749177846815 " " Order of pole (three term test) = 22.861868939351282 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3450374917784682 " " Order of pole (three term test) = 22.138131060648718 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y1[1] (analytic) = 1.3623577544766727 " " y1[1] (numeric) = 1.3623577544766734 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.889565993852901000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9320390859672267 " " y2[1] (numeric) = 1.9320390859672254 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.89565567915631300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3377315902755756 " " Order of pole (three term test) = 22.86869685777062 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33773159027557564 " " Order of pole (three term test) = 22.131303142229378 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y1[1] (analytic) = 1.3530194012193295 " " y1[1] (numeric) = 1.3530194012193302 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.923313103823787600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9356160015533863 " " y2[1] (numeric) = 1.935616001553385 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.88291287363302300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3302906006396006 " " Order of pole (three term test) = 22.875377302362747 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3302906006396005 " " Order of pole (three term test) = 22.124622697637253 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y1[1] (analytic) = 1.3436457463160463 " " y1[1] (numeric) = 1.343645746316047 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.95765953638801500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9390993563190677 " " y2[1] (numeric) = 1.9390993563190666 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72545713558823800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3227174991671856 " " Order of pole (three term test) = 22.881907601038886 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.32271749916718556 " " Order of pole (three term test) = 22.118092398961114 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y1[1] (analytic) = 1.3342377271245018 " " y1[1] (numeric) = 1.3342377271245025 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.99261714185462300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.942488801931698 " " y2[1] (numeric) = 1.9424888019316966 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.85856015347589800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3150153149979464 " " Order of pole (three term test) = 22.888285141766644 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3150153149979463 " " Order of pole (three term test) = 22.111714858233356 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y1[1] (analytic) = 1.3247962844387753 " " y1[1] (numeric) = 1.3247962844387762 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.70426412070128200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9457839994495392 " " y2[1] (numeric) = 1.945783999449538 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.7057876153737410000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30718712890285604 " " Order of pole (three term test) = 22.89450737361476 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3071871289028561 " " Order of pole (three term test) = 22.105492626385235 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y1[1] (analytic) = 1.315322362395268 " " y1[1] (numeric) = 1.3153223623952686 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.06441488276707200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9489846193555866 " " y2[1] (numeric) = 1.9489846193555853 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.83570109440211800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2992360720519784 " " Order of pole (three term test) = 22.900571807773467 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2992360720519784 " " Order of pole (three term test) = 22.099428192226537 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y1[1] (analytic) = 1.3058169083782885 " " y1[1] (numeric) = 1.3058169083782893 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.80170714593645300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.952090341590516 " " y2[1] (numeric) = 1.9520903415905149 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.68735473441548600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2911653247620412 " " Order of pole (three term test) = 22.906476018549945 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2911653247620412 " " Order of pole (three term test) = 22.09352398145006 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y1[1] (analytic) = 1.296280872925318 " " y1[1] (numeric) = 1.2962808729253188 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.85174361707407200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9551008555846925 " " y2[1] (numeric) = 1.9551008555846914 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.67859720102845100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2829781152243516 " " Order of pole (three term test) = 22.912217644338607 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2829781152243517 " " Order of pole (three term test) = 22.087782355661393 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y1[1] (analytic) = 1.2867152096319545 " " y1[1] (numeric) = 1.2867152096319556 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.62835082941717200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9580158602892253 " " y2[1] (numeric) = 1.9580158602892241 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.670143164525551000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27467771821356357 " " Order of pole (three term test) = 22.917794388565703 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2746777182135636 " " Order of pole (three term test) = 22.082205611434294 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y1[1] (analytic) = 1.2771208750565568 " " y1[1] (numeric) = 1.2771208750565577 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.95453685745127800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9608350642060728 " " y2[1] (numeric) = 1.960835064206072 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.52959270217733400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2662674537778109 " " Order of pole (three term test) = 22.923204020607884 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.26626745377781097 " " Order of pole (three term test) = 22.076795979392113 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y1[1] (analytic) = 1.2674988286245865 " " y1[1] (numeric) = 1.2674988286245874 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.00733128616712900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.963558185417193 " " y2[1] (numeric) = 1.9635581854171922 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.52331092756192430000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2577506859107322 " " Order of pole (three term test) = 22.92844437668447 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.25775068591073225 " " Order of pole (three term test) = 22.07155562331553 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y1[1] (analytic) = 1.2578500325326687 " " y1[1] (numeric) = 1.2578500325326696 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.06108356901487400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9661849516127343 " " y2[1] (numeric) = 1.9661849516127332 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.646584893829608000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24913082120591942 " " Order of pole (three term test) = 22.933513360722902 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24913082120591953 " " Order of pole (three term test) = 22.066486639277098 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y1[1] (analytic) = 1.248175451652372 " " y1[1] (numeric) = 1.2481754516523729 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.11581387475877800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9687151001182654 " " y2[1] (numeric) = 1.9687151001182643 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.63932802952780100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24041130749432432 " " Order of pole (three term test) = 22.93840894519714 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24041130749432438 " " Order of pole (three term test) = 22.06159105480286 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y1[1] (analytic) = 1.2384760534337222 " " y1[1] (numeric) = 1.2384760534337231 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.17154293970897900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9711483779210448 " " y2[1] (numeric) = 1.9711483779210437 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.632366579100961000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23159563246517267 " " Order of pole (three term test) = 22.94312917193868 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23159563246517267 " " Order of pole (three term test) = 22.056870828061324 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y1[1] (analytic) = 1.2287528078084584 " " y1[1] (numeric) = 1.2287528078084593 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.2282920865445300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9734845416953197 " " y2[1] (numeric) = 1.9734845416953184 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.75083894199497900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2226873222709356 " " Order of pole (three term test) = 22.947672152919743 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22268732227093557 " " Order of pole (three term test) = 22.052327847080253 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y1[1] (analytic) = 1.2190066870930407 " " y1[1] (numeric) = 1.2190066870930414 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.4645624329069100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9757233578266593 " " y2[1] (numeric) = 1.975723357826658 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74318914271334400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21368994011691497 " " Order of pole (three term test) = 22.952036071008532 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21368994011691497 " " Order of pole (three term test) = 22.047963928991468 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y1[1] (analytic) = 1.2092386658914185 " " y1[1] (numeric) = 1.2092386658914192 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.50870422493509900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9778646024353164 " " y2[1] (numeric) = 1.977864602435315 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.73588893754297400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20460708483600878 " " Order of pole (three term test) = 22.95621918069598 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.20460708483600878 " " Order of pole (three term test) = 22.04378081930402 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y1[1] (analytic) = 1.199449720997572 " " y1[1] (numeric) = 1.1994497209975727 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.55366184270797200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9799080613986144 " " y2[1] (numeric) = 1.979908061398613 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.72893684067869800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19544238944922626 " " Order of pole (three term test) = 22.960219808793994 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1954423894492263 " " Order of pole (three term test) = 22.039780191206013 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y1[1] (analytic) = 1.1896408312978335 " " y1[1] (numeric) = 1.1896408312978342 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.599453189988259000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.98185353037236 " " y2[1] (numeric) = 1.9818535303723586 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.72233143939691200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18619951971252774 " " Order of pole (three term test) = 22.964036355104664 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1861995197125277 " " Order of pole (three term test) = 22.035963644895332 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y1[1] (analytic) = 1.1798129776729984 " " y1[1] (numeric) = 1.1798129776729993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.5281289196523500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9837008148112767 " " y2[1] (numeric) = 1.9837008148112754 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.7160713934421400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17688217265057155 " " Order of pole (three term test) = 22.967667293060362 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17688217265057155 " " Order of pole (three term test) = 22.032332706939627 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y1[1] (analytic) = 1.1699671429002398 " " y1[1] (numeric) = 1.1699671429002407 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.59148173596066500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9854497299884604 " " y2[1] (numeric) = 1.985449729988459 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.71015543444623600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16749407507795244 " " Order of pole (three term test) = 22.971111170334332 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16749407507795241 " " Order of pole (three term test) = 22.028888829665675 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y1[1] (analytic) = 1.1601043115548302 " " y1[1] (numeric) = 1.160104311554831 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.65602205641097800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9871001010138505 " " y2[1] (numeric) = 1.9871001010138492 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.70458236537979900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1580389821085269 " " Order of pole (three term test) = 22.974366609421555 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.158038982108527 " " Order of pole (three term test) = 22.02563339057845 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y1[1] (analytic) = 1.1502254699116847 " " y1[1] (numeric) = 1.1502254699116856 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.72177666843284500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.98865176285172 " " y2[1] (numeric) = 1.9886517628517186 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.6993510600353700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14852067565341615 " " Order of pole (three term test) = 22.97743230818982 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14852067565341615 " " Order of pole (three term test) = 22.022567691810185 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y1[1] (analytic) = 1.1403316058467357 " " y1[1] (numeric) = 1.1403316058467365 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.78877315288145500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.990104560337178 " " y2[1] (numeric) = 1.9901045603371765 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.81020387296573100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1389429629082934 " " Order of pole (three term test) = 22.980307040400472 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13894296290829342 " " Order of pole (three term test) = 22.019692959599524 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y1[1] (analytic) = 1.1304237087381444 " " y1[1] (numeric) = 1.1304237087381455 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.821299889971901000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9914583481916865 " " y2[1] (numeric) = 1.9914583481916852 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.68990958691118700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1293096748305554 " " Order of pole (three term test) = 22.98298965619899 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.12930967483055542 " " Order of pole (three term test) = 22.01701034380101 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y1[1] (analytic) = 1.1205027693673655 " " y1[1] (numeric) = 1.1205027693673666 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.90825774801062900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.9927129910375885 " " y2[1] (numeric) = 1.9927129910375871 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.68569751661270400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11962466460699138 " " Order of pole (three term test) = 22.985479082574795 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11962466460699138 " " Order of pole (three term test) = 22.014520917425198 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y1[1] (analytic) = 1.1105697798200684 " " y1[1] (numeric) = 1.1105697798200695 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.9968776820582300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.993868363411645 " " y2[1] (numeric) = 1.9938683634116434 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.79546063821226700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10989180611255858 " " Order of pole (three term test) = 22.98777432379054 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10989180611255861 " " Order of pole (three term test) = 22.012225676209454 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y1[1] (analytic) = 1.1006257333869307 " " y1[1] (numeric) = 1.1006257333869318 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0087198499427161000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.994924349777581 " " y2[1] (numeric) = 1.9949243497775795 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.79133421599928400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10011499236088552 " " Order of pole (three term test) = 22.98987446178034 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10011499236088549 " " Order of pole (three term test) = 22.010125538219654 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y1[1] (analytic) = 1.0906716244643087 " " y1[1] (numeric) = 1.0906716244643098 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.01792601890642450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9958808445376401 " " y2[1] (numeric) = 1.9958808445376386 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.7876003406169600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.02981339471167200E-2 " " Order of pole (three term test) = 22.991778656517 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.02981339471167300E-2 " " Order of pole (three term test) = 22.008221343482994 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y1[1] (analytic) = 1.0807084484547995 " " y1[1] (numeric) = 1.0807084484548006 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.02731039644647640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9967377520431435 " " y2[1] (numeric) = 1.996737752043142 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.78425826268263500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.04451574837280600E-2 " " Order of pole (three term test) = 22.993486146348026 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.04451574837280200E-2 " " Order of pole (three term test) = 22.006513853651985 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y1[1] (analytic) = 1.0707372016677017 " " y1[1] (numeric) = 1.070737201667703 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.24425267701089070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9974949866040546 " " y2[1] (numeric) = 1.997494986604053 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.78130731190323900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.05600040299338400E-2 " " Order of pole (three term test) = 22.994996248300225 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.05600040299338800E-2 " " Order of pole (three term test) = 22.005003751699775 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y1[1] (analytic) = 1.0607588812193849 " " y1[1] (numeric) = 1.060758881219386 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04663090197171930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9981524724975483 " " y2[1] (numeric) = 1.9981524724975468 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.7787468967893100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.06466275153150200E-2 " " Order of pole (three term test) = 22.996308358352966 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.064662751531500E-2 " " Order of pole (three term test) = 22.003691641647023 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y1[1] (analytic) = 1.050774484933578 " " y1[1] (numeric) = 1.0507744849335794 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.267891111416169800000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.998710143975583 " " y2[1] (numeric) = 1.9987101439755817 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.66563700377388500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.07089931583012500E-2 " " Order of pole (three term test) = 22.997421951679733 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.07089931583012400E-2 " " Order of pole (three term test) = 22.002578048320274 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y1[1] (analytic) = 1.04078501124159 " " y1[1] (numeric) = 1.0407850112415913 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28006035363718180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9991679452714761 " " y2[1] (numeric) = 1.9991679452714746 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77479570013889900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.075107588013491000E-2 " " Order of pole (three term test) = 22.998336582858027 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.07510758801349240E-2 " " Order of pole (three term test) = 22.001663417141977 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y1[1] (analytic) = 1.030791459082465 " " y1[1] (numeric) = 1.0307914590824665 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50788233718850780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.999525830605479 " " y2[1] (numeric) = 1.9995258306054775 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77340412754035800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.07768587149569800E-2 " " Order of pole (three term test) = 22.99905188604757 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.07768587149569800E-2 " " Order of pole (three term test) = 22.000948113952422 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y1[1] (analytic) = 1.0207948278030914 " " y1[1] (numeric) = 1.0207948278030927 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.30512772328346740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.999783764189357 " " y2[1] (numeric) = 1.9997837641893554 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77240150814647500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.07903312166455720E-2 " " Order of pole (three term test) = 22.99956757513664 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.079033121664557000E-2 " " Order of pole (three term test) = 22.00043242486336 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y1[1] (analytic) = 1.0107961170582662 " " y1[1] (numeric) = 1.0107961170582678 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.53771092730228880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9999417202299663 " " y2[1] (numeric) = 1.9999417202299647 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77178764137434300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.079548786304837800E-2 " " Order of pole (three term test) = 22.99988344385646 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.07954878630483810E-2 " " Order of pole (three term test) = 22.000116556143535 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y1[1] (analytic) = 1.000796326710732 " " y1[1] (numeric) = 1.0007963267107336 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.55307547898751840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9999996829318345 " " y2[1] (numeric) = 1.9999996829318332 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.6613392038002400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.9632645824374860000E-4 " " Order of pole (three term test) = 22.99999936586377 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.9632645824374850000E-4 " " Order of pole (three term test) = 22.000000634136228 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y1[1] (analytic) = 0.9907964567311905 " " y1[1] (numeric) = 0.990796456731192 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.45669670314967360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.99995764649874 " " y2[1] (numeric) = 1.9999576464987385 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77172575227431600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.203153466526597000E-3 " " Order of pole (three term test) = 22.999915294791293 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.203153466526596000E-3 " " Order of pole (three term test) = 22.0000847052087 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y1[1] (analytic) = 0.9807975070983063 " " y1[1] (numeric) = 0.9807975070983077 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.4715473087637460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.999815615134291 " " y2[1] (numeric) = 1.9998156151342894 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.772277717567699000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.919895225261737400E-2 " " Order of pole (three term test) = 22.999631264266363 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.91989522526173680E-2 " " Order of pole (three term test) = 22.000368735733637 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y1[1] (analytic) = 0.97080047769871 " " y1[1] (numeric) = 0.9708004776987116 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.6010624944888040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.999573603041505 " " y2[1] (numeric) = 1.9995736030415037 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.66275863776010300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.918707171378969000E-2 " " Order of pole (three term test) = 22.99914738789738 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.9187071713789700E-2 " " Order of pole (three term test) = 22.00085261210263 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y1[1] (analytic) = 0.9608063682270112 " " y1[1] (numeric) = 0.9608063682270127 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.61771641599692150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9992316344213905 " " y2[1] (numeric) = 1.999231634421389 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77454801991997200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.916351673543229000E-2 " " Order of pole (three term test) = 22.998463859228448 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.916351673543229000E-2 " " Order of pole (three term test) = 22.001536140771556 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y1[1] (analytic) = 0.9508161780858283 " " y1[1] (numeric) = 0.9508161780858299 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.63471370207892540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.998789743470524 " " y2[1] (numeric) = 1.9987897434705224 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77626681121770700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.912429687255403500E-2 " " Order of pole (three term test) = 22.997580951661913 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.91242968725540200E-2 " " Order of pole (three term test) = 22.002419048338087 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y1[1] (analytic) = 0.9408309062858505 " " y1[1] (numeric) = 0.9408309062858521 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.6520633241218970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9982479743776325 " " y2[1] (numeric) = 1.998247974377631 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.77837512863897700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.9065427945908600E-2 " " Order of pole (three term test) = 22.99649901834904 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.90654279459086100E-2 " " Order of pole (three term test) = 22.003500981650955 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y1[1] (analytic) = 0.9308515513459368 " " y1[1] (numeric) = 0.9308515513459383 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.6697745545224780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9976063813191736 " " y2[1] (numeric) = 1.9976063813191722 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.66932005228371700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.8982933635613200E-2 " " Order of pole (three term test) = 22.99521849204873 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.89829336356132300E-2 " " Order of pole (three term test) = 22.00478150795126 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y1[1] (analytic) = 0.9208791111932648 " " y1[1] (numeric) = 0.9208791111932665 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 1.8084181915906560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9968650284539189 " " y2[1] (numeric) = 1.9968650284539173 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.78376210874228100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.88728470716238900E-2 " " Order of pole (three term test) = 22.99373988495443 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.8872847071623900E-2 " " Order of pole (three term test) = 22.006260115045563 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y1[1] (analytic) = 0.9109145830635397 " " y1[1] (numeric) = 0.9109145830635414 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.9500805810201230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9960239899165366 " " y2[1] (numeric) = 1.9960239899165353 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.67460730071634200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.8731212420429910E-2 " " Order of pole (three term test) = 22.992063788489265 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.87312124204299000E-2 " " Order of pole (three term test) = 22.007936211510742 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y1[1] (analytic) = 0.9009589634012707 " " y1[1] (numeric) = 0.9009589634012725 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.97162902147530240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.99508334981018 " " y2[1] (numeric) = 1.9950833498101788 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.67775423857326500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.85540864673346100E-2 " " Order of pole (three term test) = 22.99019087306945 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.85540864673346100E-2 " " Order of pole (three term test) = 22.00980912693055 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y1[1] (analytic) = 0.8910132477601276 " " y1[1] (numeric) = 0.8910132477601294 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.9936368441947890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9940432021980758 " " y2[1] (numeric) = 1.9940432021980745 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.68123753829205600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10833754019368956 " " Order of pole (three term test) = 22.988121887836208 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10833754019368953 " " Order of pole (three term test) = 22.011878112163796 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y1[1] (analytic) = 0.8810784307033864 " " y1[1] (numeric) = 0.8810784307033883 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.14212387466576060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9929036510941183 " " y2[1] (numeric) = 1.9929036510941172 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.57088158283837000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1180776603484481 " " Order of pole (three term test) = 22.985857660356032 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1180776603484481 " " Order of pole (three term test) = 22.014142339643968 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y1[1] (analytic) = 0.871155505704474 " " y1[1] (numeric) = 0.8711555057044759 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.1665238060299080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9916648104524683 " " y2[1] (numeric) = 1.9916648104524672 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.574346741472703000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12777055101341525 " " Order of pole (three term test) = 22.98339909628973 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.12777055101341528 " " Order of pole (three term test) = 22.016600903710263 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y1[1] (analytic) = 0.8612454650476211 " " y1[1] (numeric) = 0.861245465047623 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.19145321335120960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.990326804156158 " " y2[1] (numeric) = 1.9903268041561566 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.69371294587489300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13741233516156157 " " Order of pole (three term test) = 22.98074717903015 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1374123351615616 " " Order of pole (three term test) = 22.019252820969847 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y1[1] (analytic) = 0.851349299728635 " " y1[1] (numeric) = 0.8513492997286369 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.21692687415654480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9888897660047014 " " y2[1] (numeric) = 1.9888897660047 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.69854937323378300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14699915620778348 " " Order of pole (three term test) = 22.977902969308833 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14699915620778345 " " Order of pole (three term test) = 22.022097030691167 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y1[1] (analytic) = 0.841467999355801 " " y1[1] (numeric) = 0.8414679993558029 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.24296009272804080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9873538397007162 " " y2[1] (numeric) = 1.987353839700715 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.58643862228554900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15652717955148465 " " Order of pole (three term test) = 22.97486760477174 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1565271795514847 " " Order of pole (three term test) = 22.025132395228255 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y1[1] (analytic) = 0.8316025520509217 " " y1[1] (numeric) = 0.8316025520509236 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.26956872271262070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9857191788355533 " " y2[1] (numeric) = 1.9857191788355522 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.59103742592748200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1659925941103666 " " Order of pole (three term test) = 22.971642299524234 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16599259411036665 " " Order of pole (three term test) = 22.028357700475762 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y1[1] (analytic) = 0.8217539443505066 " " y1[1] (numeric) = 0.8217539443505085 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.29676919087319080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9839859468739367 " " y2[1] (numeric) = 1.9839859468739356 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.595921817765277000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17539161384480956 " " Order of pole (three term test) = 22.968228343645404 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17539161384480956 " " Order of pole (three term test) = 22.0317716563546 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y1[1] (analytic) = 0.8119231611071186 " " y1[1] (numeric) = 0.8119231611071205 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.3245785220478032000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9821543171376184 " " y2[1] (numeric) = 1.9821543171376172 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.60109278589571700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18472047927223817 " " Order of pole (three term test) = 22.96462710267206 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18472047927223817 " " Order of pole (three term test) = 22.035372897327935 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y1[1] (analytic) = 0.8021111853908897 " " y1[1] (numeric) = 0.8021111853908915 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.35301436538750820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9802244727880454 " " y2[1] (numeric) = 1.9802244727880443 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.606551377794179000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19397545897086493 " " Order of pole (three term test) = 22.960840017052607 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19397545897086493 " " Order of pole (three term test) = 22.039159982947403 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y1[1] (analytic) = 0.7923189983912149 " " y1[1] (numeric) = 0.7923189983912168 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.3820950219482870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9781966068080443 " " y2[1] (numeric) = 1.9781966068080434 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.48983896061404100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2031528510722081 " " Order of pole (three term test) = 22.95686860157077 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.20315285107220812 " " Order of pole (three term test) = 22.043131398429225 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y1[1] (analytic) = 0.7825475793186341 " " y1[1] (numeric) = 0.7825475793186359 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.4118394737175108000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9760709219825239 " " y2[1] (numeric) = 1.976070921982523 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.49466873794715060000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21224898474179113 " " Order of pole (three term test) = 22.952714444739815 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21224898474179113 " " Order of pole (three term test) = 22.04728555526018 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y1[1] (analytic) = 0.7727979053069116 " " y1[1] (numeric) = 0.7727979053069135 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.44226741416076420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.973847630878195 " " y2[1] (numeric) = 1.973847630878194 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.49973141698359500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22126022164742604 " " Order of pole (three term test) = 22.948379208167076 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.221260221647426 " " Order of pole (three term test) = 22.051620791832928 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y1[1] (analytic) = 0.763070951315324 " " y1[1] (numeric) = 0.763070951315326 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 2.61889335569725050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.971526955822315 " " y2[1] (numeric) = 1.9715269558223143 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.37877102216567200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23018295741449865 " " Order of pole (three term test) = 22.943864625889372 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2301829574144987 " " Order of pole (three term test) = 22.056135374110625 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y1[1] (analytic) = 0.7533676900311647 " " y1[1] (numeric) = 0.7533676900311667 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 2.6526243038676290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.969109128880456 " " y2[1] (numeric) = 1.9691091288804554 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.382919742766245500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.239013623067671 " " Order of pole (three term test) = 22.939172503679433 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23901362306767102 " " Order of pole (three term test) = 22.060827496320563 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y1[1] (analytic) = 0.743689091772476 " " y1[1] (numeric) = 0.743689091772478 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 2.6871463712912330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.966594391833297 " " y2[1] (numeric) = 1.9665943918332967 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.258163715376377600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24774868645842218 " " Order of pole (three term test) = 22.934304718323588 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24774868645842213 " " Order of pole (three term test) = 22.065695281676415 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y1[1] (analytic) = 0.7340361243910183 " " y1[1] (numeric) = 0.7340361243910204 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 2.8737328813862506000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9639829961524478 " " y2[1] (numeric) = 1.963982996152447 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.39174939946062300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2563846536778614 " " Order of pole (three term test) = 22.929263216871043 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.25638465367786156 " " Order of pole (three term test) = 22.07073678312895 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y1[1] (analytic) = 0.7244097531754858 " " y1[1] (numeric) = 0.7244097531754878 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 2.758661704325750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9612752029752996 " " y2[1] (numeric) = 1.961275202975299 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.396432146618453000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2649180704542464 " " Order of pole (three term test) = 22.924050015855205 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2649180704542465 " " Order of pole (three term test) = 22.075949984144795 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y1[1] (analytic) = 0.7148109407549779 " " y1[1] (numeric) = 0.71481094075498 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 2.951023307729229700000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.958471283078914 " " y2[1] (numeric) = 1.958471283078913 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.53505970383093600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2733455235346432 " " Order of pole (three term test) = 22.91866720048694 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2733455235346433 " " Order of pole (three term test) = 22.08133279951306 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y1[1] (analytic) = 0.7052406470027377 " " y1[1] (numeric) = 0.7052406470027398 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 2.9910694395633840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9555715168529435 " " y2[1] (numeric) = 1.9555715168529428 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.4063382956563400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2816636420501848 " " Order of pole (three term test) = 22.91311692382064 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.28166364205018474 " " Order of pole (three term test) = 22.08688307617936 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y1[1] (analytic) = 0.6956998289401652 " " y1[1] (numeric) = 0.6956998289401675 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.191672553136830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.952576194271595 " " y2[1] (numeric) = 1.9525761942715942 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.41156374193937130000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2898690988643711 " " Order of pole (three term test) = 22.907401405892955 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.28986909886437123 " " Order of pole (three term test) = 22.09259859410705 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y1[1] (analytic) = 0.6861894406411162 " " y1[1] (numeric) = 0.6861894406411184 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.23590821679756560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.94948561486463 " " y2[1] (numeric) = 1.9494856148646293 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.416972198696369700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29795861190388157 " " Order of pole (three term test) = 22.901522932834865 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2979586119038816 " " Order of pole (three term test) = 22.098477067165135 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y1[1] (analytic) = 0.6767104331364953 " " y1[1] (numeric) = 0.6767104331364974 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 3.1171733779998007000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9463000876874141 " " y2[1] (numeric) = 1.9463000876874135 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.42256478838569800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.305928945471359 " " Order of pole (three term test) = 22.89548385595721 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.305928945471359 " " Order of pole (three term test) = 22.10451614404279 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y1[1] (analytic) = 0.6672637543191533 " " y1[1] (numeric) = 0.6672637543191555 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.32768869113227800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.94301993129001 " " y2[1] (numeric) = 1.9430199312900096 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.285561782967521500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3137769115396464 " " Order of pole (three term test) = 22.88928659081022 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3137769115396465 " " Order of pole (three term test) = 22.110713409189785 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y1[1] (analytic) = 0.6578503488491003 " " y1[1] (numeric) = 0.6578503488491025 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.3753057258918406000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9396454736853244 " " y2[1] (numeric) = 1.939645473685324 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.28953804122922300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32149937102695414 " " Order of pole (three term test) = 22.882933616217315 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3214993710269541 " " Order of pole (three term test) = 22.11706638378268 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y1[1] (analytic) = 0.6484711580590388 " " y1[1] (numeric) = 0.6484711580590409 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 3.25291837666548840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9361770523163055 " " y2[1] (numeric) = 1.936177052316305 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.29363946504161700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3290932350524523 " " Order of pole (three term test) = 22.87642747328364 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.32909323505245236 " " Order of pole (three term test) = 22.123572526716348 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y1[1] (analytic) = 0.6391271198602314 " " y1[1] (numeric) = 0.6391271198602336 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.4741853071981910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9326150140222 " " y2[1] (numeric) = 1.9326150140221996 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.297866914144553500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3365554661717804 " " Order of pole (three term test) = 22.869770764379627 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3365554661717805 " " Order of pole (three term test) = 22.13022923562037 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y1[1] (analytic) = 0.6298191686487117 " " y1[1] (numeric) = 0.6298191686487139 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.52552948493822400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9289597150038689 " " y2[1] (numeric) = 1.9289597150038684 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.30222127707406220000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3438830795919867 " " Order of pole (three term test) = 22.862966152100068 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.34388307959198666 " " Order of pole (three term test) = 22.137033847899925 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y1[1] (analytic) = 0.6205482352118441 " " y1[1] (numeric) = 0.6205482352118463 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.5782005704879530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9252115207881677 " " y2[1] (numeric) = 1.9252115207881673 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.306703471565844700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3510731443654024 " " Order of pole (three term test) = 22.856016358199152 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35107314436540243 " " Order of pole (three term test) = 22.143983641800848 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y1[1] (analytic) = 0.6113152466352465 " " y1[1] (numeric) = 0.6113152466352488 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 3.8138560497967530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9213708061913948 " " y2[1] (numeric) = 1.9213708061913943 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.311314444973539600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3581227845619851 " " Order of pole (three term test) = 22.848924162501785 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35812278456198504 " " Order of pole (three term test) = 22.15107583749822 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y1[1] (analytic) = 0.6021211262100826 " " y1[1] (numeric) = 0.602121126210085 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 3.872091926731980300000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9174379552818093 " " y2[1] (numeric) = 1.9174379552818088 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.316055174702088500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3650291804196496 " " Order of pole (three term test) = 22.841692401791672 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36502918041964955 " " Order of pole (three term test) = 22.15830759820833 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y1[1] (analytic) = 0.592966793340733 " " y1[1] (numeric) = 0.5929667933407354 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 4.1191019153273740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9134133613412245 " " y2[1] (numeric) = 1.913413361341224 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.320926668656553300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37178956947213704 " " Order of pole (three term test) = 22.834323968676678 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3717895694721371 " " Order of pole (three term test) = 22.165676031323326 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y1[1] (analytic) = 0.5838531634528564 " " y1[1] (numeric) = 0.5838531634528586 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 3.80308986615536970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.909297426825681 " " y2[1] (numeric) = 1.9092974268256806 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.325929965706741200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3784012476539639 " " Order of pole (three term test) = 22.826821810431806 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3784012476539639 " " Order of pole (three term test) = 22.173178189568194 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y1[1] (analytic) = 0.5747811479018465 " " y1[1] (numeric) = 0.5747811479018486 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 3.6699598699225550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9050905633252004 " " y2[1] (numeric) = 1.9050905633251998 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.496599204252025500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3848615703820117 " " Order of pole (three term test) = 22.819188927820328 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3848615703820117 " " Order of pole (three term test) = 22.180811072179665 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y1[1] (analytic) = 0.5657516538816987 " " y1[1] (numeric) = 0.5657516538817006 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 3.3360558982253120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.9007931915226268 " " y2[1] (numeric) = 1.9007931915226262 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.50450442344802700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39116795361332624 " " Order of pole (three term test) = 22.811428373893524 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3911679536133262 " " Order of pole (three term test) = 22.188571626106476 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y1[1] (analytic) = 0.5567655843342902 " " y1[1] (numeric) = 0.5567655843342919 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 2.99108742313685060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8964057411515596 " " y2[1] (numeric) = 1.8964057411515587 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.68348307762870560000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3973178748786984 " " Order of pole (three term test) = 22.803543252769472 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39731787487869835 " " Order of pole (three term test) = 22.196456747230524 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y1[1] (analytic) = 0.5478238378590876 " " y1[1] (numeric) = 0.5478238378590891 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 2.6345876763105540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8919286509533793 " " y2[1] (numeric) = 1.8919286509533784 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.69456614683939070000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40330887429161993 " " Order of pole (three term test) = 22.795536718391514 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40330887429162 " " Order of pole (three term test) = 22.204463281608486 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y1[1] (analytic) = 0.5389273086232869 " " y1[1] (numeric) = 0.5389273086232881 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 2.26606688424714680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8873623686333754 " " y2[1] (numeric) = 1.8873623686333743 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.88240521839513300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4091385555322052 " " Order of pole (three term test) = 22.787411973266632 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4091385555322052 " " Order of pole (three term test) = 22.21258802673336 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y1[1] (analytic) = 0.5300768862723978 " " y1[1] (numeric) = 0.5300768862723988 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.88501092584740270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.882707350815974 " " y2[1] (numeric) = 1.8827073508159728 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.89694953994831300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4148045868056852 " " Order of pole (three term test) = 22.77917226718455 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4148045868056853 " " Order of pole (three term test) = 22.220827732815447 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y1[1] (analytic) = 0.5212734558412802 " " y1[1] (numeric) = 0.521273455841281 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.70386274180544900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8779640629990781 " " y2[1] (numeric) = 1.8779640629990768 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 7.09421258797986800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42030470177509716 " " Order of pole (three term test) = 22.77082089591785 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4203047017750973 " " Order of pole (three term test) = 22.22917910408215 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y1[1] (analytic) = 0.512517897665641 " " y1[1] (numeric) = 0.5125178976656417 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.29972790766746980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8731329795075167 " " y2[1] (numeric) = 1.8731329795075153 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 7.11250959822653400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42563670046778707 " " Order of pole (three term test) = 22.762361199903673 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4256367004677872 " " Order of pole (three term test) = 22.237638800096327 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y1[1] (analytic) = 0.5038110872940016 " " y1[1] (numeric) = 0.503811087294002 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.81459779369468400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8682145834456128 " " y2[1] (numeric) = 1.8682145834456114 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 7.13123450247904900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43079845015537016 " " Order of pole (three term test) = 22.753796562907638 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43079845015537005 " " Order of pole (three term test) = 22.246203437092362 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y1[1] (analytic) = 0.4951538954001432 " " y1[1] (numeric) = 0.4951538954001436 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 7.84762196619270300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8632093666488743 " " y2[1] (numeric) = 1.8632093666488727 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 8.34212333995921100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43578788620679404 " " Order of pole (three term test) = 22.74513041067035 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43578788620679404 " " Order of pole (three term test) = 22.25486958932965 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y1[1] (analytic) = 0.4865471876960412 " " y1[1] (numeric) = 0.48654718769604144 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.5636807804086700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8581178296348093 " " y2[1] (numeric) = 1.8581178296348078 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 8.36498207856226400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4406030129141624 " " Order of pole (three term test) = 22.736366209537156 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4406030129141625 " " Order of pole (three term test) = 22.263633790462848 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y1[1] (analytic) = 0.4779918248452938 " " y1[1] (numeric) = 0.4779918248452938 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.852940481552877 " " y2[1] (numeric) = 1.8529404815528752 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.58669130004410800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44524190429099414 " " Order of pole (three term test) = 22.727507465071657 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4452419042909941 " " Order of pole (three term test) = 22.272492534928347 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y1[1] (analytic) = 0.46948866237705633 " " y1[1] (numeric) = 0.4694886623770562 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.36474938287969300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8476778401335705 " " y2[1] (numeric) = 1.8476778401335687 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.61399655727773300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4497027048425886 " " Order of pole (three term test) = 22.718557720653514 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44970270484258873 " " Order of pole (three term test) = 22.28144227934649 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y1[1] (analytic) = 0.4610385506004899 " " y1[1] (numeric) = 0.46103855060048965 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.02022880287950900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8423304316366464 " " y2[1] (numeric) = 1.8423304316366447 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.6419014140813600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45398363030820255 " " Order of pole (three term test) = 22.70952055606118 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45398363030820266 " " Order of pole (three term test) = 22.290479443938825 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y1[1] (analytic) = 0.45264233451973046 " " y1[1] (numeric) = 0.45264233451973 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.81104010788688000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y2[1] (analytic) = 1.8368987907984988 " " y2[1] (numeric) = 1.8368987907984966 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.20880151937227130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4580829683747273 " " Order of pole (three term test) = 22.70039958603999 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45808296837472734 " " Order of pole (three term test) = 22.29960041396001 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y1[1] (analytic) = 0.4443008537493891 " " y1[1] (numeric) = 0.4443008537493885 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.37434501507454230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8313834607786843 " " y2[1] (numeric) = 1.831383460778682 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.21244190351386260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4619990793615938 " " Order of pole (three term test) = 22.691198458856338 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4619990793615938 " " Order of pole (three term test) = 22.308801541143655 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y1[1] (analytic) = 0.4360149424305918 " " y1[1] (numeric) = 0.43601494243059097 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 1.90972186372125930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8257849931056094 " " y2[1] (numeric) = 1.825784993105607 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.33777562166328020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4657303968766212 " " Order of pole (three term test) = 22.681920854838427 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46573039687662127 " " Order of pole (three term test) = 22.318079145161565 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y1[1] (analytic) = 0.42778542914756534 " " y1[1] (numeric) = 0.4277854291475644 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.20598811140399030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8201039476213756 " " y2[1] (numeric) = 1.8201039476213732 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.34195118766010170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46927542844255377 " " Order of pole (three term test) = 22.67257048490416 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4692754284425538 " " Order of pole (three term test) = 22.32742951509584 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y1[1] (analytic) = 0.4196131368447803 " " y1[1] (numeric) = 0.4196131368447792 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 2.6458252307668834000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8143408924257975 " " y2[1] (numeric) = 1.8143408924257949 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.46859681674145430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47263275609403166 " " Order of pole (three term test) = 22.663151089076848 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47263275609403166 " " Order of pole (three term test) = 22.33684891092316 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y1[1] (analytic) = 0.4114988827446566 " " y1[1] (numeric) = 0.4114988827446554 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 2.9677974310454680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8084964038195919 " " y2[1] (numeric) = 1.8084964038195892 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.47334285734425970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4758010369447579 " " Order of pole (three term test) = 22.653666434989216 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4758010369447579 " " Order of pole (three term test) = 22.34633356501079 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y1[1] (analytic) = 0.4034434782658426 " " y1[1] (numeric) = 0.4034434782658412 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 3.43983446391712630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.8025710662467491 " " y2[1] (numeric) = 1.8025710662467462 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.60136813359361400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4787790037246356 " " Order of pole (three term test) = 22.64412031637644 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47877900372463555 " " Order of pole (three term test) = 22.355879683623556 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y1[1] (analytic) = 0.39544772894207314 " " y1[1] (numeric) = 0.39544772894207164 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 3.79013703594568400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7965654722360886 " " y2[1] (numeric) = 1.7965654722360855 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.73031515800050440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48156546528665817 " " Order of pole (three term test) = 22.634516551558697 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48156546528665817 " " Order of pole (three term test) = 22.365483448441296 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y1[1] (analytic) = 0.38751243434161764 " " y1[1] (numeric) = 0.387512434341616 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 4.29749961383079900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.790480222342007 " " y2[1] (numeric) = 1.7904802223420038 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.86020992151415380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4841593070833534 " " Order of pole (three term test) = 22.624858981913864 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48415930708335353 " " Order of pole (three term test) = 22.375141018086136 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y1[1] (analytic) = 0.3796383879873233 " " y1[1] (numeric) = 0.3796383879873215 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.6790759196342540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7843159250844223 " " y2[1] (numeric) = 1.784315925084419 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.86663641065574430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4865594916125866 " " Order of pole (three term test) = 22.615151470341022 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4865594916125869 " " Order of pole (three term test) = 22.384848529658974 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y1[1] (analytic) = 0.371826377277264 " " y1[1] (numeric) = 0.3718263772772621 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 5.0759689392756090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7780731968879238 " " y2[1] (numeric) = 1.7780731968879202 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.9980694186373460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48876505883254845 " " Order of pole (three term test) = 22.60539789971539 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48876505883254834 " " Order of pole (three term test) = 22.394602100284608 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y1[1] (analytic) = 0.3640771834060007 " " y1[1] (numeric) = 0.36407718340599865 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 5.6414208007814610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7717526620201285 " " y2[1] (numeric) = 1.7717526620201247 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.13052214603228180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4907751265457578 " " Order of pole (three term test) = 22.595602171335152 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4907751265457577 " " Order of pole (three term test) = 22.404397828664848 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y1[1] (analytic) = 0.35639158128646287 " " y1[1] (numeric) = 0.3563915812864607 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 6.0745960670684560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7653549525292562 " " y2[1] (numeric) = 1.7653549525292525 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.13824323449364530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4925888907519296 " " Order of pole (three term test) = 22.585768203361052 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4925888907519297 " " Order of pole (three term test) = 22.414231796638944 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y1[1] (analytic) = 0.34877033947245784 " " y1[1] (numeric) = 0.34877033947245556 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 6.5256615683665430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.758880708180925 " " y2[1] (numeric) = 1.7588807081809208 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.39859785484760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4942056259695653 " " Order of pole (three term test) = 22.575899929249186 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49420562596956524 " " Order of pole (three term test) = 22.424100070750818 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y1[1] (analytic) = 0.3412142200818159 " " y1[1] (numeric) = 0.34121422008181357 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 6.8328581122843960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7523305763941739 " " y2[1] (numeric) = 1.7523305763941697 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.40756370425085580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49562468552613337 " " Order of pole (three term test) = 22.566001296177582 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49562468552613353 " " Order of pole (three term test) = 22.433998703822418 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y1[1] (analytic) = 0.33372397872017956 " " y1[1] (numeric) = 0.33372397872017706 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 7.4852332007617700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7457052121767236 " " y2[1] (numeric) = 1.7457052121767191 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.543895766320860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49684550181673215 " " Order of pole (three term test) = 22.556076263467528 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49684550181673215 " " Order of pole (three term test) = 22.443923736532476 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y1[1] (analytic) = 0.32630036440544297 " " y1[1] (numeric) = 0.3263003644054404 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 7.8256515627576950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7390052780594745 " " y2[1] (numeric) = 1.7390052780594698 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.6813815704049770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49786758653112273 " " Order of pole (three term test) = 22.54612880099976 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4978675865311227 " " Order of pole (three term test) = 22.453871199000247 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y1[1] (analytic) = 0.3189441194928514 " " y1[1] (numeric) = 0.3189441194928487 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 8.5282851888184720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.732231444030255 " " y2[1] (numeric) = 1.7322314440302502 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.8200511687890640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4986905308490466 " " Order of pole (three term test) = 22.536162887626627 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4986905308490466 " " Order of pole (three term test) = 22.46383711237337 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y1[1] (analytic) = 0.31165597960076585 " " y1[1] (numeric) = 0.311655979600763 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 9.0839544180117250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7253843874668235 " " y2[1] (numeric) = 1.7253843874668184 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.9599351601724870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49931400560374944 " " Order of pole (three term test) = 22.526182509580615 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49931400560374933 " " Order of pole (three term test) = 22.473817490419382 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y1[1] (analytic) = 0.30443667353710213 " " y1[1] (numeric) = 0.3044366735370992 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 9.6640492785377520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y2[1] (analytic) = 1.7184647930691304 " " y2[1] (numeric) = 1.718464793069125 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.10106470594790500000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4997377614136419 " " Order of pole (three term test) = 22.516191658879862 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.499737761413642 " " Order of pole (three term test) = 22.483808341120138 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y1[1] (analytic) = 0.29728692322645045 " " y1[1] (numeric) = 0.29728692322644745 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 1.0083195500007172000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.7114733527908488 " " y2[1] (numeric) = 1.7114733527908434 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.11373268506389240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49996162878205047 " " Order of pole (three term test) = 22.506194331731447 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49996162878205036 " " Order of pole (three term test) = 22.493805668268553 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y1[1] (analytic) = 0.29020744363788387 " " y1[1] (numeric) = 0.2902074436378808 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.05204514379335000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.7044107657701806 " " y2[1] (numeric) = 1.7044107657701753 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.1266350959668330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49998551816501247 " " Order of pole (three term test) = 22.496194526932932 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49998551816501213 " " Order of pole (three term test) = 22.503805473067068 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y1[1] (analytic) = 0.2831989427134617 " " y1[1] (numeric) = 0.2831989427134585 " " absolute error = 3.164135620181696000000000000000E-15 " " relative error = 1.1172836981185844000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6972777382599427 " " y2[1] (numeric) = 1.6972777382599369 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.40142311297235660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49980942000709266 " " Order of pole (three term test) = 22.486196244272897 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4998094200070928 " " Order of pole (three term test) = 22.513803755727107 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y1[1] (analytic) = 0.276262121297436 " " y1[1] (numeric) = 0.27626212129743266 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.2056191627840013000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6900749835569413 " " y2[1] (numeric) = 1.6900749835569355 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.41591928418500670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49943340474520714 " " Order of pole (three term test) = 22.476203482931105 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49943340474520714 " " Order of pole (three term test) = 22.5237965170689 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y1[1] (analytic) = 0.2693976730661676 " " y1[1] (numeric) = 0.2693976730661642 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 1.2569448676251327000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6828032219306448 " " y2[1] (numeric) = 1.682803221930639 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.4306802202502260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49885762278044676 " " Order of pole (three term test) = 22.466220239878865 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49885762278044665 " " Order of pole (three term test) = 22.533779760121135 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y1[1] (analytic) = 0.26260628445875933 " " y1[1] (numeric) = 0.26260628445875583 " " absolute error = 3.497202527569243000000000000000E-15 " " relative error = 1.331728421799615000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6754631805511564 " " y2[1] (numeric) = 1.6754631805511502 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.71076428898644300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49808230441792034 " " Order of pole (three term test) = 22.456250508280277 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49808230441792034 " " Order of pole (three term test) = 22.54374949171972 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y1[1] (analytic) = 0.2558886346084125 " " y1[1] (numeric) = 0.25588863460840894 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.388382756521107000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6680555934164967 " " y2[1] (numeric) = 1.6680555934164902 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.8603590721080250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4971077597746357 " " Order of pole (three term test) = 22.446298275895057 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4971077597746357 " " Order of pole (three term test) = 22.55370172410494 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y1[1] (analytic) = 0.24924539527451406 " " y1[1] (numeric) = 0.24924539527451045 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 1.4476595750375765000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6605812012792063 " " y2[1] (numeric) = 1.6605812012791998 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.8777348183066780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49593437865545636 " " Order of pole (three term test) = 22.436367523483472 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49593437865545636 " " Order of pole (three term test) = 22.56363247651653 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y1[1] (analytic) = 0.24267723077546144 " " y1[1] (numeric) = 0.24267723077545775 " " absolute error = 3.6914915568786455000000000000000E-15 " " relative error = 1.5211528271864203000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.653040751572271 " " y2[1] (numeric) = 1.653040751572264 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.1640732366270580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49456263039718484 " " Order of pole (three term test) = 22.426462223214067 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4945626303971849 " " Order of pole (three term test) = 22.57353777678593 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y1[1] (analytic) = 0.23618479792223113 " " y1[1] (numeric) = 0.2361847979222273 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.6217256439247998000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6454349983343768 " " y2[1] (numeric) = 1.64543499833437 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.1833209817730920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4929930636808351 " " Order of pole (three term test) = 22.416586337074886 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4929930636808353 " " Order of pole (three term test) = 22.58341366292511 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y1[1] (analytic) = 0.22976874595269792 " " y1[1] (numeric) = 0.2297687459526941 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.66701063674923000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.63776470213451 " " y2[1] (numeric) = 1.637764702134503 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.33849096169947270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4912263063121664 " " Order of pole (three term test) = 22.406743815288714 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4912263063121664 " " Order of pole (three term test) = 22.593256184711286 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y1[1] (analytic) = 0.22342971646671228 " " y1[1] (numeric) = 0.22342971646670837 " " absolute error = 3.913536161803677000000000000000E-15 " " relative error = 1.7515737045599017000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6300306299958987 " " y2[1] (numeric) = 1.6300306299958913 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.49529709913762100000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4892630649705694 " " Order of pole (three term test) = 22.396938594733022 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4892630649705692 " " Order of pole (three term test) = 22.603061405266978 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y1[1] (analytic) = 0.21716834336194013 " " y1[1] (numeric) = 0.21716834336193622 " " absolute error = 3.913536161803677000000000000000E-15 " " relative error = 1.80207487943178000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6222335553193115 " " y2[1] (numeric) = 1.622233555319304 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.6537790706499470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4871041249264046 " " Order of pole (three term test) = 22.3871745973653 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48710412492640465 " " Order of pole (three term test) = 22.612825402634698 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y1[1] (analytic) = 0.2109852527704743 " " y1[1] (numeric) = 0.21098525277047034 " " absolute error = 3.969047313034934600000000000000E-15 " " relative error = 1.881196558013826800000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6143742578057187 " " y2[1] (numeric) = 1.6143742578057108 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.9515195987863153000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4847503497269044 " " Order of pole (three term test) = 22.377455728654322 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48475034972690445 " " Order of pole (three term test) = 22.62254427134568 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y1[1] (analytic) = 0.20488106299622133 " " y1[1] (numeric) = 0.2048810629962173 " " absolute error = 4.0245584642661925000000000000000E-15 " " relative error = 1.9643389220117520000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.6064535233783221 " " y2[1] (numeric) = 1.606453523378314 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.1141537944707540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4822026808507654 " " Order of pole (three term test) = 22.367785876017972 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48220268085076523 " " Order of pole (three term test) = 22.632214123982028 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y1[1] (analytic) = 0.19885638445307185 " " y1[1] (numeric) = 0.19885638445306775 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 2.0657245692217063000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.598472144103964 " " y2[1] (numeric) = 1.5984721441039556 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2785999545090640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47946213733156934 " " Order of pole (three term test) = 22.35816890726839 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4794621373315691 " " Order of pole (three term test) = 22.641831092731607 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y1[1] (analytic) = 0.1929118196038596 " " y1[1] (numeric) = 0.19291181960385545 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 2.1581551357991755000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5904309181139205 " " y2[1] (numeric) = 1.5904309181139118 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 5.4449014373700290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47652981535018385 " " Order of pole (three term test) = 22.34860866906484 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47652981535018385 " " Order of pole (three term test) = 22.651391330935166 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y1[1] (analytic) = 0.18704796290011572 " " y1[1] (numeric) = 0.18704796290011153 " " absolute error = 4.191091917959966000000000000000E-15 " " relative error = 2.2406509287663423000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5823306495240899 " " y2[1] (numeric) = 1.582330649524081 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.613102545711660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4734068877963044 " " Order of pole (three term test) = 22.339108985375137 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4734068877963045 " " Order of pole (three term test) = 22.660891014624863 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y1[1] (analytic) = 0.18126540072262398 " " y1[1] (numeric) = 0.1812654007226198 " " absolute error = 4.191091917959966000000000000000E-15 " " relative error = 2.3121301148768375000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5741721483545805 " " y2[1] (numeric) = 1.5741721483545716 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.6421937119679240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4700946037993144 " " Order of pole (three term test) = 22.329673655946102 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4700946037993144 " " Order of pole (three term test) = 22.670326344053898 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y1[1] (analytic) = 0.1755647113227835 " " y1[1] (numeric) = 0.17556471132277926 " " absolute error = 4.246603069191224000000000000000E-15 " " relative error = 2.418824966130953000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5659562304487111 " " y2[1] (numeric) = 1.565956230448702 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 5.8135908430324780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46659428822864885 " " Order of pole (three term test) = 22.320306454783704 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4665942882286489 " " Order of pole (three term test) = 22.679693545216296 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y1[1] (analytic) = 0.1699464647647836 " " y1[1] (numeric) = 0.16994646476477931 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 2.515120659157476000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5576837173914255 " " y2[1] (numeric) = 1.5576837173914162 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 5.9870134756681460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4629073411638663 " " Order of pole (three term test) = 22.31101112864351 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46290734116386617 " " Order of pole (three term test) = 22.68898887135649 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y1[1] (analytic) = 0.16441122286859822 " " y1[1] (numeric) = 0.16441122286859391 " " absolute error = 4.3021142204224816000000000000000E-15 " " relative error = 2.6166791690740265000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5493554364271356 " " y2[1] (numeric) = 1.549355436427126 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 6.1625097684454890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4590352373346337 " " Order of pole (three term test) = 22.301791395532035 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4590352373346338 " " Order of pole (three term test) = 22.69820860446796 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y1[1] (analytic) = 0.15895953915380434 " " y1[1] (numeric) = 0.1589595391538 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 2.72388169913393000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5409722203769975 " " y2[1] (numeric) = 1.5409722203769878 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 6.3401289702102250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45497952553085536 " " Order of pole (three term test) = 22.292650943219613 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45497952553085547 " " Order of pole (three term test) = 22.707349056780394 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y1[1] (analytic) = 0.15359195878423038 " " y1[1] (numeric) = 0.15359195878422602 " " absolute error = 4.3576253716537394000000000000000E-15 " " relative error = 2.8371442138943190000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5325349075556305 " " y2[1] (numeric) = 1.5325349075556205 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 6.5199214532499660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45074182798317747 " " Order of pole (three term test) = 22.283593427765272 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4507418279831775 " " Order of pole (three term test) = 22.716406572234725 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y1[1] (analytic) = 0.14830901851344025 " " y1[1] (numeric) = 0.14830901851343592 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 2.919491909148953000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5240443416872855 " " y2[1] (numeric) = 1.5240443416872753 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 6.7019387475585890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44632383971411765 " " Order of pole (three term test) = 22.274622472054453 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44632383971411754 " " Order of pole (three term test) = 22.72537752794555 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y1[1] (analytic) = 0.14311124663105868 " " y1[1] (numeric) = 0.14311124663105435 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 3.0255272719414783000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.515501371821474 " " y2[1] (numeric) = 1.5155013718214636 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 6.8862335762410930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4417273278600768 " " Order of pole (three term test) = 22.26574166434981 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4417273278600768 " " Order of pole (three term test) = 22.73425833565019 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y1[1] (analytic) = 0.1379991629099424 " " y1[1] (numeric) = 0.13799916290993808 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 3.1376058410323565000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.5069068522480635 " " y2[1] (numeric) = 1.5069068522480527 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 7.2202111398558180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43695413096451136 " " Order of pole (three term test) = 22.256954556856034 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4369541309645113 " " Order of pole (three term test) = 22.743045443143973 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y1[1] (analytic) = 0.1329732785542035 " " y1[1] (numeric) = 0.1329732785541992 " " absolute error = 4.3021142204224816000000000000000E-15 " " relative error = 3.2353223649132060000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.498261642411849 " " y2[1] (numeric) = 1.498261642411838 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 7.261872915475560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4320061582425374 " " Order of pole (three term test) = 22.24826466429894 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43200615824253724 " " Order of pole (three term test) = 22.75173533570105 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y1[1] (analytic) = 0.12803409614808936 " " y1[1] (numeric) = 0.12803409614808503 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 3.3818099446181976000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.48956660682661 " " y2[1] (numeric) = 1.4895666068265987 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 7.6023957567778480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4268853888172716 " " Order of pole (three term test) = 22.23967546251971 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4268853888172717 " " Order of pole (three term test) = 22.76032453748029 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y1[1] (analytic) = 0.12318210960572451 " " y1[1] (numeric) = 0.12318210960572022 " " absolute error = 4.288236432614667000000000000000E-15 " " relative error = 3.4812169123748990000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4808226149886592 " " y2[1] (numeric) = 1.4808226149886476 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 7.7972333345206610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4215938709282084 " " Order of pole (three term test) = 22.23119038708452 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4215938709282084 " " Order of pole (three term test) = 22.768809612915476 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y1[1] (analytic) = 0.11841780412171998 " " y1[1] (numeric) = 0.11841780412171571 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 3.6095574280479814000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4720305412898935 " " y2[1] (numeric) = 1.472030541289882 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 7.8438042773106840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41613372111195057 " " Order of pole (three term test) = 22.222812831910417 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4161337211119505 " " Order of pole (three term test) = 22.777187168089583 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y1[1] (analytic) = 0.11374165612265397 " " y1[1] (numeric) = 0.11374165612264964 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 3.806758177820948000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4631912649303564 " " y2[1] (numeric) = 1.4631912649303447 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 8.0429430813932570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4105071233556236 " " Order of pole (three term test) = 22.21454614790777 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41050712335562367 " " Order of pole (three term test) = 22.78545385209223 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y1[1] (analytic) = 0.10915413321942935 " " y1[1] (numeric) = 0.10915413321942515 " " absolute error = 4.2049697057677804000000000000000E-15 " " relative error = 3.852322932485436000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.454305669830318 " " y2[1] (numeric) = 1.4543056698303058 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 8.3974459594189820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4047163282233099 " " Order of pole (three term test) = 22.206393641639963 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4047163282233099 " " Order of pole (three term test) = 22.793606358360037 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y1[1] (analytic) = 0.1046556941605139 " " y1[1] (numeric) = 0.10465569416050963 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 4.084210304172391500000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4453746445418831 " " y2[1] (numeric) = 1.4453746445418707 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.6029583559928260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3987636519558524 " " Order of pole (three term test) = 22.1983585740008 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3987636519558524 " " Order of pole (three term test) = 22.8016414259992 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y1[1] (analytic) = 0.10024678878606452 " " y1[1] (numeric) = 0.10024678878606029 " " absolute error = 4.232725281383409300000000000000E-15 " " relative error = 4.222305105868695000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4363990821601382 " " y2[1] (numeric) = 1.4363990821601258 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 8.6567152751880430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39265147554439056 " " Order of pole (three term test) = 22.190444158910203 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39265147554439056 " " Order of pole (three term test) = 22.8095558410898 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y1[1] (analytic) = 9.59278579829446800E-2 " " y1[1] (numeric) = 9.5927857982940500E-2 " " absolute error = 4.1772141301521515000000000000000E-15 " " relative error = 4.354537063565863700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4273798802338422 " " y2[1] (numeric) = 1.4273798802338296 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 8.8669755374815220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38638224377799396 " " Order of pole (three term test) = 22.18265356202868 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.386382243777994 " " Order of pole (three term test) = 22.81734643797132 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y1[1] (analytic) = 9.16993336406356500E-2 " " y1[1] (numeric) = 9.16993336406314800E-2 " " absolute error = 4.1772141301521515000000000000000E-15 " " relative error = 4.55533749735021030000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4183179406756714 " " y2[1] (numeric) = 1.4183179406756585 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 9.0801834456924350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3799584642657807 " " Order of pole (three term test) = 22.174989899491123 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3799584642657806 " " Order of pole (three term test) = 22.825010100508873 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y1[1] (analytic) = 8.75616386080477800E-2 " " y1[1] (numeric) = 8.75616386080436800E-2 " " absolute error = 4.093947403305265000000000000000E-15 " " relative error = 4.675503414949787000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4092141696720302 " " y2[1] (numeric) = 1.409214169672017 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 9.296409284350149000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3733827064339064 " " Order of pole (three term test) = 22.16745623666036 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37338270643390636 " " Order of pole (three term test) = 22.83254376333964 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y1[1] (analytic) = 8.35151866512363600E-2 " " y1[1] (numeric) = 8.35151866512323200E-2 " " absolute error = 4.038436252074007000000000000000E-15 " " relative error = 4.835571126648763000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.4000694775924325 " " y2[1] (numeric) = 1.4000694775924192 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 9.5157251184502840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3666576004978283 " " Order of pole (three term test) = 22.160055586901077 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36665760049782836 " " Order of pole (three term test) = 22.83994441309893 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y1[1] (analytic) = 7.95603824120250100E-2 " " y1[1] (numeric) = 7.95603824120210400E-2 " " absolute error = 3.969047313034934600000000000000E-15 " " relative error = 4.9887232724450054000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3908847788984657 " " y2[1] (numeric) = 1.3908847788984522 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 9.7382048505512280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3597858364102542 " " Order of pole (three term test) = 22.152790910374495 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35978583641025413 " " Order of pole (three term test) = 22.84720908962551 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y1[1] (analytic) = 7.5697621367542100E-2 " " y1[1] (numeric) = 7.5697621367538100E-2 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 5.2799583612336950000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3816609920523453 " " y2[1] (numeric) = 1.3816609920523315 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 9.9639242799368090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35277016278519624 " " Order of pole (three term test) = 22.145665112854374 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3527701627851963 " " Order of pole (three term test) = 22.854334887145637 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y1[1] (analytic) = 7.19272897906728700E-2 " " y1[1] (numeric) = 7.192728979066899E-2 " " absolute error = 3.8719027983802334000000000000000E-15 " " relative error = 5.383078953271392000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3723990394250694 " " y2[1] (numeric) = 1.3723990394250554 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 1.0192961163931750000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3456133857985637 " " Order of pole (three term test) = 22.138681044564706 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3456133857985638 " " Order of pole (three term test) = 22.861318955435298 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y1[1] (analytic) = 6.82497647114332900E-2 " " y1[1] (numeric) = 6.82497647114294700E-2 " " absolute error = 3.816391647148975600000000000000E-15 " " relative error = 5.591801910651347000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3630998472041824 " " y2[1] (numeric) = 1.3630998472041682 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.0425395281460495000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.33831836806572885 " " Order of pole (three term test) = 22.131841499039687 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3383183680657289 " " Order of pole (three term test) = 22.868158500960313 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y1[1] (analytic) = 6.46654138792666100E-2 " " y1[1] (numeric) = 6.46654138792628800E-2 " " absolute error = 3.733124920302089000000000000000E-15 " " relative error = 5.77298542814866900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3537643453011572 " " y2[1] (numeric) = 1.3537643453011428 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 1.066130849894433000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.33088802749651886 " " Order of pole (three term test) = 22.125149212006345 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33088802749651886 " " Order of pole (three term test) = 22.87485078799365 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y1[1] (analytic) = 6.117459572626915000E-2 " " y1[1] (numeric) = 6.117459572626546000E-2 " " absolute error = 3.698430450782553000000000000000E-15 " " relative error = 6.045696594925595000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3443934672584046 " " y2[1] (numeric) = 1.34439346725839 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 1.0900784838636272000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32332533612809217 " " Order of pole (three term test) = 22.118606860290257 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.32332533612809217 " " Order of pole (three term test) = 22.881393139709743 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y1[1] (analytic) = 5.77776593313471500E-2 " " y1[1] (numeric) = 5.77776593313435100E-2 " " absolute error = 3.642919299551295000000000000000E-15 " " relative error = 6.30506555943992100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3349881501559198 " " y2[1] (numeric) = 1.3349881501559049 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 1.1143910549497792000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31563331893616103 " " Order of pole (three term test) = 22.112217060744875 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.315633318936161 " " Order of pole (three term test) = 22.887782939255125 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y1[1] (analytic) = 5.44749443853093100E-2 " " y1[1] (numeric) = 5.447494438530577000E-2 " " absolute error = 3.5457747848965937000000000000000E-15 " " relative error = 6.509001202124789000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.325549334517575 " " y2[1] (numeric) = 1.32554933451756 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.1390774180726607000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3078150526250436 " " Order of pole (three term test) = 22.105982369204828 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30781505262504366 " " Order of pole (three term test) = 22.894017630795172 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y1[1] (analytic) = 5.12667811568979800E-2 " " y1[1] (numeric) = 5.12667811568945700E-2 " " absolute error = 3.406996906818449000000000000000E-15 " " relative error = 6.645622818393067000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.316077964217069 " " y2[1] (numeric) = 1.3160779642170535 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 1.181018356613754800000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29987366439702207 " " Order of pole (three term test) = 22.099905279463602 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2998736643970221 " " Order of pole (three term test) = 22.90009472053641 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y1[1] (analytic) = 4.81534904597626930E-2 " " y1[1] (numeric) = 4.81534904597593070E-2 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 7.032055605473164000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3065749863835385 " " y2[1] (numeric) = 1.3065749863835228 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 1.2066025382372839000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2918123307015039 " " Order of pole (three term test) = 22.09398822227606 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2918123307015038 " " Order of pole (three term test) = 22.906011777723943 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y1[1] (analytic) = 4.5135383620378500E-2 " " y1[1] (numeric) = 4.51353836203752860E-2 " " absolute error = 3.2127078775090470000000000000000E-15 " " relative error = 7.117936350182074000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2970413513068482 " " y2[1] (numeric) = 1.297041351306832 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.2497100530523159000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28363427596448454 " " Order of pole (three term test) = 22.088233564386186 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2836342759644845 " " Order of pole (three term test) = 22.911766435613803 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y1[1] (analytic) = 4.22127624469145200E-2 " " y1[1] (numeric) = 4.22127624469113670E-2 " " absolute error = 3.1502578323738817000000000000000E-15 " " relative error = 7.462808993691302000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2874780123425604 " " y2[1] (numeric) = 1.2874780123425442 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 1.2589928530146016000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2753427712988191 " " Order of pole (three term test) = 22.082643607580422 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.27534277129881907 " " Order of pole (three term test) = 22.917356392419585 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y1[1] (analytic) = 3.93859191990524300E-2 " " y1[1] (numeric) = 3.938591919904938500E-2 " " absolute error = 3.0461744238152730000000000000000E-15 " " relative error = 7.73417121083354000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2778859258166029 " " y2[1] (numeric) = 1.2778859258165864 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 1.285819057280272000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26694113319582224 " " Order of pole (three term test) = 22.077220587766938 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2669411331958222 " " Order of pole (three term test) = 22.92277941223306 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y1[1] (analytic) = 3.6655136558761403E-2 " " y1[1] (numeric) = 3.66551365587584330E-2 " " absolute error = 2.9698465908722940000000000000000E-15 " " relative error = 8.102129386726928000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2682660509296346 " " y2[1] (numeric) = 1.2682660509296177 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.3305875342111992000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25843272219871466 " " Order of pole (three term test) = 22.071966674081377 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2584327221987146 " " Order of pole (three term test) = 22.928033325918626 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y1[1] (analytic) = 3.4020687602029700E-2 " " y1[1] (numeric) = 3.402068760202689400E-2 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 8.240024922398312000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2586193496611275 " " y2[1] (numeric) = 1.2586193496611104 " " absolute error = 1.70974345792274100000000000000E-14 " " relative error = 1.3584277552884236000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24982094155845133 " " Order of pole (three term test) = 22.066883968019138 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24982094155845128 " " Order of pole (three term test) = 22.933116031980862 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y1[1] (analytic) = 3.14828357715577500E-2 " " y1[1] (numeric) = 3.14828357715550800E-2 " " absolute error = 2.671474153004283000000000000000E-15 " " relative error = 8.485494039954776000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2489467866731698 " " y2[1] (numeric) = 1.2489467866731525 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 1.3867267500072190000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2411092358724661 " " Order of pole (three term test) = 22.061974502594882 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24110923587246613 " " Order of pole (three term test) = 22.938025497405114 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y1[1] (analytic) = 2.904183485041378400E-2 " " y1[1] (numeric) = 2.904183485041116000E-2 " " absolute error = 2.626371342628886000000000000000E-15 " " relative error = 9.043407057978865000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2392493292139997 " " y2[1] (numeric) = 1.2392493292139821 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 1.4154959277003018000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23230108970687863 " " Order of pole (three term test) = 22.05724024152934 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23230108970687857 " " Order of pole (three term test) = 22.942759758470654 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y1[1] (analytic) = 2.66979289366555700E-2 " " y1[1] (numeric) = 2.66979289366530900E-2 " " absolute error = 2.4771851236948805000000000000000E-15 " " relative error = 9.278566624296348000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2295279470212819 " " y2[1] (numeric) = 1.2295279470212641 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.444747021573397000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22340002620271535 " " Order of pole (three term test) = 22.052683078463797 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22340002620271543 " " Order of pole (three term test) = 22.947316921536206 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y1[1] (analytic) = 2.44513524189213800E-2 " " y1[1] (numeric) = 2.445135241891900300E-2 " " absolute error = 2.3765711620882257000000000000000E-15 " " relative error = 9.719589826242678000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2197836122251347 " " y2[1] (numeric) = 1.2197836122251167 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.4744920999650177000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.214409605666698 " " Order of pole (three term test) = 22.04830483620272 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21440960566669803 " " Order of pole (three term test) = 22.951695163797282 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y1[1] (analytic) = 2.23023299529907510E-2 " " y1[1] (numeric) = 2.230232995298852800E-2 " " absolute error = 2.2239154962022667000000000000000E-15 " " relative error = 9.971673367266449000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.2100172992509175 " " y2[1] (numeric) = 1.210017299250899 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.5230941094963543000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2053334241471707 " " Order of pole (three term test) = 22.04410726598464 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2053334241471707 " " Order of pole (three term test) = 22.95589273401536 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y1[1] (analytic) = 2.02510764393194500E-2 " " y1[1] (numeric) = 2.025107643931741100E-2 " " absolute error = 2.0365653607967715000000000000000E-15 " " relative error = 1.005657831028962300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.2002299847217888 " " y2[1] (numeric) = 1.2002299847217703 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.5355142300539654000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19617511199572715 " " Order of pole (three term test) = 22.04009204678168 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19617511199572712 " " Order of pole (three term test) = 22.95990795321832 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y1[1] (analytic) = 1.829779700154954300E-2 " " y1[1] (numeric) = 1.82977970015476500E-2 " " absolute error = 1.8943180357666733000000000000000E-15 " " relative error = 1.035271096081267800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.1904226473610457 " " y2[1] (numeric) = 1.190422647361027 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 1.566817201861055000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1869383324151184 " " Order of pole (three term test) = 22.036260784627988 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18693833241511848 " " Order of pole (three term test) = 22.96373921537202 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y1[1] (analytic) = 1.644268696599704400E-2 " " y1[1] (numeric) = 1.64426869659952900E-2 " " absolute error = 1.7555401576885288000000000000000E-15 " " relative error = 1.067672310078596300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.1805962678942516 " " y2[1] (numeric) = 1.1805962678942328 " " absolute error = 1.88737914186276600000000000000E-14 " " relative error = 1.5986660242702228000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17762677999402146 " " Order of pole (three term test) = 22.032615011977324 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17762677999402152 " " Order of pole (three term test) = 22.96738498802268 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y1[1] (analytic) = 1.468593184211952600E-2 " " y1[1] (numeric) = 1.468593184211796600E-2 " " absolute error = 1.5595164049031496000000000000000E-15 " " relative error = 1.061911781743687100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.1707518289511647 " " y2[1] (numeric) = 1.1707518289511454 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.6500406107231055000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16824417922925244 " " Order of pole (three term test) = 22.029156187090162 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16824417922925247 " " Order of pole (three term test) = 22.970843812909838 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y1[1] (analytic) = 1.302770730396552000E-2 " " y1[1] (numeric) = 1.302770730396411200E-2 " " absolute error = 1.4068607390171906000000000000000E-15 " " relative error = 1.079898946293454500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.160890314967475 " " y2[1] (numeric) = 1.1608903149674556 " " absolute error = 1.931788062847772400000000000000E-14 " " relative error = 1.6640573514491727000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1587942830360175 " " Order of pole (three term test) = 22.025885693450327 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.15879428303601753 " " Order of pole (three term test) = 22.974114306549676 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y1[1] (analytic) = 1.146817917260700700E-2 " " y1[1] (numeric) = 1.146817917260569100E-2 " " absolute error = 1.3149203947904198000000000000000E-15 " " relative error = 1.146581663051838300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.1510127120863636 " " y2[1] (numeric) = 1.151012712086344 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.697628968665692900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14928087124679726 " " Order of pole (three term test) = 22.02280483921167 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14928087124679726 " " Order of pole (three term test) = 22.977195160788327 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y1[1] (analytic) = 1.00075033995573600E-2 " " y1[1] (numeric) = 1.00075033995562390E-2 " " absolute error = 1.1206313654810174000000000000000E-15 " " relative error = 1.119791141445511500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.141120008059887 " " y2[1] (numeric) = 1.1411200080598671 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 1.7318046917717930000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13970774909946304 " " Order of pole (three term test) = 22.019914856674824 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13970774909946304 " " Order of pole (three term test) = 22.980085143325184 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y1[1] (analytic) = 8.645826051176808000E-3 " " y1[1] (numeric) = 8.645826051175834000E-3 " " absolute error = 9.7317987002298880000000000000000E-16 " " relative error = 1.125606580866297300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.131213192150204 " " y2[1] (numeric) = 1.131213192150184 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 1.7666001936617545000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13007874571523442 " " Order of pole (three term test) = 22.01721690179424 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1300787457152344 " " Order of pole (three term test) = 22.98278309820576 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y1[1] (analytic) = 7.383283294065346000E-3 " " y1[1] (numeric) = 7.383283294064588000E-3 " " absolute error = 7.5807415900186470000000000000000E-16 " " relative error = 1.026743968514931300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.12129325503065 " " y2[1] (numeric) = 1.1212932550306298 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.802031623531484000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12039771256707989 " " Order of pole (three term test) = 22.014712053715925 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.12039771256707986 " " Order of pole (three term test) = 22.98528794628408 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y1[1] (analytic) = 6.220001381446738000E-3 " " y1[1] (numeric) = 6.2200013814460940000E-3 " " absolute error = 6.4358240958739540000000000000000E-16 " " relative error = 1.034698177892850700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.1113611886866703 " " y2[1] (numeric) = 1.11136118868665 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 1.8381156244301997000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11066852193917978 " " Order of pole (three term test) = 22.0124013143457 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1106685219391798 " " Order of pole (three term test) = 22.98759868565429 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y1[1] (analytic) = 5.156096640542618000E-3 " " y1[1] (numeric) = 5.156096640542217000E-3 " " absolute error = 4.00721122950642440000000000000000E-16 " " relative error = 7.771792324444704000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.1014179863166227 " " y2[1] (numeric) = 1.101417986316602 " " absolute error = 2.065014825802791200000000000000E-14 " " relative error = 1.8748693515607479000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10089506537806485 " " Order of pole (three term test) = 22.01028560794851 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10089506537806488 " " Order of pole (three term test) = 22.989714392051486 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y1[1] (analytic) = 4.19167546094068030E-3 " " y1[1] (numeric) = 4.191675460940463000E-3 " " absolute error = 2.1770779623508930000000000000000E-16 " " relative error = 5.193813267839016000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.091464642232458 " " y2[1] (numeric) = 1.0914646422324372 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 1.9123104913652000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.10812521360481900E-2 " " Order of pole (three term test) = 22.008365780778714 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.10812521360481700E-2 " " Order of pole (three term test) = 22.991634219221293 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y1[1] (analytic) = 3.3268342839551934000E-3 " " y1[1] (numeric) = 3.3268342839551090000E-3 " " absolute error = 8.41340885848751400000000000000000E-17 " " relative error = 2.5289533954438560000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.0815021517602903 " " y2[1] (numeric) = 1.0815021517602694 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 1.9299261521561137000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.12310076075775200E-2 " " Order of pole (three term test) = 22.006642600741547 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.12310076075775700E-2 " " Order of pole (three term test) = 22.99335739925845 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y1[1] (analytic) = 2.5616595929830455000E-3 " " y1[1] (numeric) = 2.5616595929831576000E-3 " " absolute error = 1.11889664200504060000000000000000E-16 " " relative error = 4.3678584190887304000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.071531511140865 " " y2[1] (numeric) = 1.0715315111408439 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 1.9686063590812028000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.13482717591296100E-2 " " Order of pole (three term test) = 22.005116757086093 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.13482717591296100E-2 " " Order of pole (three term test) = 22.994883242913904 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y1[1] (analytic) = 1.896227904855663000E-3 " " y1[1] (numeric) = 1.8962279048560600000E-3 " " absolute error = 3.9725167599868880000000000000000E-16 " " relative error = 2.094957441462854400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.0615537174299348 " " y2[1] (numeric) = 1.0615537174299137 " " absolute error = 2.109423746787797400000000000000E-14 " " relative error = 1.9871097544595284000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.143699755327570000E-2 " " Order of pole (three term test) = 22.003788860129443 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.14369975532756500E-2 " " Order of pole (three term test) = 22.99621113987055 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y1[1] (analytic) = 1.3306057621875755000E-3 " " y1[1] (numeric) = 1.3306057621881054000E-3 " " absolute error = 5.2995802191091460000000000000000E-16 " " relative error = 3.98283275911596730000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.0515697683985563 " " y2[1] (numeric) = 1.051569768398535 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 2.027091564762815000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.150114936754937000E-2 " " Order of pole (three term test) = 22.00265944101267 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.15011493675493900E-2 " " Order of pole (three term test) = 22.99734055898732 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y1[1] (analytic) = 8.6484972672140610000E-4 " " y1[1] (numeric) = 8.6484972672221060000E-4 " " absolute error = 8.0447801198424430000000000000000E-16 " " relative error = 9.30193982987047400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 1.0415806624333126 " " y2[1] (numeric) = 1.041580662433291 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 2.0678500911692024000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.154470140874884000E-2 " " Order of pole (three term test) = 22.001728951488396 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.154470140874884000E-2 " " Order of pole (three term test) = 22.998271048511608 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y1[1] (analytic) = 4.990063736728389500E-4 " " y1[1] (numeric) = 4.990063736737940000E-4 " " absolute error = 9.5507369374248090000000000000000E-16 " " relative error = 1.91395089147428620000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 1.031587398436476 " " y2[1] (numeric) = 1.0315873984364543 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 2.1094064657666567000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.15716361233068230E-2 " " Order of pole (three term test) = 22.000997763739985 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.157163612330682000E-2 " " Order of pole (three term test) = 22.99900223626001 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y1[1] (analytic) = 2.33112287072123610000E-4 " " y1[1] (numeric) = 2.33112287073291460000E-4 " " absolute error = 1.1678483700927611000000000000000E-15 " " relative error = 5.00981044268780000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 1.0215909757261186 " " y2[1] (numeric) = 1.0215909757260966 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 2.1517825049260647000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.158594260436499700E-2 " " Order of pole (three term test) = 22.0004661702328 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.158594260436500200E-2 " " Order of pole (three term test) = 22.999533829767195 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999999772 " " y1[1] (analytic) = 6.71940561064454700000E-5 " " y1[1] (numeric) = 6.71940561077858600000E-5 " " absolute error = 1.3403991458438290000000000000000E-15 " " relative error = 1.9948180293215756000000000E-9 "%" Correct digits = 12 h = 1.00E-2 " " y2[1] (analytic) = 1.0115923939361808 " " y2[1] (numeric) = 1.0115923939361586 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 2.1950007360280688000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.159161499619010100E-2 " " Order of pole (three term test) = 22.00013438359717 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.159161499619009700E-2 " " Order of pole (three term test) = 22.99986561640283 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999977 " " y1[1] (analytic) = 1.2682724604973217000000E-6 " " y1[1] (numeric) = 1.2682724621095573000000E-6 " " absolute error = 1.6122357355402572000000000000000E-15 " " relative error = 1.2712061372901362000000E-7 "%" Correct digits = 10 h = 1.00E-2 " " y2[1] (analytic) = 1.00159265291651 " " y2[1] (numeric) = 1.0015926529164874 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 2.2612535781291435000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5926508965695288000E-3 " " Order of pole (three term test) = 22.000002536543313 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.5926508965695285000E-3 " " Order of pole (three term test) = 22.999997463456683 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999977 " " y1[1] (analytic) = 3.534152865780626500000E-5 " " y1[1] (numeric) = 3.53415286596890640000E-5 " " absolute error = 1.882798387684015000000000000000E-15 " " relative error = 5.327439019161219000000000E-9 "%" Correct digits = 12 h = 1.00E-2 " " y2[1] (analytic) = 0.9915927526328745 " " y2[1] (numeric) = 0.9915927526328517 " " absolute error = 2.27595720048157100000000000000E-14 " " relative error = 2.2952539683639836000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.406950242174513000E-3 " " Order of pole (three term test) = 22.000070681808293 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.406950242174508000E-3 " " Order of pole (three term test) = 22.999929318191704 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.1599999999999766 " " y1[1] (analytic) = 1.69410417401261170000E-4 " " y1[1] (numeric) = 1.69410417403298040000E-4 " " absolute error = 2.036863516394205000000000000000E-15 " " relative error = 1.2023248319905512000000000E-9 "%" Correct digits = 12 h = 1.00E-2 " " y2[1] (analytic) = 0.9815936930669698 " " y2[1] (numeric) = 0.9815936930669468 " " absolute error = 2.29816166097407400000000000000E-14 " " relative error = 2.34125552884668020000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.840318871291291300E-2 " " Order of pole (three term test) = 22.00033879213491 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.840318871291291600E-2 " " Order of pole (three term test) = 22.999661207865092 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.1699999999999764 " " y1[1] (analytic) = 4.0346153191350710000E-4 " " y1[1] (numeric) = 4.0346153191578620000E-4 " " absolute error = 2.279101386781779000000000000000E-15 " " relative error = 5.648869115161060000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 0.9715964741164197 " " y2[1] (numeric) = 0.9715964741163966 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 2.3767726136721473000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.839206615353869000E-2 " " Order of pole (three term test) = 22.00080676028262 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.839206615353868600E-2 " " Order of pole (three term test) = 22.999193239717385 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999976 " " y1[1] (analytic) = 7.3747146727820570000E-4 " " y1[1] (numeric) = 7.374714672807440000E-4 " " absolute error = 2.538334126223063000000000000000E-15 " " relative error = 3.44194214806888940000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 0.9616020954947886 " " y2[1] (numeric) = 0.9616020954947653 " " absolute error = 2.331468351712828700000000000000E-14 " " relative error = 2.4245666296236396000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.83695871462588770E-2 " " Order of pole (three term test) = 22.001474399070393 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.83695871462588660E-2 " " Order of pole (three term test) = 22.998525600929604 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999976 " " y1[1] (analytic) = 1.1714068227801633000E-3 " " y1[1] (numeric) = 1.1714068227829755000E-3 " " absolute error = 2.8122035949929014000000000000000E-15 " " relative error = 2.40070617679906150000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 0.9516115566316098 " " y2[1] (numeric) = 0.9516115566315864 " " absolute error = 2.342570581959080300000000000000E-14 " " relative error = 2.4616878238122766000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.83317608157081800E-2 " " Order of pole (three term test) = 22.002341441451613 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.833176081570817500E-2 " " Order of pole (three term test) = 22.99765855854838 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999758 " " y1[1] (analytic) = 1.705224205245548000E-3 " " y1[1] (numeric) = 1.7052242052485417000E-3 " " absolute error = 2.993699038666975000000000000000E-15 " " relative error = 1.75560435364327330000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 0.9416258565724442 " " y2[1] (numeric) = 0.9416258565724207 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 2.499583880133448000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.827460242524612000E-2 " " Order of pole (three term test) = 22.003407540620902 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.82746024252461100E-2 " " Order of pole (three term test) = 22.996592459379094 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999999755 " " y1[1] (analytic) = 2.338870233380752000E-3 " " y1[1] (numeric) = 2.338870233384042800E-3 " " absolute error = 3.290770433928003000000000000000E-15 " " relative error = 1.40699145551624440000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 0.9316459938789766 " " y2[1] (numeric) = 0.9316459938789529 " " absolute error = 2.37587727269783500000000000000E-14 " " relative error = 2.550193193882255000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.81941349707982900E-2 " " Order of pole (three term test) = 22.004672270152795 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.8194134970798300E-2 " " Order of pole (three term test) = 22.995327729847197 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999999753 " " y1[1] (analytic) = 3.0722815431111217000E-3 " " y1[1] (numeric) = 3.0722815431147010000E-3 " " absolute error = 3.5796018926781414000000000000000E-15 " " relative error = 1.16512820926342760000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " y2[1] (analytic) = 0.9216729665291595 " " y2[1] (numeric) = 0.9216729665291356 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 2.601879213427563000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.80863907716051300E-2 " " Order of pole (three term test) = 22.006135124172342 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.80863907716051600E-2 " " Order of pole (three term test) = 22.99386487582766 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.229999999999975 " " y1[1] (analytic) = 3.9053847939168884000E-3 " " y1[1] (numeric) = 3.905384793920719000E-3 " " absolute error = 3.830703115825784000000000000000E-15 " " relative error = 9.80877254859129400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.9117077718174171 " " y2[1] (numeric) = 0.911707771817393 " " absolute error = 2.409183963436589700000000000000E-14 " " relative error = 2.642495806122253700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.79474130572415000E-2 " " Order of pole (three term test) = 22.007795517557447 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.79474130572414700E-2 " " Order of pole (three term test) = 22.99220448244255 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999975 " " y1[1] (analytic) = 4.838096676167192000E-3 " " y1[1] (numeric) = 4.838096676171265700E-3 " " absolute error = 4.0739980833315315000000000000000E-15 " " relative error = 8.42066282676891400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.9017514062549166 " " y2[1] (numeric) = 0.9017514062548923 " " absolute error = 2.431388423929092800000000000000E-14 " " relative error = 2.6962956831161980000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.77732575502713800E-2 " " Order of pole (three term test) = 22.00965278617289 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.77732575502713500E-2 " " Order of pole (three term test) = 22.990347213827107 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999747 " " y1[1] (analytic) = 5.8703239194510810000E-3 " " y1[1] (numeric) = 5.870323919455374000E-3 " " absolute error = 4.291705879566621000000000000000E-15 " " relative error = 7.3108501991623100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8918048654699168 " " y2[1] (numeric) = 0.8918048654698923 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 2.7388173677302470000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10755999404390723 " " Order of pole (three term test) = 22.011706187135985 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10755999404390719 " " Order of pole (three term test) = 22.988293812864008 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.2599999999999745 " " y1[1] (analytic) = 7.001963301904279000E-3 " " y1[1] (numeric) = 7.001963301908900000E-3 " " absolute error = 4.621303340002214000000000000000E-15 " " relative error = 6.60001079803629800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8818691441082078 " " y2[1] (numeric) = 0.8818691441081832 " " absolute error = 2.464695114667847500000000000000E-14 " " relative error = 2.794853557508553000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11730370797403963 " " Order of pole (three term test) = 22.01395489911373 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11730370797403966 " " Order of pole (three term test) = 22.986045100886276 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.2699999999999743 " " y1[1] (analytic) = 8.23290166053181100E-3 " " y1[1] (numeric) = 8.232901660536631000E-3 " " absolute error = 4.820796539739547000000000000000E-15 " " relative error = 5.85552547390459600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8719452357336459 " " y2[1] (numeric) = 0.8719452357336211 " " absolute error = 2.47579734491409900000000000000E-14 " " relative error = 2.839395461380081000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12700050198501084 " " Order of pole (three term test) = 22.016398022651323 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1270005019850108 " " Order of pole (three term test) = 22.98360197734868 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999974 " " y1[1] (analytic) = 9.563015902523286000E-3 " " y1[1] (numeric) = 9.56301590252848000E-3 " " absolute error = 5.1937620870745600000000000000000E-15 " " relative error = 5.43109217846656400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8620341327287987 " " y2[1] (numeric) = 0.8620341327287738 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 2.8849200753663710000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13664649748850569 " " Order of pole (three term test) = 22.019034580531898 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13664649748850574 " " Order of pole (three term test) = 22.9809654194681 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999974 " " y1[1] (analytic) = 1.099217301756327800E-2 " " y1[1] (numeric) = 1.099217301756867400E-2 " " absolute error = 5.39499001028787000000000000000E-15 " " relative error = 4.90802865062964600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8521368261957074 " " y2[1] (numeric) = 0.8521368261956824 " " absolute error = 2.498001805406602200000000000000E-14 " " relative error = 2.9314562269990370000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14623783621493416 " " Order of pole (three term test) = 22.02186351816749 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14623783621493416 " " Order of pole (three term test) = 22.978136481832518 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999999736 " " y1[1] (analytic) = 1.252023009113090200E-2 " " y1[1] (numeric) = 1.252023009113667000E-2 " " absolute error = 5.766220834146907000000000000000E-15 " " relative error = 4.60552305522850650000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8422543058567776 " " y2[1] (numeric) = 0.8422543058567525 " " absolute error = 2.509104035652854000000000000000E-14 " " relative error = 2.979033788495132000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15577068175668846 " " Order of pole (three term test) = 22.024883704020734 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.15577068175668846 " " Order of pole (three term test) = 22.975116295979262 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999999734 " " y1[1] (analytic) = 1.414703431879249500E-2 " " y1[1] (numeric) = 1.414703431879848500E-2 " " absolute error = 5.988265439071938000000000000000E-15 " " relative error = 4.232876873082372000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8323875599558079 " " y2[1] (numeric) = 0.8323875599557826 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 3.0410215360255340000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16524122110265482 " " Order of pole (three term test) = 22.028093930057576 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16524122110265482 " " Order of pole (three term test) = 22.971906069942424 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.319999999999973 " " y1[1] (analytic) = 1.58724230214807300E-2 " " y1[1] (numeric) = 1.58724230214870200E-2 " " absolute error = 6.2901073238919030000000000000000E-15 " " relative error = 3.96291562755054450000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8225375751591661 " " y2[1] (numeric) = 0.8225375751591406 " " absolute error = 2.5535129566378600000000000000E-14 " " relative error = 3.104433200080543000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1746456661633671 " " Order of pole (three term test) = 22.031492912230398 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17464566616336707 " " Order of pole (three term test) = 22.9685070877696 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.329999999999973 " " y1[1] (analytic) = 1.769622366176326600E-2 " " y1[1] (numeric) = 1.769622366176982800E-2 " " absolute error = 6.5607241861442840000000000000000E-15 " " relative error = 3.707414819987966000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8127053364571234 " " y2[1] (numeric) = 0.8127053364570979 " " absolute error = 2.5535129566378600000000000000E-14 " " relative error = 3.141991127767841000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18398025528619155 " " Order of pole (three term test) = 22.035079290991654 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18398025528619158 " " Order of pole (three term test) = 22.964920709008357 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999728 " " y1[1] (analytic) = 1.961825386109583600E-2 " " y1[1] (numeric) = 1.961825386110270500E-2 " " absolute error = 6.869504964868156000000000000000E-15 " " relative error = 3.50158837453459200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.8028918270653567 " " y2[1] (numeric) = 0.802891827065331 " " absolute error = 2.564615186884111600000000000000E-14 " " relative error = 3.1942225595420687000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19324125475993917 " " Order of pole (three term test) = 22.038851631837645 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19324125475993914 " " Order of pole (three term test) = 22.961148368162362 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.3499999999999726 " " y1[1] (analytic) = 2.163832141806021300E-2 " " y1[1] (numeric) = 2.16383214180674080E-2 " " absolute error = 7.195632978351796000000000000000E-15 " " relative error = 3.325411818841932400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7930980283266271 " " y2[1] (numeric) = 0.7930980283266014 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 3.2476658939184594000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20242496030829837 " " Order of pole (three term test) = 22.04280842588234 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.20242496030829832 " " Order of pole (three term test) = 22.95719157411766 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.3599999999999723 " " y1[1] (analytic) = 2.375622432758417400E-2 " " y1[1] (numeric) = 2.375622432759162400E-2 " " absolute error = 7.44890260584441000000000000000E-15 " " relative error = 3.13555828701079900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7833249196126473 " " y2[1] (numeric) = 0.7833249196126213 " " absolute error = 2.597921877622866300000000000000E-14 " " relative error = 3.3165316365877057000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2115276985714978 " " Order of pole (three term test) = 22.046948090460884 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21152769857149784 " " Order of pole (three term test) = 22.95305190953912 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999972 " " y1[1] (analytic) = 2.597175080114156000E-2 " " y1[1] (numeric) = 2.597175080114931000E-2 " " absolute error = 7.754213937616328000000000000000E-15 " " relative error = 2.98563389006316070000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7735734782261441 " " y2[1] (numeric) = 0.773573478226118 " " absolute error = 2.60902410786911800000000000000E-14 " " relative error = 3.372690741481708000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22054582857560034 " " Order of pole (three term test) = 22.051268969762614 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22054582857560037 " " Order of pole (three term test) = 22.948731030237383 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999972 " " y1[1] (analytic) = 2.828467928793132500E-2 " " y1[1] (numeric) = 2.828467928793938500E-2 " " absolute error = 8.059525269388246000000000000000E-15 " " relative error = 2.849431378501482000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7638446793031302 " " y2[1] (numeric) = 0.763844679303104 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 3.430182089512962000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22947574318884456 " " Order of pole (three term test) = 22.055769335493455 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22947574318884456 " " Order of pole (three term test) = 22.944230664506552 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999717 " " y1[1] (analytic) = 3.06947784970321700E-2 " " y1[1] (numeric) = 3.06947784970405900E-2 " " absolute error = 8.420347752391422000000000000000E-15 " " relative error = 2.74325086046982600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7541394957153905 " " y2[1] (numeric) = 0.7541394957153642 " " absolute error = 2.63122856836162100000000000000E-14 " " relative error = 3.4890475612414246000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23831387056444903 " " Order of pole (three term test) = 22.060447387567095 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2383138705644491 " " Order of pole (three term test) = 22.939552612432905 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999999715 " " y1[1] (analytic) = 3.32018074205316900E-2 " " y1[1] (numeric) = 3.320180742054043600E-2 " " absolute error = 8.743006318923108000000000000000E-15 " " relative error = 2.633292280804120400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7444588979731963 " " y2[1] (numeric) = 0.7444588979731698 " " absolute error = 2.65343302885412400000000000000E-14 " " relative error = 3.5642438233704327000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24705667556930364 " " Order of pole (three term test) = 22.06530125482509 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24705667556930358 " " Order of pole (three term test) = 22.934698745174913 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999999713 " " y1[1] (analytic) = 3.58055153576266600E-2 " " y1[1] (numeric) = 3.58055153576357530E-2 " " absolute error = 9.089951014118469000000000000000E-15 " " relative error = 2.538701349031773400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7348038541282544 " " y2[1] (numeric) = 0.7348038541282278 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 3.6261857421277230000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2557006611979756 " " Order of pole (three term test) = 22.070328995785246 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2557006611979755 " " Order of pole (three term test) = 22.929671004214757 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.419999999999971 " " y1[1] (analytic) = 3.85056419396931900E-2 " " y1[1] (numeric) = 3.85056419397025800E-2 " " absolute error = 9.38832345198648000000000000000E-15 " " relative error = 2.43816827328584600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7251753296769037 " " y2[1] (numeric) = 0.725175329676877 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 3.674332468380494000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26424236997146494 " " Order of pole (three term test) = 22.075528599418213 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2642423699714649 " " Order of pole (three term test) = 22.924471400581783 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.429999999999971 " " y1[1] (analytic) = 4.13019171563231400E-2 " " y1[1] (numeric) = 4.13019171563328070E-2 " " absolute error = 9.665879208142769000000000000000E-15 " " relative error = 2.340297950712190000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7155742874635656 " " y2[1] (numeric) = 0.7155742874635388 " " absolute error = 2.675637489346627000000000000000E-14 " " relative error = 3.739147054641564500000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2726783853201503 " " Order of pole (three term test) = 22.080897985951875 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2726783853201502 " " Order of pole (three term test) = 22.919102014048125 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999999706 " " y1[1] (analytic) = 4.419406138232495600E-2 " " y1[1] (numeric) = 4.419406138233500E-2 " " absolute error = 1.00405794789537600000000000000E-14 " " relative error = 2.271929568113739000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.7060016875844604 " " y2[1] (numeric) = 0.7060016875844335 " " absolute error = 2.686739719592879000000000000000E-14 " " relative error = 3.805571242733693000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28100533295037106 " " Order of pole (three term test) = 22.086435007703198 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.281005332950371 " " Order of pole (three term test) = 22.913564992296795 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.4499999999999704 " " y1[1] (analytic) = 4.718178540568629400E-2 " " y1[1] (numeric) = 4.71817854056966630E-2 " " absolute error = 1.036670749243739900000000000000E-14 " " relative error = 2.197184231859953500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6964584872915991 " " y2[1] (numeric) = 0.696458487291572 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 3.8895989201308684000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2892198821940995 " " Order of pole (three term test) = 22.092137449937322 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2892198821940995 " " Order of pole (three term test) = 22.907862550062678 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999997 " " y1[1] (analytic) = 5.02647904564945700E-2 " " y1[1] (numeric) = 5.026479045650523000E-2 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 2.120398979008256400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.686945640897058 " " y2[1] (numeric) = 0.6869456408970309 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 3.943462217109155000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29731874734116387 " " Order of pole (three term test) = 22.09800303175337 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.297318747341164 " " Order of pole (three term test) = 22.901996968246632 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.46999999999997 " " y1[1] (analytic) = 5.34427682368137100E-2 " " y1[1] (numeric) = 5.34427682368247700E-2 " " absolute error = 1.106059688282812200000000000000E-14 " " relative error = 2.069615262782944800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6774640996775496 " " y2[1] (numeric) = 0.6774640996775224 " " absolute error = 2.720046410331633500000000000000E-14 " " relative error = 4.015041404594405500000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.305298688953489 " " Order of pole (three term test) = 22.104029406996837 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30529868895348894 " " Order of pole (three term test) = 22.89597059300317 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.47999999999997 " " y1[1] (analytic) = 5.67154009515141700E-2 " " y1[1] (numeric) = 5.671540095152556000E-2 " " absolute error = 1.139366379021566900000000000000E-14 " " relative error = 2.008918847273261400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6680148117792943 " " y2[1] (numeric) = 0.6680148117792671 " " absolute error = 2.720046410331633500000000000000E-14 " " relative error = 4.071835477849121000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3131565151608275 " " Order of pole (three term test) = 22.110214165197956 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3131565151608275 " " Order of pole (three term test) = 22.889785834802044 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999999696 " " y1[1] (analytic) = 6.00823613400516300E-2 " " y1[1] (numeric) = 6.008236134006333000E-2 " " absolute error = 1.169897512198758700000000000000E-14 " " relative error = 1.94715634689758900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6585987221232079 " " y2[1] (numeric) = 0.6585987221231805 " " absolute error = 2.742250870824136700000000000000E-14 " " relative error = 4.1637658542421646000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3208890829374661 " " Order of pole (three term test) = 22.116554832535925 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.320889082937466 " " Order of pole (three term test) = 22.883445167464075 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999999694 " " y1[1] (analytic) = 6.35433127091928900E-2 " " y1[1] (numeric) = 6.35433127092049900E-2 " " absolute error = 1.210143096841420600000000000000E-14 " " relative error = 1.904438162328209700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6492167723104089 " " y2[1] (numeric) = 0.6492167723103814 " " absolute error = 2.742250870824136700000000000000E-14 " " relative error = 4.2239371929118750000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3284932993593939 " " Order of pole (three term test) = 22.123048872828345 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.328493299359394 " " Order of pole (three term test) = 22.876951127171655 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.509999999999969 " " y1[1] (analytic) = 6.70979089666853300E-2 " " y1[1] (numeric) = 6.70979089666977600E-2 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.853187091415261000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6398699005280604 " " y2[1] (numeric) = 0.6398699005280329 " " absolute error = 2.742250870824136700000000000000E-14 " " relative error = 4.285638172011312400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3359661228414305 " " Order of pole (three term test) = 22.12969368854569 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3359661228414306 " " Order of pole (three term test) = 22.870306311454318 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.519999999999969 " " y1[1] (analytic) = 7.07457946558652800E-2 " " y1[1] (numeric) = 7.07457946558780500E-2 " " absolute error = 1.2767564783189300000000000000E-14 " " relative error = 1.804710067262038400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6305590414555517 " " y2[1] (numeric) = 0.6305590414555242 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 4.366527034034247000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3433045643538187 " " Order of pole (three term test) = 22.13648662185026 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3433045643538186 " " Order of pole (three term test) = 22.863513378149737 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999687 " " y1[1] (analytic) = 7.44866049912037400E-2 " " y1[1] (numeric) = 7.44866049912168300E-2 " " absolute error = 1.308675390276903300000000000000E-14 " " relative error = 1.756927155468352000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6212851261710312 " " y2[1] (numeric) = 0.6212851261710035 " " absolute error = 2.764455331316640000000000000000E-14 " " relative error = 4.449575911069894000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3505056886177987 " " Order of pole (three term test) = 22.143424955659313 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3505056886177987 " " Order of pole (three term test) = 22.856575044340687 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999999685 " " y1[1] (analytic) = 7.8319965894784400E-2 " " y1[1] (numeric) = 7.8319965894797890E-2 " " absolute error = 1.348920974919565200000000000000E-14 " " relative error = 1.722320687334970300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6120490820582988 " " y2[1] (numeric) = 0.612049082058271 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 4.5348610804688930000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35756661527967837 " " Order of pole (three term test) = 22.15050591473183 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35756661527967853 " " Order of pole (three term test) = 22.849494085268173 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.5499999999999683 " " y1[1] (analytic) = 8.22454940337115100E-2 " " y1[1] (numeric) = 8.22454940337253400E-2 " " absolute error = 1.383615444439101300000000000000E-14 " " relative error = 1.68229939000910200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.6028518327140692 " " y2[1] (numeric) = 0.6028518327140414 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 4.6040459876636550000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3644845200629376 " " Order of pole (three term test) = 22.157726666778597 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3644845200629376 " " Order of pole (three term test) = 22.842273333221403 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999968 " " y1[1] (analytic) = 8.62627968584422900E-2 " " y1[1] (numeric) = 8.62627968584565500E-2 " " absolute error = 1.425248807862544700000000000000E-14 " " relative error = 1.65221724749011500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5936942978556125 " " y2[1] (numeric) = 0.5936942978555847 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 4.6750618484766243000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37125663589790003 " " Order of pole (three term test) = 22.165084323595067 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3712566358979001 " " Order of pole (three term test) = 22.834915676404933 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999968 " " y1[1] (analytic) = 9.03714726420421500E-2 " " y1[1] (numeric) = 9.03714726420567800E-2 " " absolute error = 1.462718834943643700000000000000E-14 " " relative error = 1.618562575313357600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5845773932287832 " " y2[1] (numeric) = 0.5845773932287555 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 4.747972798319683000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3778802540285264 " " Order of pole (three term test) = 22.17257594221662 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3778802540285264 " " Order of pole (three term test) = 22.827424057783382 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999999677 " " y1[1] (analytic) = 9.4571110520356600E-2 " " y1[1] (numeric) = 9.45711105203715500E-2 " " absolute error = 1.49463774690161700000000000000E-14 " " relative error = 1.580437978022784800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5755020305164468 " " y2[1] (numeric) = 0.5755020305164189 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 4.84213720203286960000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38435272509587737 " " Order of pole (three term test) = 22.180198526095687 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.38435272509587737 " " Order of pole (three term test) = 22.819801473904324 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999999674 " " y1[1] (analytic) = 9.88612905330974500E-2 " " y1[1] (numeric) = 9.88612905331127200E-2 " " absolute error = 1.527944437640371700000000000000E-14 " " relative error = 1.545543689952981200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5664691172473115 " " y2[1] (numeric) = 0.5664691172472837 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 4.9193498938663790000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39067146019782467 " " Order of pole (three term test) = 22.18794902630035 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39067146019782467 " " Order of pole (three term test) = 22.81205097369964 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999999672 " " y1[1] (analytic) = 0.10324158366583847 " " y1[1] (numeric) = 0.10324158366585418 " " absolute error = 1.570965579844596500000000000000E-14 " " relative error = 1.52164033528324500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.557479556705177 " " y2[1] (numeric) = 0.5574795567051491 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 4.9986761994984996000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3968339319245761 " " Order of pole (three term test) = 22.19582434273387 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39683393192457606 " " Order of pole (three term test) = 22.804175657266132 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.609999999999967 " " y1[1] (analytic) = 0.10771155189291681 " " y1[1] (numeric) = 0.10771155189293284 " " absolute error = 1.602884491802569800000000000000E-14 " " relative error = 1.48812681985689280000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5485342478386062 " " y2[1] (numeric) = 0.5485342478385783 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 5.080192900970979000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4028376753696061 " " Order of pole (three term test) = 22.203821325374676 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.402837675369606 " " Order of pole (three term test) = 22.79617867462532 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.619999999999967 " " y1[1] (analytic) = 0.11227074822123462 " " y1[1] (numeric) = 0.112270748221251 " " absolute error = 1.63757896132210600000000000000E-14 " " relative error = 1.458598065183623600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5396340851710313 " " y2[1] (numeric) = 0.5396340851710034 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 5.16398031255928000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40868028911558574 " " Order of pole (three term test) = 22.21193677553634 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40868028911558557 " " Order of pole (three term test) = 22.78806322446366 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999999666 " " y1[1] (analytic) = 0.11691871673495835 " " y1[1] (numeric) = 0.11691871673497511 " " absolute error = 1.676436767183986400000000000000E-14 " " relative error = 1.433848073259545700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5307799587113022 " " y2[1] (numeric) = 0.5307799587112744 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 5.250122477448026000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.414359436194917 " " Order of pole (three term test) = 22.22016744714699 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41435943619491705 " " Order of pole (three term test) = 22.779832552853 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999999664 " " y1[1] (analytic) = 0.1216549926411099 " " y1[1] (numeric) = 0.12165499264112711 " " absolute error = 1.720845688168992600000000000000E-14 " " relative error = 1.414529441669195300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5219727538646868 " " y2[1] (numeric) = 0.5219727538646588 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 5.359977127811293000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41987284502448946 " " Order of pole (three term test) = 22.228510048047738 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41987284502448946 " " Order of pole (three term test) = 22.771489951952262 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999966 " " y1[1] (analytic) = 0.12647910231604564 " " y1[1] (numeric) = 0.12647910231606327 " " absolute error = 1.76247905159243600000000000000E-14 " " relative error = 1.393494276381214400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5132133513443301 " " y2[1] (numeric) = 0.5132133513443021 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 5.4514599332360170000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42521831031428176 " " Order of pole (three term test) = 22.236961241309448 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4252183103142817 " " Order of pole (three term test) = 22.763038758690556 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999966 " " y1[1] (analytic) = 0.13139056335281818 " " y1[1] (numeric) = 0.13139056335283616 " " absolute error = 1.798561299892753600000000000000E-14 " " relative error = 1.368866419320498600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.5045026270831847 " " y2[1] (numeric) = 0.5045026270831569 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 5.523578356609162000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4303936939494503 " " Order of pole (three term test) = 22.245517646567492 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43039369394945043 " " Order of pole (three term test) = 22.754482353432504 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999657 " " y1[1] (analytic) = 0.13638888460941667 " " y1[1] (numeric) = 0.136388884609435 " " absolute error = 1.831867990631508300000000000000E-14 " " relative error = 1.343121175803670000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.49584145214641806 " " y2[1] (numeric) = 0.4958414521463901 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 5.6424528646089010000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4353969258455451 " " Order of pole (three term test) = 22.254175841373865 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43539692584554496 " " Order of pole (three term test) = 22.745824158626135 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999999655 " " y1[1] (analytic) = 0.14147356625788066 " " y1[1] (numeric) = 0.14147356625789934 " " absolute error = 1.86795023893182600000000000000E-14 " " relative error = 1.320352832222304600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.48723069264430596 " " y2[1] (numeric) = 0.487230692644278 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 5.742171140474212000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44022600477651674 " " Order of pole (three term test) = 22.262932362566065 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4402260047765167 " " Order of pole (three term test) = 22.737067637433935 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999999653 " " y1[1] (analytic) = 0.1466440998342825 " " y1[1] (numeric) = 0.1466440998343016 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 1.302189180821611300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.47867120964562304 " " y2[1] (numeric) = 0.4786712096455951 " " absolute error = 2.792210906932268700000000000000E-14 " " relative error = 5.8332543312965070000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4448789991751794 " " Order of pole (three term test) = 22.271783707652386 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4448789991751795 " " Order of pole (three term test) = 22.72821629234761 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.699999999999965 " " y1[1] (analytic) = 0.1518999682895733 " " y1[1] (numeric) = 0.15189996828959287 " " absolute error = 1.956768080901838400000000000000E-14 " " relative error = 1.28819518722450900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.47016385909153635 " " y2[1] (numeric) = 0.4701638590915085 " " absolute error = 2.78665979180914300000000000000E-14 " " relative error = 5.9269970201316700000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4493540479058131 " " Order of pole (three term test) = 22.280726336212805 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44935404790581307 " " Order of pole (three term test) = 22.719273663787202 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.709999999999965 " " y1[1] (analytic) = 0.15724064604128762 " " y1[1] (numeric) = 0.15724064604130752 " " absolute error = 1.99007477164059300000000000000E-14 " " relative error = 1.265623629604045000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.46170949171001197 " " y2[1] (numeric) = 0.46170949170998404 " " absolute error = 2.792210906932268700000000000000E-14 " " relative error = 6.047549286004251000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45364936100859166 " " Order of pole (three term test) = 22.289756671315125 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4536493610085916 " " Order of pole (three term test) = 22.710243328684875 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999647 " " y1[1] (analytic) = 0.16266559902610056 " " y1[1] (numeric) = 0.1626655990261209 " " absolute error = 2.034483692625599400000000000000E-14 " " relative error = 1.250715396990088600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4533089529307426 " " y2[1] (numeric) = 0.45330895293071466 " " absolute error = 2.792210906932268700000000000000E-14 " " relative error = 6.1596200315039170000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45776322041554457 " " Order of pole (three term test) = 22.298871100945714 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45776322041554435 " " Order of pole (three term test) = 22.701128899054282 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999999645 " " y1[1] (analytic) = 0.1681742847532346 " " y1[1] (numeric) = 0.16817428475325535 " " absolute error = 2.076117056049042700000000000000E-14 " " relative error = 1.23450327682104900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4449630828006057 " " y2[1] (numeric) = 0.4449630828005779 " " absolute error = 2.78110867668601700000000000000E-14 " " relative error = 6.2502009361802980000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4616939806377591 " " Order of pole (three term test) = 22.308065979454245 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46169398063775896 " " Order of pole (three term test) = 22.69193402054576 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999999642 " " y1[1] (analytic) = 0.17376615235870763 " " y1[1] (numeric) = 0.1737661523587287 " " absolute error = 2.106648189226234500000000000000E-14 " " relative error = 1.212346685836407600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4366727158996596 " " y2[1] (numeric) = 0.4366727158996318 " " absolute error = 2.78110867668601700000000000000E-14 " " relative error = 6.368862938817251000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46544006942355637 " " Order of pole (three term test) = 22.3173376290119 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46544006942355637 " " Order of pole (three term test) = 22.682662370988105 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999964 " " y1[1] (analytic) = 0.1794406426604187 " " y1[1] (numeric) = 0.17944064266044024 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 1.20030369699957590000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4284386812576857 " " y2[1] (numeric) = 0.42843868125765794 " " absolute error = 2.775557561562891400000000000000E-14 " " relative error = 6.478307592151149000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4689999883873692 " " Order of pole (three term test) = 22.32668234108249 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46899998838736917 " " Order of pole (three term test) = 22.673317658917508 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999964 " " y1[1] (analytic) = 0.1851971882140666 " " y1[1] (numeric) = 0.18519718821408857 " " absolute error = 2.19546603119624700000000000000E-14 " " relative error = 1.18547481868814390000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4202618022712865 " " y2[1] (numeric) = 0.4202618022712588 " " absolute error = 2.770006446439765600000000000000E-14 " " relative error = 6.591144927922040000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47237231360907667 " " Order of pole (three term test) = 22.336096377905765 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4723723136090768 " " Order of pole (three term test) = 22.663903622094235 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.7699999999999636 " " y1[1] (analytic) = 0.19103521336989304 " " y1[1] (numeric) = 0.19103521336991539 " " absolute error = 2.234323837058127500000000000000E-14 " " relative error = 1.169587427178624400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4121428966215467 " " y2[1] (numeric) = 0.412142896621519 " " absolute error = 2.770006446439765600000000000000E-14 " " relative error = 6.72098553474123100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4755556962035541 " " Order of pole (three term test) = 22.345575973992535 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47555569620355426 " " Order of pole (three term test) = 22.65442402600747 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999999634 " " y1[1] (analytic) = 0.19695413433024744 " " y1[1] (numeric) = 0.19695413433027015 " " absolute error = 2.27040608535844500000000000000E-14 " " relative error = 1.152758784718623100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.4040827761922654 " " y2[1] (numeric) = 0.4040827761922377 " " absolute error = 2.770006446439765600000000000000E-14 " " relative error = 6.855047058778316000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47854886286020853 " " Order of pole (three term test) = 22.355117337630755 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47854886286020837 " " Order of pole (three term test) = 22.644882662369245 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.789999999999963 " " y1[1] (analytic) = 0.2029533592079661 " " y1[1] (numeric) = 0.20295335920798924 " " absolute error = 2.314815006343451400000000000000E-14 " " relative error = 1.140565012265435200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.3960822469887688 " " y2[1] (numeric) = 0.39608224698874117 " " absolute error = 2.764455331316640000000000000000E-14 " " relative error = 6.9794982035512120000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4813506163522849 " " Order of pole (three term test) = 22.36471665240217 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4813506163522849 " " Order of pole (three term test) = 22.635283347597827 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.799999999999963 " " y1[1] (analytic) = 0.20903228808556062 " " y1[1] (numeric) = 0.2090322880855842 " " absolute error = 2.356448369766894800000000000000E-14 " " relative error = 1.127313101410610100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.38814210905731017 " " y2[1] (numeric) = 0.38814210905728264 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 7.093672747225291000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4839598360157431 " " Order of pole (three term test) = 22.374370078708875 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.483959836015743 " " Order of pole (three term test) = 22.625629921291125 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999627 " " y1[1] (analytic) = 0.21519031307520908 " " y1[1] (numeric) = 0.21519031307523304 " " absolute error = 2.395306175628775200000000000000E-14 " " relative error = 1.113110595638947300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.380263156405066 " " y2[1] (numeric) = 0.38026315640503855 " " absolute error = 2.747801985947262400000000000000E-14 " " relative error = 7.226053693774722000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4863754781975068 " " Order of pole (three term test) = 22.384073755309046 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48637547819750665 " " Order of pole (three term test) = 22.615926244690947 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999999625 " " y1[1] (analytic) = 0.22142681837954403 " " y1[1] (numeric) = 0.22142681837956846 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 1.103069028426679500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.37244617692073567 " " y2[1] (numeric) = 0.3724461769207083 " " absolute error = 2.73669975570101100000000000000E-14 " " relative error = 7.347906691718944000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48859657667291134 " " Order of pole (three term test) = 22.393823800861433 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4885965766729113 " " Order of pole (three term test) = 22.60617619913856 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999999623 " " y1[1] (analytic) = 0.22774118035323232 " " y1[1] (numeric) = 0.2277411803532571 " " absolute error = 2.47857290247566200000000000000E-14 " " relative error = 1.088328820739109500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.36469195229575346 " " y2[1] (numeric) = 0.3646919522957262 " " absolute error = 2.725597525454759300000000000000E-14 " " relative error = 7.473698030068915000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49062224303218094 " " Order of pole (three term test) = 22.40361631547782 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49062224303218094 " " Order of pole (three term test) = 22.59638368452218 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999962 " " y1[1] (analytic) = 0.2341327675653383 " " y1[1] (numeric) = 0.23413276756536355 " " absolute error = 2.52575738102223100000000000000E-14 " " relative error = 1.078771419860050400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.35700125794612014 " " y2[1] (numeric) = 0.35700125794609294 " " absolute error = 2.720046410331633500000000000000E-14 " " relative error = 7.61915077269042000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4924516670357802 " " Order of pole (three term test) = 22.413447382282907 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4924516670357802 " " Order of pole (three term test) = 22.58655261771709 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999962 " " y1[1] (analytic) = 0.2406009408624673 " " y1[1] (numeric) = 0.2406009408624929 " " absolute error = 2.559064071760986000000000000000E-14 " " relative error = 1.063613493192365200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.34937486293486164 " " y2[1] (numeric) = 0.34937486293483455 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 7.753689424961419000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4940841169385 " " Order of pole (three term test) = 22.423313068981066 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49408411693849996 " " Order of pole (three term test) = 22.576686931018934 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999617 " " y1[1] (analytic) = 0.24714505343267956 " " y1[1] (numeric) = 0.24714505343270554 " " absolute error = 2.597921877622866300000000000000E-14 " " relative error = 1.051172921140629100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.3418135298951238 " " y2[1] (numeric) = 0.34181352989509683 " " absolute error = 2.697841949839130400000000000000E-14 " " relative error = 7.89273014051518000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4955189397821448 " " Order of pole (three term test) = 22.43320942942915 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49551893978214473 " " Order of pole (three term test) = 22.566790570570845 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.8699999999999615 " " y1[1] (analytic) = 0.2537644508701714 " " y1[1] (numeric) = 0.2537644508701979 " " absolute error = 2.647881913730998300000000000000E-14 " " relative error = 1.043440838403990200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.33431801495390967 " " y2[1] (numeric) = 0.33431801495388275 " " absolute error = 2.692290834716004600000000000000E-14 " " relative error = 8.053083334702063000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.496755561656708 " " Order of pole (three term test) = 22.443132505214944 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4967555616567078 " " Order of pole (three term test) = 22.556867494785056 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999999613 " " y1[1] (analytic) = 0.26045847124071553 " " y1[1] (numeric) = 0.26045847124074234 " " absolute error = 2.68118860446975300000000000000E-14 " " relative error = 1.029411173189218600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.32688906765646697 " " y2[1] (numeric) = 0.3268890676564401 " " absolute error = 2.686739719592879000000000000000E-14 " " relative error = 8.219117692906199000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4977934879299274 " " Order of pole (three term test) = 22.45307832724042 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49779348792992734 " " Order of pole (three term test) = 22.54692167275958 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.889999999999961 " " y1[1] (analytic) = 0.2672264451478529 " " y1[1] (numeric) = 0.2672264451478802 " " absolute error = 2.73114864057788500000000000000E-14 " " relative error = 1.022035315055280600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.3195274308913346 " " y2[1] (numeric) = 0.3195274308913079 " " absolute error = 2.670086374223501500000000000000E-14 " " relative error = 8.356360412547956000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4986323034451329 " " Order of pole (three term test) = 22.463042917309384 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49863230344513304 " " Order of pole (three term test) = 22.536957082690616 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.899999999999961 " " y1[1] (analytic) = 0.2740676957998329 " " y1[1] (numeric) = 0.2740676957998606 " " absolute error = 2.770006446439765600000000000000E-14 " " relative error = 1.0107015488840601000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " y2[1] (analytic) = 0.31223384081605465 " " y2[1] (numeric) = 0.312233840816028 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 8.533781130630632000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4992716726873024 " " Order of pole (three term test) = 22.47302228971867 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49927167268730244 " " Order of pole (three term test) = 22.526977710281326 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999999606 " " y1[1] (analytic) = 0.2809815390772914 " " y1[1] (numeric) = 0.2809815390773195 " " absolute error = 2.80886425230164600000000000000E-14 " " relative error = 9.996614943193808000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.30500902678355646 " " y2[1] (numeric) = 0.30500902678353 " " absolute error = 2.647881913730998300000000000000E-14 " " relative error = 8.6813231124796000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49971133991726385 " " Order of pole (three term test) = 22.48301245285237 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49971133991726396 " " Order of pole (three term test) = 22.51698754714762 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999999604 " " y1[1] (analytic) = 0.2879672836016621 " " y1[1] (numeric) = 0.2879672836016906 " " absolute error = 2.847722058163526500000000000000E-14 " " relative error = 9.889047195037296000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.29785371126922267 " " y2[1] (numeric) = 0.29785371126919635 " " absolute error = 2.63122856836162100000000000000E-14 " " relative error = 8.833962676339856000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999511292739876 " " Order of pole (three term test) = 22.493009410778438 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999511292739876 " " Order of pole (three term test) = 22.506990589221562 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.92999999999996 " " y1[1] (analytic) = 0.29502423080431395 " " y1[1] (numeric) = 0.2950242308043429 " " absolute error = 2.897682094271658600000000000000E-14 " " relative error = 9.821844417225705000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.29076860979864205 " " y2[1] (numeric) = 0.29076860979861585 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 9.011035750832296000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999909448449279 " " Order of pole (three term test) = 22.503009164846993 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999909448449278 " " Order of pole (three term test) = 22.496990835153007 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.93999999999996 " " y1[1] (analytic) = 0.3021516749964076 " " y1[1] (numeric) = 0.30215167499643697 " " absolute error = 2.93653990013353900000000000000E-14 " " relative error = 9.718760950666425000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.28375443087605734 " " y2[1] (numeric) = 0.2837544308760313 " " absolute error = 2.60347299274599200000000000000E-14 " " relative error = 9.175091943791276000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49983077070438703 " " Order of pole (three term test) = 22.513007715289717 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49983077070438714 " " Order of pole (three term test) = 22.48699228471028 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999598 " " y1[1] (analytic) = 0.3093489034394632 " " y1[1] (numeric) = 0.309348903439493 " " absolute error = 2.98094882111854530000000000000E-14 " " relative error = 9.636202966860977000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.27681187591351575 " " y2[1] (numeric) = 0.2768118759134898 " " absolute error = 2.592370762499740500000000000000E-14 " " relative error = 9.365099506459303000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4994706709198861 " " Order of pole (three term test) = 22.52300106281977 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49947067091988606 " " Order of pole (three term test) = 22.476998937180234 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.9599999999999596 " " y1[1] (analytic) = 0.31661519641663427 " " y1[1] (numeric) = 0.31661519641666447 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 9.537781702071746000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.269941639160728 " " y2[1] (numeric) = 0.26994163916070224 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.541756600198815000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4989107895265371 " " Order of pole (three term test) = 22.532985210231367 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4989107895265373 " " Order of pole (three term test) = 22.467014789768637 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.9699999999999593 " " y1[1] (analytic) = 0.32394982730467814 " " y1[1] (numeric) = 0.3239498273047088 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 9.458920146555614000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.2631444076356443 " " y2[1] (numeric) = 0.26314440763561864 " " absolute error = 2.564615186884111600000000000000E-14 " " relative error = 9.746037204161814000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4981513504694328 " " Order of pole (three term test) = 22.54295616399866 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49815135046943293 " " Order of pole (three term test) = 22.457043836001333 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999959 " " y1[1] (analytic) = 0.3313520626466183 " " y1[1] (numeric) = 0.3313520626466494 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 9.3816360885785000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.2564208610557527 " " y2[1] (numeric) = 0.2564208610557272 " " absolute error = 2.547961841514734000000000000000E-14 " " relative error = 9.936640221174283000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49719265751407027 " " Order of pole (three term test) = 22.552909935873107 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49719265751407027 " " Order of pole (three term test) = 22.447090064126893 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.989999999999959 " " y1[1] (analytic) = 0.33882116222508907 " " y1[1] (numeric) = 0.3388211622251206 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 9.305892728863229000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.24977167177010828 " " y2[1] (numeric) = 0.249771671770083 " " absolute error = 2.52853293858379400000000000000E-14 " " relative error = 1.012337756585572500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4960350941248491 " " Order of pole (three term test) = 22.56284254447866 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4960350941248491 " " Order of pole (three term test) = 22.437157455521337 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999587 " " y1[1] (analytic) = 0.34635637913635686 " " y1[1] (numeric) = 0.3463563791363887 " " absolute error = 3.18634008067419900000000000000E-14 " " relative error = 9.199599812826806000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.24319750469209878 " " y2[1] (numeric) = 0.24319750469207357 " " absolute error = 2.520206265899105300000000000000E-14 " " relative error = 1.036279656359888600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.494679123311691 " " Order of pole (three term test) = 22.57275001690431 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.494679123311691 " " Order of pole (three term test) = 22.427249983095695 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999959 " " y1[1] (analytic) = 0.3539569598650101 " " y1[1] (numeric) = 0.353956959865042 " " absolute error = 3.19189119579732500000000000000E-14 " " relative error = 9.017738193408117000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.23669901723295306 " " y2[1] (numeric) = 0.2366990172329283 " " absolute error = 2.47579734491409900000000000000E-14 " " relative error = 1.045968578094045400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.493125287444842 " " Order of pole (three term test) = 22.58262839029318 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4931252874448421 " " Order of pole (three term test) = 22.417371609706823 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999959 " " y1[1] (analytic) = 0.36162214435930906 " " y1[1] (numeric) = 0.36162214435934137 " " absolute error = 3.230749001659205500000000000000E-14 " " relative error = 8.934046357650934000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.23027685923600227 " " y2[1] (numeric) = 0.2302768592359777 " " absolute error = 2.45636844198315880000000000000E-14 " " relative error = 1.066702251425844400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4913742080379312 " " Order of pole (three term test) = 22.592473713427633 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4913742080379312 " " Order of pole (three term test) = 22.40752628657237 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999999585 " " y1[1] (analytic) = 0.3693511661071923 " " y1[1] (numeric) = 0.36935116610722507 " " absolute error = 3.27515792264421200000000000000E-14 " " relative error = 8.867327960983619000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.22393167291169402 " " y2[1] (numeric) = 0.2239316729116697 " " absolute error = 2.431388423929092800000000000000E-14 " " relative error = 1.085772455640026800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48942658549937385 " " Order of pole (three term test) = 22.602282048309682 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48942658549937396 " " Order of pole (three term test) = 22.397717951690314 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999958 " " y1[1] (analytic) = 0.3771432522129259 " " y1[1] (numeric) = 0.3771432522129591 " " absolute error = 3.31956684362921800000000000000E-14 " " relative error = 8.801872562087023000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.21766409277337329 " " y2[1] (numeric) = 0.21766409277334908 " " absolute error = 2.420286193682841300000000000000E-14 " " relative error = 1.111936361594921400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4872831988522177 " " Order of pole (three term test) = 22.612049471736153 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4872831988522176 " " Order of pole (three term test) = 22.38795052826385 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999958 " " y1[1] (analytic) = 0.3849976234743926 " " y1[1] (numeric) = 0.38499762347442623 " " absolute error = 3.363975764614224300000000000000E-14 " " relative error = 8.737653324340516000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.21147474557383072 " " y2[1] (numeric) = 0.21147474557380672 " " absolute error = 2.40085729075190100000000000000E-14 " " relative error = 1.135292672530350100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4849449054225433 " " Order of pole (three term test) = 22.62177207686789 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4849449054225434 " " Order of pole (three term test) = 22.37822792313211 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999958 " " y1[1] (analytic) = 0.39291349446101165 " " y1[1] (numeric) = 0.3929134944610457 " " absolute error = 3.40283357047610500000000000000E-14 " " relative error = 8.660515911127007000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.2053642502426285 " " y2[1] (numeric) = 0.20536425024260477 " " absolute error = 2.37310171513627200000000000000E-14 " " relative error = 1.155557363237545300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48241264049654575 " " Order of pole (three term test) = 22.6314459747925 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4824126404965456 " " Order of pole (three term test) = 22.368554025207498 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999958 " " y1[1] (analytic) = 0.4008900735922809 " " y1[1] (numeric) = 0.40089007359231527 " " absolute error = 3.436140261214859500000000000000E-14 " " relative error = 8.571277982576174000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.19933321782420788 " " y2[1] (numeric) = 0.1993332178241843 " " absolute error = 2.356448369766894800000000000000E-14 " " relative error = 1.182165419034698200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47968741694643247 " " Order of pole (three term test) = 22.641067296079783 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47968741694643224 " " Order of pole (three term test) = 22.358932703920217 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999957 " " y1[1] (analytic) = 0.4089265632169342 " " y1[1] (numeric) = 0.408926563216969 " " absolute error = 3.48054918219986600000000000000E-14 " " relative error = 8.511428445291401000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.19338225141678467 " " y2[1] (numeric) = 0.19338225141676135 " " absolute error = 2.331468351712828700000000000000E-14 " " relative error = 1.205626852842849900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4767703248252875 " " Order of pole (three term test) = 22.650632192329493 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47677032482528736 " " Order of pole (three term test) = 22.349367807670504 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999957 " " y1[1] (analytic) = 0.4170221596927063 " " y1[1] (numeric) = 0.41702215969274153 " " absolute error = 3.52495810318487200000000000000E-14 " " relative error = 8.452687755927238000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.18751194611204058 " " y2[1] (numeric) = 0.1875119461120175 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.231528944742813100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4736625309310651 " " Order of pole (three term test) = 22.66013683771068 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47366253093106514 " " Order of pole (three term test) = 22.33986316228932 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999957 " " y1[1] (analytic) = 0.42517605346669596 " " y1[1] (numeric) = 0.42517605346673154 " " absolute error = 3.55826479392362670000000000000E-14 " " relative error = 8.368920979700343000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.18172288893561417 " " y2[1] (numeric) = 0.18172288893559133 " " absolute error = 2.284283873166259600000000000000E-14 " " relative error = 1.2570149454181300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4703652783398866 " " Order of pole (three term test) = 22.669577430491916 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4703652783398867 " " Order of pole (three term test) = 22.33042256950808 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999957 " " y1[1] (analytic) = 0.43338742915632045 " " y1[1] (numeric) = 0.4333874291563565 " " absolute error = 3.60267371490863300000000000000E-14 " " relative error = 8.312824674961138000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.17601565878839887 " " y2[1] (numeric) = 0.17601565878837627 " " absolute error = 2.259303855112193600000000000000E-14 " " relative error = 1.283581171507170200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46687988590882584 " " Order of pole (three term test) = 22.67895019456196 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4668798859088257 " " Order of pole (three term test) = 22.321049805438044 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999957 " " y1[1] (analytic) = 0.4416554656308538 " " y1[1] (numeric) = 0.4416554656308902 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 8.245186132971334000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.17039082638865344 " " y2[1] (numeric) = 0.17039082638863104 " " absolute error = 2.239874952181253300000000000000E-14 " " relative error = 1.314551375595893000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4632077477483835 " " Order of pole (three term test) = 22.688251380940144 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4632077477483835 " " Order of pole (three term test) = 22.31174861905986 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999956 " " y1[1] (analytic) = 0.4499793360935386 " " y1[1] (numeric) = 0.4499793360935753 " " absolute error = 3.67483821150926800000000000000E-14 " " relative error = 8.16668214903399000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.1648489542149304 " " y2[1] (numeric) = 0.16484895421490828 " " absolute error = 2.212119376565624400000000000000E-14 " " relative error = 1.341906830468247200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4593503326648625 " " Order of pole (three term test) = 22.697477269275936 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45935033266486247 " " Order of pole (three term test) = 22.30252273072406 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999956 " " y1[1] (analytic) = 0.45835820816426487 " " y1[1] (numeric) = 0.45835820816430206 " " absolute error = 3.719247132494274400000000000000E-14 " " relative error = 8.114280635204384000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.15939059644982911 " " y2[1] (numeric) = 0.15939059644980713 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 1.379153875899914700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4553091835728652 " " Order of pole (three term test) = 22.70662416933701 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45530918357286515 " " Order of pole (three term test) = 22.29337583066298 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999956 " " y1[1] (analytic) = 0.466791243962808 " " y1[1] (numeric) = 0.4667912439628457 " " absolute error = 3.769207168602406500000000000000E-14 " " relative error = 8.074716947567082000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.15401629892457713 " " y2[1] (numeric) = 0.1540162989245555 " " absolute error = 2.162159340457492400000000000000E-14 " " relative error = 1.40385099210591800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45108591687814703 " " Order of pole (three term test) = 22.715688422485314 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4510859168781471 " " Order of pole (three term test) = 22.284311577514686 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999956 " " y1[1] (analytic) = 0.4752776001926159 " " y1[1] (numeric) = 0.4752776001926539 " " absolute error = 3.80251385934116100000000000000E-14 " " relative error = 8.000616603433689000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.14872659906444874 " " y2[1] (numeric) = 0.14872659906442737 " " absolute error = 2.137179322403426300000000000000E-14 " " relative error = 1.436985270857506200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44668222183107625 " " Order of pole (three term test) = 22.72466640314041 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4466822218310764 " " Order of pole (three term test) = 22.275333596859582 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.1699999999999555 " " y1[1] (analytic) = 0.48381642822513726 " " y1[1] (numeric) = 0.4838164282251756 " " absolute error = 3.83582055007991600000000000000E-14 " " relative error = 7.928256103562838000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.14352202583502183 " " y2[1] (numeric) = 0.14352202583500065 " " absolute error = 2.11775041947248600000000000000E-14 " " relative error = 1.475557780871093700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44209985985095657 " " Order of pole (three term test) = 22.73355452022978 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4420998598509565 " " Order of pole (three term test) = 22.266445479770212 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999955 " " y1[1] (analytic) = 0.49240687418468443 " " y1[1] (numeric) = 0.4924068741847233 " " absolute error = 3.88578058618804800000000000000E-14 " " relative error = 7.891401988694878000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.138403099689282 " " y2[1] (numeric) = 0.13840309968926118 " " absolute error = 2.081668171172168500000000000000E-14 " " relative error = 1.5040618135327600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4373406638214828 " " Order of pole (three term test) = 22.74234921862508 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43734066382148284 " " Order of pole (three term test) = 22.257650781374924 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999955 " " y1[1] (analytic) = 0.5010480790338204 " " y1[1] (numeric) = 0.5010480790338596 " " absolute error = 3.919087276926802600000000000000E-14 " " relative error = 7.821778868974103000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.13337033251557828 " " y2[1] (numeric) = 0.13337033251555774 " " absolute error = 2.053912595556539600000000000000E-14 " " relative error = 1.5400071041411200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43240653735761153 " " Order of pole (three term test) = 22.751046980564194 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43240653735761153 " " Order of pole (three term test) = 22.248953019435803 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999955 " " y1[1] (analytic) = 0.5097391786592611 " " y1[1] (numeric) = 0.5097391786593006 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 7.753757476639958000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.12842422758643401 " " y2[1] (numeric) = 0.12842422758641378 " " absolute error = 2.023381462379347800000000000000E-14 " " relative error = 1.575544973410520000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4272994540441406 " " Order of pole (three term test) = 22.75964432705834 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42729945404414066 " " Order of pole (three term test) = 22.240355672941657 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999955 " " y1[1] (analytic) = 0.5184793039582865 " " y1[1] (numeric) = 0.5184793039583264 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 7.708702851082597000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.12356527950822038 " " y2[1] (numeric) = 0.12356527950820044 " " absolute error = 1.994238107982937400000000000000E-14 " " relative error = 1.613914617374589700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4220214566463021 " " Order of pole (three term test) = 22.768137819283538 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4220214566463022 " " Order of pole (three term test) = 22.23186218071646 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.2199999999999545 " " y1[1] (analytic) = 0.5272675809256502 " " y1[1] (numeric) = 0.5272675809256905 " " absolute error = 4.03010957938931800000000000000E-14 " " relative error = 7.64338587309733000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.11879397417169613 " " y2[1] (numeric) = 0.11879397417167645 " " absolute error = 1.9678703111480900000000000000E-14 " " relative error = 1.656540514676169000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4165746562926833 " " Order of pole (three term test) = 22.77652405995615 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41657465629268325 " " Order of pole (three term test) = 22.223475940043848 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999954 " " y1[1] (analytic) = 0.5361031307409789 " " y1[1] (numeric) = 0.5361031307410196 " " absolute error = 4.06341627012807300000000000000E-14 " " relative error = 7.579542138677295000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.11411078870341873 " " y2[1] (numeric) = 0.11411078870339939 " " absolute error = 1.934563620409335300000000000000E-14 " " relative error = 1.695338050320018800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4109612316308018 " " Order of pole (three term test) = 22.784799694691717 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41096123163080184 " " Order of pole (three term test) = 22.215200305308283 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999954 " " y1[1] (analytic) = 0.5449850698566542 " " y1[1] (numeric) = 0.5449850698566951 " " absolute error = 4.096722960866827600000000000000E-14 " " relative error = 7.517128793903248000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.10951619141803248 " " y2[1] (numeric) = 0.10951619141801343 " " absolute error = 1.90542026601292500000000000000E-14 " " relative error = 1.739852565489404300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40518342795567813 " " Order of pole (three term test) = 22.79296141334668 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4051834279556781 " " Order of pole (three term test) = 22.207038586653315 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999954 " " y1[1] (analytic) = 0.5539125100861659 " " y1[1] (numeric) = 0.5539125100862072 " " absolute error = 4.130029651605582300000000000000E-14 " " relative error = 7.45610466707661100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.10501064177143704 " " y2[1] (numeric) = 0.1050106417714183 " " absolute error = 1.873501354054951700000000000000E-14 " " relative error = 1.784106184335829400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3992435563117455 " " Order of pole (three term test) = 22.801005951342404 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3992435563117458 " " Order of pole (three term test) = 22.19899404865759 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999954 " " y1[1] (analytic) = 0.5628845586929306 " " y1[1] (numeric) = 0.5628845586929724 " " absolute error = 4.174438572590588600000000000000E-14 " " relative error = 7.416154001957376000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.10059459031484252 " " y2[1] (numeric) = 0.10059459031482407 " " absolute error = 1.845745778439322700000000000000E-14 " " relative error = 1.834836021164238400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39314399256846483 " " Order of pole (three term test) = 22.80893009097096 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39314399256846483 " " Order of pole (three term test) = 22.191069909029036 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999953 " " y1[1] (analytic) = 0.5719003184795644 " " y1[1] (numeric) = 0.5719003184796065 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 7.376893065546258000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 9.62684786497144400E-2 " " y2[1] (numeric) = 9.62684786496963300E-2 " " absolute error = 1.811051308919786600000000000000E-14 " " relative error = 1.88125057580844900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3868871764700069 " " Order of pole (three term test) = 22.816730662682136 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.38688717647000687 " " Order of pole (three term test) = 22.183269337317864 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999953 " " y1[1] (analytic) = 0.5809588878776017 " " y1[1] (numeric) = 0.5809588878776442 " " absolute error = 4.24105195406809800000000000000E-14 " " relative error = 7.300089632093926000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 9.20327393836143400E-2 " " y2[1] (numeric) = 9.20327393835965300E-2 " " absolute error = 1.780520175742594800000000000000E-14 " " relative error = 1.93465954362280100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3804756106593878 " " Order of pole (three term test) = 22.824404546351253 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.38047561065938784 " " Order of pole (three term test) = 22.17559545364874 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999953 " " y1[1] (analytic) = 0.5900593610376514 " " y1[1] (numeric) = 0.5900593610376943 " " absolute error = 4.28546087505310400000000000000E-14 " " relative error = 7.262762288046559000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.78877960869389700E-2 " " y2[1] (numeric) = 8.78877960869215200E-2 " " absolute error = 1.745825706223058700000000000000E-14 " " relative error = 1.98642562898730600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3739118596774454 " " Order of pole (three term test) = 22.83194867252718 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3739118596774454 " " Order of pole (three term test) = 22.16805132747282 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999953 " " y1[1] (analytic) = 0.5992008279199814 " " y1[1] (numeric) = 0.5992008279200246 " " absolute error = 4.31876756579185900000000000000E-14 " " relative error = 7.2075460589460270000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.38340632505639700E-2 " " y2[1] (numeric) = 8.38340632505468300E-2 " " absolute error = 1.713906794265085400000000000000E-14 " " relative error = 2.044403823231788200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36719854893705706 " " Order of pole (three term test) = 22.839360023660003 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36719854893705717 " " Order of pole (three term test) = 22.160639976339993 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.3099999999999525 " " y1[1] (analytic) = 0.6083823743855212 " " y1[1] (numeric) = 0.6083823743855648 " " absolute error = 4.352074256530613600000000000000E-14 " " relative error = 7.1535179843536700000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.98719462443947500E-2 " " y2[1] (numeric) = 7.98719462443780300E-2 " " absolute error = 1.67227343084164200000000000000E-14 " " relative error = 2.093693104365788300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36033836367300925 " " Order of pole (three term test) = 22.84663563530811 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36033836367300925 " " Order of pole (three term test) = 22.153364364691885 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999952 " " y1[1] (analytic) = 0.6176030822872753 " " y1[1] (numeric) = 0.6176030822873194 " " absolute error = 4.407585407761871500000000000000E-14 " " relative error = 7.136598786778241000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.6001841276830410E-2 " " y2[1] (numeric) = 7.60018412768139800E-2 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 2.161960879947982500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3533340478679397 " " Order of pole (three term test) = 22.85377259732384 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35333404786793987 " " Order of pole (three term test) = 22.14622740267616 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999952 " " y1[1] (analytic) = 0.6268620295621379 " " y1[1] (numeric) = 0.6268620295621823 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 7.08432141216558100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.22241353551423800E-2 " " y2[1] (numeric) = 7.22241353551263400E-2 " " absolute error = 1.604272270583351200000000000000E-14 " " relative error = 2.221241227319347400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34618840315478094 " " Order of pole (three term test) = 22.860768055017548 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3461884031547809 " " Order of pole (three term test) = 22.139231944982452 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999952 " " y1[1] (analytic) = 0.6361582903230969 " " y1[1] (numeric) = 0.6361582903231416 " " absolute error = 4.47419878923938100000000000000E-14 " " relative error = 7.0331533162398800000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.8539206246774900E-2 " " y2[1] (numeric) = 6.85392062467592200E-2 " " absolute error = 1.568190022283033600000000000000E-14 " " relative error = 2.28801894296350200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3389042876961437 " " Order of pole (three term test) = 22.86761921029942 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3389042876961437 " " Order of pole (three term test) = 22.13238078970058 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999952 " " y1[1] (analytic) = 0.6454909349518232 " " y1[1] (numeric) = 0.6454909349518683 " " absolute error = 4.507505479978135600000000000000E-14 " " relative error = 6.9830655024064080000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.49474224415679300E-2 " " y2[1] (numeric) = 6.49474224415526700E-2 " " absolute error = 1.525168880078808800000000000000E-14 " " relative error = 2.348313178172662400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3314846150410918 " " Order of pole (three term test) = 22.874323322798695 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33148461504109183 " " Order of pole (three term test) = 22.125676677201298 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.3599999999999515 " " y1[1] (analytic) = 0.654859030191631 " " y1[1] (numeric) = 0.6548590301916765 " " absolute error = 4.5408121707168900000000000000E-14 " " relative error = 6.9340300146553900000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.14491431149090100E-2 " " y2[1] (numeric) = 6.144914311489409000E-2 " " absolute error = 1.492556078730444800000000000000E-14 " " relative error = 2.42892903476194380000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3239323529597596 " " Order of pole (three term test) = 22.880877710959773 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3239323529597595 " " Order of pole (three term test) = 22.11912228904023 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999951 " " y1[1] (analytic) = 0.6642616392408032 " " y1[1] (numeric) = 0.664261639240849 " " absolute error = 4.585221091701896500000000000000E-14 " " relative error = 6.902733532742353000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.80447180918154400E-2 " " y2[1] (numeric) = 5.8044718091800910E-2 " " absolute error = 1.453698272868564300000000000000E-14 " " relative error = 2.504445401163112000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31625052225628386 " " Order of pole (three term test) = 22.887279753114754 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3162505222562839 " " Order of pole (three term test) = 22.112720246885242 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999951 " " y1[1] (analytic) = 0.6736978218462704 " " y1[1] (numeric) = 0.6736978218463164 " " absolute error = 4.607425552194399600000000000000E-14 " " relative error = 6.839009126625555000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.47344878119525600E-2 " " y2[1] (numeric) = 5.473448781193843000E-2 " " absolute error = 1.413452688225902400000000000000E-14 " " relative error = 2.58238040535247700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3084421955605229 " " Order of pole (three term test) = 22.893526888532158 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30844219556052305 " " Order of pole (three term test) = 22.10647311146784 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999950 " " y1[1] (analytic) = 0.6831666343976351 " " y1[1] (numeric) = 0.6831666343976817 " " absolute error = 4.65183447317940600000000000000E-14 " " relative error = 6.809223751509825000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.1518783295589900E-2 " " y2[1] (numeric) = 5.15187832955761200E-2 " " absolute error = 1.378064329315975600000000000000E-14 " " relative error = 2.67487747412299700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30051049609904545 " " Order of pole (three term test) = 22.899616618441108 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3005104960990455 " " Order of pole (three term test) = 22.100383381558892 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999950 " " y1[1] (analytic) = 0.6926671300215334 " " y1[1] (numeric) = 0.6926671300215802 " " absolute error = 4.685141163918160600000000000000E-14 " " relative error = 6.7639143837711930000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.8397926110499200E-2 " " y2[1] (numeric) = 4.83979261104858700E-2 " " absolute error = 1.332961518940578600000000000000E-14 " " relative error = 2.75417073842635700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29245859644588174 " " Order of pole (three term test) = 22.90554650703083 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.29245859644588174 " " Order of pole (three term test) = 22.09445349296917 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.40999999999995 " " y1[1] (analytic) = 0.7021983586763194 " " y1[1] (numeric) = 0.7021983586763667 " " absolute error = 4.72955008490316700000000000000E-14 " " relative error = 6.735347678423254000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.53722283397984800E-2 " " y2[1] (numeric) = 4.53722283397854900E-2 " " absolute error = 1.298960938811433200000000000000E-14 " " relative error = 2.862898707736694600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2842897172535355 " " Order of pole (three term test) = 22.91131418242495 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.28428971725353547 " " Order of pole (three term test) = 22.088685817575048 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999995 " " y1[1] (analytic) = 0.7117593672470708 " " y1[1] (numeric) = 0.7117593672471183 " " absolute error = 4.7517545453956700000000000000E-14 " " relative error = 6.676068857055460000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.24419925507432100E-2 " " y2[1] (numeric) = 4.244199255073064500E-2 " " absolute error = 1.25663368599759900000000000000E-14 " " relative error = 2.960826319582382500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27600712596476695 " " Order of pole (three term test) = 22.91691733763022 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2760071259647669 " " Order of pole (three term test) = 22.083082662369776 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.42999999999995 " " y1[1] (analytic) = 0.7213491996408976 " " y1[1] (numeric) = 0.7213491996409455 " " absolute error = 4.78506123613442470000000000000E-14 " " relative error = 6.63348796743175900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.96075117644705270E-2 " " y2[1] (numeric) = 3.96075117644583750E-2 " " absolute error = 1.215000322574155700000000000000E-14 " " relative error = 3.06760073644428700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26761413550565843 " " Order of pole (three term test) = 22.922353731459257 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.26761413550565843 " " Order of pole (three term test) = 22.07764626854074 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.43999999999995 " " y1[1] (analytic) = 0.7309668968825522 " " y1[1] (numeric) = 0.7309668968826003 " " absolute error = 4.80726569662692800000000000000E-14 " " relative error = 6.57658468137078100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.68690694266969900E-2 " " y2[1] (numeric) = 3.686906942668525000E-2 " " absolute error = 1.173366959150712300000000000000E-14 " " relative error = 3.18252393509306840000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25911410296048865 " " Order of pole (three term test) = 22.92762118942702 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2591141029604886 " " Order of pole (three term test) = 22.07237881057298 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.4499999999999496 " " y1[1] (analytic) = 0.740611497210325 " " y1[1] (numeric) = 0.7406114972103734 " " absolute error = 4.840572387365682500000000000000E-14 " " relative error = 6.5359131009966160000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.422693937937426600E-2 " " y2[1] (numeric) = 3.42269393793630300E-2 " " absolute error = 1.123406923042580300000000000000E-14 " " relative error = 3.282230147985607500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25051042822894287 " " Order of pole (three term test) = 22.932717604620553 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2505104282289429 " " Order of pole (three term test) = 22.067282395379447 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999950 " " y1[1] (analytic) = 0.7502820361722203 " " y1[1] (numeric) = 0.7502820361722692 " " absolute error = 4.88498130835068900000000000000E-14 " " relative error = 6.51086001375273000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.168138583330548700E-2 " " y2[1] (numeric) = 3.168138583329467300E-2 " " absolute error = 1.081079670228746200000000000000E-14 " " relative error = 3.41234968671176750000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2418065526662005 " " Order of pole (three term test) = 22.937640938541737 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2418065526662004 " " Order of pole (three term test) = 22.062359061458263 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999950 " " y1[1] (analytic) = 0.7599775467224009 " " y1[1] (numeric) = 0.7599775467224501 " " absolute error = 4.918287999089443500000000000000E-14 " " relative error = 6.471622773989611000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.92326633417239200E-2 " " y2[1] (numeric) = 2.923266334171349400E-2 " " absolute error = 1.042221864366865700000000000000E-14 " " relative error = 3.565264827851992000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23300595770643592 " " Order of pole (three term test) = 22.94238922192263 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23300595770643592 " " Order of pole (three term test) = 22.057610778077375 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999949 " " y1[1] (analytic) = 0.7696970593178912 " " y1[1] (numeric) = 0.7696970593179406 " " absolute error = 4.940492459581946600000000000000E-14 " " relative error = 6.418749298536014000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.688101677483800700E-2 " " y2[1] (numeric) = 2.688101677482806500E-2 " " absolute error = 9.943434964299058000000000000000E-15 " " relative error = 3.699054633084644700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22411216347029334 " " Order of pole (three term test) = 22.946960555513193 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22411216347029336 " " Order of pole (three term test) = 22.053039444486803 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999949 " " y1[1] (analytic) = 0.7794396020155312 " " y1[1] (numeric) = 0.7794396020155809 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 6.381250243712396000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.462668129534484300E-2 " " y2[1] (numeric) = 2.462668129533536500E-2 " " absolute error = 9.478529072737274000000000000000E-15 " " relative error = 3.84888607566013800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21512872735688515 " " Order of pole (three term test) = 22.95135311084095 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2151287273568851 " " Order of pole (three term test) = 22.04864688915904 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999999485 " " y1[1] (analytic) = 0.78920420056917 " " y1[1] (numeric) = 0.7892042005692199 " " absolute error = 4.996003610813204400000000000000E-14 " " relative error = 6.330432107697997000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.24698823349137600E-2 " " y2[1] (numeric) = 2.246988233490474200E-2 " " absolute error = 9.017092628127443000000000000000E-15 " " relative error = 4.012968334113909400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.206059242620879 " " Order of pole (three term test) = 22.955565130942336 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.206059242620879 " " Order of pole (three term test) = 22.04443486905766 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999948 " " y1[1] (analytic) = 0.7989898785270891 " " y1[1] (numeric) = 0.7989898785271394 " " absolute error = 5.02931030155195900000000000000E-14 " " relative error = 6.294585747222885000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.04108355716434700E-2 " " y2[1] (numeric) = 2.041083557163491700E-2 " " absolute error = 8.555656183517613000000000000000E-15 " " relative error = 4.19172265314012140000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19690733693524443 " " Order of pole (three term test) = 22.959594931065467 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19690733693524443 " " Order of pole (three term test) = 22.040405068934536 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999948 " " y1[1] (analytic) = 0.8087956573296478 " " y1[1] (numeric) = 0.8087956573296984 " " absolute error = 5.06261699229071400000000000000E-14 " " relative error = 6.259451254975397000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.844974690849443500E-2 " " y2[1] (numeric) = 1.84497469084863420E-2 " " absolute error = 8.094219738907782000000000000000E-15 " " relative error = 4.387171151481285600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18767667094023174 " " Order of pole (three term test) = 22.96344089934402 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18767667094023172 " " Order of pole (three term test) = 22.03655910065598 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999948 " " y1[1] (analytic) = 0.818620556407137 " " y1[1] (numeric) = 0.8186205564071879 " " absolute error = 5.08482145278321700000000000000E-14 " " relative error = 6.211450974429605000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.658681245269877400E-2 " " y2[1] (numeric) = 1.6586812452691100E-2 " " absolute error = 7.674416657721395000000000000000E-15 " " relative error = 4.626818250707790400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17837093677916532 " " Order of pole (three term test) = 22.967101497441963 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17837093677916535 " " Order of pole (three term test) = 22.032898502558037 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999948 " " y1[1] (analytic) = 0.8284635932778366 " " y1[1] (numeric) = 0.8284635932778877 " " absolute error = 5.1070259132757200000000000000E-14 " " relative error = 6.164454243631451000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.482221849614950800E-2 " " y2[1] (numeric) = 1.48222184961423300E-2 " " absolute error = 7.178285743592028000000000000000E-15 " " relative error = 4.8429226336508200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16899385662163455 " " Order of pole (three term test) = 22.970575261168868 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16899385662163463 " " Order of pole (three term test) = 22.029424738831132 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999947 " " y1[1] (analytic) = 0.8383237836462618 " " y1[1] (numeric) = 0.8383237836463131 " " absolute error = 5.12923037376822300000000000000E-14 " " relative error = 6.118435947813389000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.315614149677191100E-2 " " y2[1] (numeric) = 1.3156141496765200E-2 " " absolute error = 6.711645128554267000000000000000E-15 " " relative error = 5.10153005742685700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15954918117467673 " " Order of pole (three term test) = 22.973860801065562 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1595491811746767 " " Order of pole (three term test) = 22.02613919893444 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999947 " " y1[1] (analytic) = 0.8482001415015926 " " y1[1] (numeric) = 0.8482001415016442 " " absolute error = 5.16253706450697800000000000000E-14 " " relative error = 6.086460980031898000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.158874806087750700E-2 " " y2[1] (numeric) = 1.158874806087125100E-2 " " absolute error = 6.255412854372366000000000000000E-15 " " relative error = 5.397833158087226000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15004068818254288 " " Order of pole (three term test) = 22.976956802959876 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1500406881825429 " " Order of pole (three term test) = 22.02304319704012 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999947 " " y1[1] (analytic) = 0.8580916792162738 " " y1[1] (numeric) = 0.8580916792163258 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 6.055114949944841000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.012019492650362300E-2 " " y2[1] (numeric) = 1.012019492649791900E-2 " " absolute error = 5.703770789011742000000000000000E-15 " " relative error = 5.636028584858800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14047218091565183 " " Order of pole (three term test) = 22.979862028492356 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14047218091565183 " " Order of pole (three term test) = 22.020137971507644 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999947 " " y1[1] (analytic) = 0.867997407644777 " " y1[1] (numeric) = 0.8679974076448291 " " absolute error = 5.21804821573823600000000000000E-14 " " relative error = 6.011594239546039000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.750628947740147000E-3 " " y2[1] (numeric) = 8.750628947734849000E-3 " " absolute error = 5.297845495633169000000000000000E-15 " " relative error = 6.05424538884298100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1308474866493321 " " Order of pole (three term test) = 22.98257531561151 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13084748664933207 " " Order of pole (three term test) = 22.01742468438848 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999947 " " y1[1] (analytic) = 0.8779163362225137 " " y1[1] (numeric) = 0.8779163362225662 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 5.968965902580677000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.480187080043388000E-3 " " y2[1] (numeric) = 7.480187080038616000E-3 " " absolute error = 4.772224282412196300000000000000E-15 " " relative error = 6.37981942342612600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12117045513296247 " " Order of pole (three term test) = 22.985095579038678 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.12117045513296246 " " Order of pole (three term test) = 22.01490442096132 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999946 " " y1[1] (analytic) = 0.8878474730648922 " " y1[1] (numeric) = 0.8878474730649449 " " absolute error = 5.273559366969494000000000000000E-14 " " relative error = 5.939713213087054000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.308996366541586000E-3 " " y2[1] (numeric) = 6.308996366537292000E-3 " " absolute error = 4.294307964780586000000000000000E-15 " " relative error = 6.80664200023086100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11144495705012411 " " Order of pole (three term test) = 22.987421810702084 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11144495705012411 " " Order of pole (three term test) = 22.01257818929792 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999946 " " y1[1] (analytic) = 0.8977898250665041 " " y1[1] (numeric) = 0.897789825066557 " " absolute error = 5.29576382746199700000000000000E-14 " " relative error = 5.898667683240575000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.237173925329963000E-3 " " y2[1] (numeric) = 5.237173925326238000E-3 " " absolute error = 3.724451302922205000000000000000E-15 " " relative error = 7.11156695581300300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10167488247037888 " " Order of pole (three term test) = 22.989553080140073 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10167488247037887 " " Order of pole (three term test) = 22.010446919859927 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999946 " " y1[1] (analytic) = 0.9077423980004344 " " y1[1] (numeric) = 0.9077423980004876 " " absolute error = 5.317968287954500000000000000E-14 " " relative error = 5.8584553279309910000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.264826937759647000E-3 " " y2[1] (numeric) = 4.264826937756393500E-3 " " absolute error = 3.2534738791945017000000000000000E-15 " " relative error = 7.62861876150027700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.18641392932923500E-2 " " Order of pole (three term test) = 22.991488534873298 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.18641392932922900E-2 " " Order of pole (three term test) = 22.008511465126695 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999946 " " y1[1] (analytic) = 0.9177041966176837 " " y1[1] (numeric) = 0.9177041966177371 " " absolute error = 5.34017274844700300000000000000E-14 " " relative error = 5.8190566940076050000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.392052637718912000E-3 " " y2[1] (numeric) = 3.3920526377162286000E-3 " " absolute error = 2.6836172173361206000000000000000E-15 " " relative error = 7.91148459046555400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.20166516853274100E-2 " " Order of pole (three term test) = 22.993227400745667 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.20166516853274100E-2 " " Order of pole (three term test) = 22.006772599254333 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.6399999999999455 " " y1[1] (analytic) = 0.9276742247466915 " " y1[1] (numeric) = 0.9276742247467451 " " absolute error = 5.36237720893950600000000000000E-14 " " relative error = 5.780452949852891000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.6189383019106227000E-3 " " y2[1] (numeric) = 2.6189383019084367000E-3 " " absolute error = 2.186185260599771100000000000000E-15 " " relative error = 8.34760123598505500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.2136358510229100E-2 " " Order of pole (three term test) = 22.99476898223401 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.2136358510229100E-2 " " Order of pole (three term test) = 22.005231017765986 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999945 " " y1[1] (analytic) = 0.9376514853929534 " " y1[1] (numeric) = 0.9376514853930072 " " absolute error = 5.38458166943200900000000000000E-14 " " relative error = 5.742625861863191000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.9455612411239942000E-3 " " y2[1] (numeric) = 1.9455612411223394000E-3 " " absolute error = 1.654926196081874000000000000000E-15 " " relative error = 8.50616347150186000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.22272117535320500E-2 " " Order of pole (three term test) = 22.9961126627263 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.22272117535320400E-2 " " Order of pole (three term test) = 22.003887337273696 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999945 " " y1[1] (analytic) = 0.9476349808387191 " " y1[1] (numeric) = 0.9476349808387732 " " absolute error = 5.406786129924512000000000000000E-14 " " relative error = 5.705557771980042000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.3719887925039975000E-3 " " y2[1] (numeric) = 1.37198879250287000E-3 " " absolute error = 1.1275702593849246000000000000000E-15 " " relative error = 8.21850925857063200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.2293174941818600E-2 " " Order of pole (three term test) = 22.997257904768244 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.22931749418186000E-2 " " Order of pole (three term test) = 22.002742095231753 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999945 " " y1[1] (analytic) = 0.9576237127427635 " " y1[1] (numeric) = 0.9576237127428179 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 5.680825096824417000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.9827831281752420000E-4 " " y2[1] (numeric) = 8.982783128169151000E-4 " " absolute error = 6.0921320071960490000000000000000E-16 " " relative error = 6.78200945104371200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.23382215573614200E-2 " " Order of pole (three term test) = 22.9982042502783 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.23382215573614100E-2 " " Order of pole (three term test) = 22.0017957497217 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999945 " " y1[1] (analytic) = 0.9676166822402202 " " y1[1] (numeric) = 0.9676166822402749 " " absolute error = 5.4622972811557700000000000000E-14 " " relative error = 5.6451044937645070000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.2447717271775220000E-4 " " y2[1] (numeric) = 5.2447717271768590000E-4 " " absolute error = 6.62447527388643200000000000000000E-17 " " relative error = 1.263062649525720800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.23663334487834130E-2 " " Order of pole (three term test) = 22.998951320730878 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.23663334487834200E-2 " " Order of pole (three term test) = 22.00104867926913 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999944 " " y1[1] (analytic) = 0.9776128900424669 " " y1[1] (numeric) = 0.9776128900425217 " " absolute error = 5.48450174164827300000000000000E-14 " " relative error = 5.6100955680013900000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.5062275200726790000E-4 " " y2[1] (numeric) = 2.5062275200769290000E-4 " " absolute error = 4.25007251614317740000000000000000E-16 " " relative error = 1.6958047432261570000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.23814992383713270E-2 " " Order of pole (three term test) = 22.999498817307757 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.238149923837132500E-2 " " Order of pole (three term test) = 22.00050118269225 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999944 " " y1[1] (analytic) = 0.9876113365370535 " " y1[1] (numeric) = 0.9876113365371085 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 5.575782697522907000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.67424358998347600000E-5 " " y2[1] (numeric) = 7.6742435900794790000E-5 " " absolute error = 9.600339186816020000000000000000E-16 " " relative error = 1.25098181654626000000000E-9 "%" Correct digits = 12 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.23877127266798100E-2 " " Order of pole (three term test) = 22.999846521017602 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.238771272667981100E-2 " " Order of pole (three term test) = 22.0001534789824 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999944 " " y1[1] (analytic) = 0.9976110218876625 " " y1[1] (numeric) = 0.9976110218877178 " " absolute error = 5.528910662633280000000000000000E-14 " " relative error = 5.542150739445089000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.853612282138762000000E-6 " " y2[1] (numeric) = 2.8536122837031574000000E-6 " " absolute error = 1.5643953146793343000000000000000E-15 " " relative error = 5.482157910768561000000000E-8 "%" Correct digits = 11 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.388971295064947000E-3 " " Order of pole (three term test) = 22.99999429278358 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.3889712950649467000E-3 " " Order of pole (three term test) = 22.000005707216413 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999944 " " y1[1] (analytic) = 1.0076109461340919 " " y1[1] (numeric) = 1.0076109461341474 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 5.5091850127509890000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.896366997506838500000E-5 " " y2[1] (numeric) = 2.896366997720585000000E-5 " " absolute error = 2.1374673136054928000000000000000E-15 " " relative error = 7.379822085548556000000000E-9 "%" Correct digits = 12 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.610725693215352000E-3 " " Order of pole (three term test) = 22.99994207349895 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.6107256932153490000E-3 " " Order of pole (three term test) = 22.000057926501054 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999944 " " y1[1] (analytic) = 1.0176101092922505 " " y1[1] (numeric) = 1.017610109292306 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 5.455051077456957000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.55069997994639050000E-4 " " y2[1] (numeric) = 1.55069997997291150000E-4 " " absolute error = 2.6520940391711045000000000000000E-15 " " relative error = 1.710256060790554000000000E-9 "%" Correct digits = 12 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.760737849269336000E-2 " " Order of pole (three term test) = 22.99968988405071 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.760737849269336500E-2 " " Order of pole (three term test) = 22.000310115949286 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999943 " " y1[1] (analytic) = 1.0276075114541547 " " y1[1] (numeric) = 1.0276075114542105 " " absolute error = 5.57331958361828600000000000000E-14 " " relative error = 5.4235878207347380000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.8115998581300660000E-4 " " y2[1] (numeric) = 3.8115998581624544000E-4 " " absolute error = 3.2388371498659474000000000000000E-15 " " relative error = 8.4973167971910080000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.75969885755362630E-2 " " Order of pole (three term test) = 22.9992378253113 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.759698857553627000E-2 " " Order of pole (three term test) = 22.000762174688703 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999943 " " y1[1] (analytic) = 1.0376021528879198 " " y1[1] (numeric) = 1.0376021528879757 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 5.392745214085162000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.0721102461990260000E-4 " " y2[1] (numeric) = 7.0721102462369490000E-4 " " absolute error = 3.7923223589197974000000000000000E-15 " " relative error = 5.3623631800112540000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.757556023090391500E-2 " " Order of pole (three term test) = 22.998586078098192 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.7575560230903904E-2 " " Order of pole (three term test) = 22.001413921901808 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999943 " " y1[1] (analytic) = 1.047593034137731 " " y1[1] (numeric) = 1.0475930341377873 " " absolute error = 5.61772850460329200000000000000E-14 " " relative error = 5.362510365704386000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.1331905095831596000E-3 " " y2[1] (numeric) = 1.1331905095874674000E-3 " " absolute error = 4.307752071719406000000000000000E-15 " " relative error = 3.80143677103684740000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.753910216318000000E-2 " " Order of pole (three term test) = 22.997734903101563 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.75391021631799900E-2 " " Order of pole (three term test) = 22.002265096898437 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999943 " " y1[1] (analytic) = 1.0575791561237893 " " y1[1] (numeric) = 1.0575791561238457 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 5.3328707666356880000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.659055843109103000E-3 " " y2[1] (numeric) = 1.6590558431140484000E-3 " " absolute error = 4.94547978957538000000000000000E-15 " " relative error = 2.98090013673527330000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.748362908843697000E-2 " " Order of pole (three term test) = 22.996684640780074 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.74836290884369600E-2 " " Order of pole (three term test) = 22.003315359219933 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.7799999999999425 " " y1[1] (analytic) = 1.0675595202422177 " " y1[1] (numeric) = 1.067559520242274 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 5.283015005866986000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.2847544391028096000E-3 " " y2[1] (numeric) = 2.2847544391083044000E-3 " " absolute error = 5.4947366101565360000000000000000E-15 " " relative error = 2.404957187571650200000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.7405163328496710E-2 " " Order of pole (three term test) = 22.99543571122463 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.7405163328496710E-2 " " Order of pole (three term test) = 22.004564288775367 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999942 " " y1[1] (analytic) = 1.0775331284649212 " " y1[1] (numeric) = 1.0775331284649778 " " absolute error = 5.662137425588298000000000000000E-14 " " relative error = 5.2547223616731960000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.0102237282260136000E-3 " " y2[1] (numeric) = 3.0102237282320490000E-3 " " absolute error = 6.035102972923312000000000000000E-15 " " relative error = 2.00486858047588420000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.72997364019487700E-2 " " Order of pole (three term test) = 22.993988613990435 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.72997364019488200E-2 " " Order of pole (three term test) = 22.006011386009572 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999942 " " y1[1] (analytic) = 1.0874989834393889 " " y1[1] (numeric) = 1.0874989834394457 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 5.226985930693162000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.8353911641542116000E-3 " " y2[1] (numeric) = 3.8353911641609270000E-3 " " absolute error = 6.71511457550622000000000000000E-15 " " relative error = 1.75082913009397070000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.71633906114893400E-2 " " Order of pole (three term test) = 22.99234392789706 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.71633906114893600E-2 " " Order of pole (three term test) = 22.007656072102943 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999942 " " y1[1] (analytic) = 1.0974560885884284 " " y1[1] (numeric) = 1.0974560885884852 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 5.179562030032677000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.7601742308317485000E-3 " " y2[1] (numeric) = 4.7601742308389816000E-3 " " absolute error = 7.232929533085297000000000000000E-15 " " relative error = 1.51946739391122710000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.69921806269482400E-2 " " Order of pole (three term test) = 22.99050231079703 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.69921806269482700E-2 " " Order of pole (three term test) = 22.009497689202966 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999942 " " y1[1] (analytic) = 1.107403448209822 " " y1[1] (numeric) = 1.1074034482098791 " " absolute error = 5.70654634657330500000000000000E-14 " " relative error = 5.1530870305652810000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.784480450722329000E-3 " " y2[1] (numeric) = 5.784480450730194000E-3 " " absolute error = 7.865236240078843000000000000000E-15 " " relative error = 1.35971351395900770000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10678217506336841 " " Order of pole (three term test) = 22.98846449931263 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1067821750633684 " " Order of pole (three term test) = 22.01153550068737 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.8299999999999415 " " y1[1] (analytic) = 1.1173400675758973 " " y1[1] (numeric) = 1.1173400675759546 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 5.127132708571441000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.90820739405773000E-3 " " y2[1] (numeric) = 6.908207394066165000E-3 " " absolute error = 8.434225540199236000000000000000E-15 " " relative error = 1.22089929544589940000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11652945805350656 " " Order of pole (three term test) = 22.986231308541267 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11652945805350659 " " Order of pole (three term test) = 22.013768691458736 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999941 " " y1[1] (analytic) = 1.1272649530329981 " " y1[1] (numeric) = 1.1272649530330554 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 5.08199140907569000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.131242689079943000E-3 " " y2[1] (numeric) = 8.131242689088994000E-3 " " absolute error = 9.05178709764697900000000000000E-15 " " relative error = 1.11321079000671130000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1262301308141285 " " Order of pole (three term test) = 22.9838036317295 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1262301308141285 " " Order of pole (three term test) = 22.01619636827051 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999941 " " y1[1] (analytic) = 1.1371771121008492 " " y1[1] (numeric) = 1.1371771121009067 " " absolute error = 5.75095526755831100000000000000E-14 " " relative error = 5.05722038050331000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 9.453464033278736000E-3 " " y2[1] (numeric) = 9.45346403328837000E-3 " " absolute error = 9.634654185575187000000000000000E-15 " " relative error = 1.01916653532066260000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13588031320547098 " " Order of pole (three term test) = 22.981182439915663 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13588031320547095 " " Order of pole (three term test) = 22.018817560084344 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999940 " " y1[1] (analytic) = 1.1470755535718042 " " y1[1] (numeric) = 1.1470755535718618 " " absolute error = 5.75095526755831100000000000000E-14 " " relative error = 5.013580186283967000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.087473920562143100E-2 " " y2[1] (numeric) = 1.087473920563172100E-2 " " absolute error = 1.02903796594944200000000000000E-14 " " relative error = 9.4626450022590500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14547614528324437 " " Order of pole (three term test) = 22.97836878154153 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14547614528324435 " " Order of pole (three term test) = 22.02163121845847 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999940 " " y1[1] (analytic) = 1.1569592876099646 " " y1[1] (numeric) = 1.1569592876100223 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 4.989941988345114600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.239492607977532600E-2 " " y2[1] (numeric) = 1.239492607978620600E-2 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 8.77793507706320500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15501378884256087 " " Order of pole (three term test) = 22.975363782032957 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.15501378884256084 " " Order of pole (three term test) = 22.02463621796705 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.87999999999994 " " y1[1] (analytic) = 1.166827325850163 " " y1[1] (numeric) = 1.1668273258502209 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 4.966771055280826000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.401387263831977000E-2 " " y2[1] (numeric) = 1.401387263833123000E-2 " " absolute error = 1.145958328230278800000000000000E-14 " " relative error = 8.17731370768099500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16448942895316307 " " Order of pole (three term test) = 22.972168643349665 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1644894289531631 " " Order of pole (three term test) = 22.02783135665034 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.88999999999994 " " y1[1] (analytic) = 1.1766786814967987 " " y1[1] (numeric) = 1.1766786814968566 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 4.9251883965224064000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.573141698794800E-2 " " y2[1] (numeric) = 1.573141698796005000E-2 " " absolute error = 1.205285871108685600000000000000E-14 " " relative error = 7.6616484836176400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17389927548534703 " " Order of pole (three term test) = 22.96878464350453 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17389927548534712 " " Order of pole (three term test) = 22.031215356495466 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999994 " " y1[1] (analytic) = 1.1865123694225164 " " y1[1] (numeric) = 1.1865123694225743 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 4.8843689605730456000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.75473873756563100E-2 " " y2[1] (numeric) = 1.754738737566899400E-2 " " absolute error = 1.268429805634241300000000000000E-14 " " relative error = 7.22859636297736500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18323956462596314 " " Order of pole (three term test) = 22.965213136052373 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18323956462596314 " " Order of pole (three term test) = 22.034786863947627 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.90999999999994 " " y1[1] (analytic) = 1.1963274062667184 " " y1[1] (numeric) = 1.1963274062667764 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 4.84429610003539000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 1.946160220591930400E-2 " " y2[1] (numeric) = 1.946160220593258500E-2 " " absolute error = 1.328104293207843500000000000000E-14 " " relative error = 6.82422895687332700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1925065603838904 " " Order of pole (three term test) = 22.961455549548553 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1925065603838904 " " Order of pole (three term test) = 22.038544450451447 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.9199999999999395 " " y1[1] (analytic) = 1.2061228105338992 " " y1[1] (numeric) = 1.2061228105339574 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 4.823363423879389000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.147387005884904300E-2 " " y2[1] (numeric) = 2.147387005886297600E-2 " " absolute error = 1.393329895904571500000000000000E-14 " " relative error = 6.48848992792709100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20169655608438422 " " Order of pole (three term test) = 22.957513386977578 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2016965560843843 " " Order of pole (three term test) = 22.042486613022422 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999940 " " y1[1] (analytic) = 1.2158976026917951 " " y1[1] (numeric) = 1.2158976026918533 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 4.7845876463253906000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.358398970933717200E-2 " " y2[1] (numeric) = 2.358398970935175800E-2 " " absolute error = 1.458555498601299400000000000000E-14 " " relative error = 6.18451549791781200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2108058758516956 " " Order of pole (three term test) = 22.95338822515191 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21080587585169563 " " Order of pole (three term test) = 22.04661177484809 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999939 " " y1[1] (analytic) = 1.225650805269336 " " y1[1] (numeric) = 1.2256508052693942 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 4.746513953260458000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.57917501471770500E-2 " " y2[1] (numeric) = 2.57917501471923100E-2 " " absolute error = 1.525862769469199500000000000000E-14 " " relative error = 5.91608851963156700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21983087607937402 " " Order of pole (three term test) = 22.94908171408127 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.219830876079374 " " Order of pole (three term test) = 22.050918285918726 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999939 " " y1[1] (analytic) = 1.2353814429543917 " " y1[1] (numeric) = 1.2353814429544498 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 4.709127437695044000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 2.80969305981647600E-2 " " y2[1] (numeric) = 2.809693059818063600E-2 " " absolute error = 1.58761892521397390000000000000E-14 " " relative error = 5.650506626220851000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22876794688765983 " " Order of pole (three term test) = 22.944595576312675 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22876794688765983 " " Order of pole (three term test) = 22.055404423687317 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999939 " " y1[1] (analytic) = 1.2450885426913023 " " y1[1] (numeric) = 1.2450885426913607 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.690247246919043000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.04993005461761100E-2 " " y2[1] (numeric) = 3.049930054619262000E-2 " " absolute error = 1.65110980443472500000000000000E-14 " " relative error = 5.41359891822743700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23761351356738922 " " Order of pole (three term test) = 22.939931606241426 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23761351356738927 " " Order of pole (three term test) = 22.060068393758574 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999385 " " y1[1] (analytic) = 1.2547711337781837 " " y1[1] (numeric) = 1.2547711337782421 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.654054394720135000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.29986197562183170E-2 " " y2[1] (numeric) = 3.299861975623543700E-2 " " absolute error = 1.711825126093913200000000000000E-14 " " relative error = 5.18756583984496500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24636403800982978 " " Order of pole (three term test) = 22.935091669393348 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24636403800982984 " " Order of pole (three term test) = 22.064908330606656 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999938 " " y1[1] (analytic) = 1.2644282479639957 " " y1[1] (numeric) = 1.2644282479640543 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.63606976470186000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.55946382984531100E-2 " " y2[1] (numeric) = 3.55946382984708200E-2 " " absolute error = 1.771499613667515400000000000000E-14 " " relative error = 4.97687207498468230000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2550160201218763 " " Order of pole (three term test) = 22.93007770167867 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2550160201218763 " " Order of pole (three term test) = 22.06992229832134 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999938 " " y1[1] (analytic) = 1.2740589195453675 " " y1[1] (numeric) = 1.2740589195454262 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.601025494262543400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 3.828709657318951600E-2 " " y2[1] (numeric) = 3.82870965732079100E-2 " " absolute error = 1.839500773925806200000000000000E-14 " " relative error = 4.80449273663105100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2635659992260423 " " Order of pole (three term test) = 22.924891708617594 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2635659992260423 " " Order of pole (three term test) = 22.075108291382406 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999938 " " y1[1] (analytic) = 1.2836621854631667 " " y1[1] (numeric) = 1.283662185463225 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.5493068002320536000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.107572533684389300E-2 " " y2[1] (numeric) = 4.10757253368629300E-2 " " absolute error = 1.903338597841752700000000000000E-14 " " relative error = 4.63373094993043400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27201055544468433 " " Order of pole (three term test) = 22.91953576453823 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.27201055544468433 " " Order of pole (three term test) = 22.08046423546177 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.009999999999938 " " y1[1] (analytic) = 1.2932370853988036 " " y1[1] (numeric) = 1.2932370853988622 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.5327942078100336000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.3960245728863700E-2 " " y2[1] (numeric) = 4.39602457288833570E-2 " " absolute error = 1.965788642976917800000000000000E-14 " " relative error = 4.47174170749961900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28034631106790764 " " Order of pole (three term test) = 22.914012011746788 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2803463110679076 " " Order of pole (three term test) = 22.08598798825322 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.019999999999937 " " y1[1] (analytic) = 1.3027826618702643 " " y1[1] (numeric) = 1.3027826618703227 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.482538247127723000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 4.69403692996134270E-2 " " y2[1] (numeric) = 4.694036929963376600E-2 " " absolute error = 2.033789803235208600000000000000E-14 " " relative error = 4.332709421721481000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28856993190460467 " " Order of pole (three term test) = 22.908322659670723 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2885699319046046 " " Order of pole (three term test) = 22.091677340329277 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.029999999999937 " " y1[1] (analytic) = 1.312297960327856 " " y1[1] (numeric) = 1.3122979603279143 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.450035956825958000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.00157980392195200E-2 " " y2[1] (numeric) = 5.00157980392404900E-2 " " absolute error = 2.09762762715115500000000000000E-14 " " relative error = 4.19393013684659400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.296678128616088 " " Order of pole (three term test) = 22.902469983975028 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.29667812861608805 " " Order of pole (three term test) = 22.097530016024976 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.039999999999937 " " y1[1] (analytic) = 1.321782029249662 " " y1[1] (numeric) = 1.3217820292497207 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.434904878642134000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.31862244073708600E-2 " " y2[1] (numeric) = 5.318622440739244000E-2 " " absolute error = 2.157302114724757300000000000000E-14 " " relative error = 4.05612945600587800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30466765803177986 " " Order of pole (three term test) = 22.896456325651933 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3046676580317798 " " Order of pole (three term test) = 22.10354367434807 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.049999999999937 " " y1[1] (analytic) = 1.3312339202366943 " " y1[1] (numeric) = 1.3312339202367527 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.386737011997115500000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.64513313640725400E-2 " " y2[1] (numeric) = 5.64513313640947900E-2 " " absolute error = 2.224609385592657400000000000000E-14 " " relative error = 3.940756279502862000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31253532444644067 " " Order of pole (three term test) = 22.89028409008459 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.31253532444644067 " " Order of pole (three term test) = 22.10971590991541 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.0599999999999365 " " y1[1] (analytic) = 1.3406526881077299 " " y1[1] (numeric) = 1.3406526881077885 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.3724803761776215000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 5.9810792401349900E-2 " " y2[1] (numeric) = 5.9810792401372790E-2 " " absolute error = 2.289834988289385400000000000000E-14 " " relative error = 3.82846455690445800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3202779808984049 " " Order of pole (three term test) = 22.883955746084933 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3202779808984049 " " Order of pole (three term test) = 22.116044253915064 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.069999999999936 " " y1[1] (analytic) = 1.3500373909938312 " " y1[1] (numeric) = 1.3500373909938896 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.3256380515723114000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.32642715758986500E-2 " " y2[1] (numeric) = 6.32642715759222800E-2 " " absolute error = 2.36338726367080200000000000000E-14 " " relative error = 3.735737731264996400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32789253042832595 " " Order of pole (three term test) = 22.877473824906186 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.32789253042832606 " " Order of pole (three term test) = 22.12252617509381 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.079999999999936 " " y1[1] (analytic) = 1.35938709043253 " " y1[1] (numeric) = 1.3593870904325884 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.29588683799419060000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 6.68114235426794400E-2 " " y2[1] (numeric) = 6.68114235427036500E-2 " " absolute error = 2.421673972463622700000000000000E-14 " " relative error = 3.6246405839813400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3353759273179181 " " Order of pole (three term test) = 22.870840919230396 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33537592731791815 " " Order of pole (three term test) = 22.129159080769604 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.089999999999936 " " y1[1] (analytic) = 1.3687008514616736 " " y1[1] (numeric) = 1.368700851461732 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.266654107281271400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.04518935894512500E-2 " " y2[1] (numeric) = 7.0451893589476210E-2 " " absolute error = 2.495226247845039300000000000000E-14 " " relative error = 3.54174475761521500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.342725178308202 " " Order of pole (three term test) = 22.864059682131394 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3427251783082019 " " Order of pole (three term test) = 22.135940317868606 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.099999999999936 " " y1[1] (analytic) = 1.377977742712921 " " y1[1] (numeric) = 1.3779777427129793 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.237929923331819000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.41853176722433400E-2 " " y2[1] (numeric) = 7.41853176722689800E-2 " " absolute error = 2.563227408103330000000000000000E-14 " " relative error = 3.455168069007769600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34993734379677094 " " Order of pole (three term test) = 22.8571328260136 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3499373437967709 " " Order of pole (three term test) = 22.142867173986396 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.1099999999999355 " " y1[1] (analytic) = 1.3872168365048774 " " y1[1] (numeric) = 1.3872168365049358 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.209704608431482000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 7.80113224517585700E-2 " " y2[1] (numeric) = 7.80113224517848600E-2 " " absolute error = 2.62845301080005800000000000000E-14 " " relative error = 3.36932246267901400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35700953901359034 " " Order of pole (three term test) = 22.850063121527107 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3570095390135904 " " Order of pole (three term test) = 22.149936878472893 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.119999999999935 " " y1[1] (analytic) = 1.3964172089358629 " " y1[1] (numeric) = 1.3964172089359213 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.181968735531777000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.1929525330707300E-2 " " y2[1] (numeric) = 8.19295253307342200E-2 " " absolute error = 2.692290834716004600000000000000E-14 " " relative error = 3.2861057400840700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3639389351748679 " " Order of pole (three term test) = 22.842853396459446 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3639389351748679 " " Order of pole (three term test) = 22.157146603540546 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.129999999999935 " " y1[1] (analytic) = 1.4055779399763013 " " y1[1] (numeric) = 1.4055779399763597 " " absolute error = 5.83977310952832300000000000000E-14 " " relative error = 4.154713120801244000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 8.5939534492066700E-2 " " y2[1] (numeric) = 8.59395344920943400E-2 " " absolute error = 2.763067552535858300000000000000E-14 " " relative error = 3.21512976404465400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37072276061452986 " " Order of pole (three term test) = 22.835506534604534 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37072276061452974 " " Order of pole (three term test) = 22.164493465395466 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.139999999999935 " " y1[1] (analytic) = 1.4146981135607228 " " y1[1] (numeric) = 1.414698113560781 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 4.1122332696078157000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 9.00409489382624200E-2 " " y2[1] (numeric) = 9.00409489382907200E-2 " " absolute error = 2.829680934013368000000000000000E-14 " " relative error = 3.14266005343143400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37735830189285036 " " Order of pole (three term test) = 22.82802547460913 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37735830189285036 " " Order of pole (three term test) = 22.171974525390873 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.149999999999935 " " y1[1] (analytic) = 1.4237768176793688 " " y1[1] (numeric) = 1.4237768176794268 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 4.070416175190471000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 9.42333585312676900E-2 " " y2[1] (numeric) = 9.4233358531296600E-2 " " absolute error = 2.890743200367751300000000000000E-14 " " relative error = 3.067643184349171400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3838429048817905 " " Order of pole (three term test) = 22.820413208797497 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.38384290488179057 " " Order of pole (three term test) = 22.179586791202503 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.159999999999934 " " y1[1] (analytic) = 1.4328131444693928 " " y1[1] (numeric) = 1.4328131444694507 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 4.044745269760551000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 9.85163440336167500E-2 " " y2[1] (numeric) = 9.85163440336463100E-2 " " absolute error = 2.95596880306447930000000000000E-14 " " relative error = 3.00048568799489100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39017397582661534 " " Order of pole (three term test) = 22.812672781974467 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39017397582661534 " " Order of pole (three term test) = 22.187327218025533 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.169999999999934 " " y1[1] (analytic) = 1.4418061903056465 " " y1[1] (numeric) = 1.4418061903057042 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 4.004116341619375000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.10288947715032859 " " y2[1] (numeric) = 0.1028894771503588 " " absolute error = 3.02119440576120700000000000000E-14 " " relative error = 2.936349264703750400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39634898238335975 " " Order of pole (three term test) = 22.80480729020756 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39634898238335975 " " Order of pole (three term test) = 22.19519270979244 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.179999999999934 " " y1[1] (analytic) = 1.45075505589104 " " y1[1] (numeric) = 1.4507550558910978 " " absolute error = 5.77315972805081400000000000000E-14 " " relative error = 3.97941727282486950000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.10735232057173572 " " y2[1] (numeric) = 0.10735232057176664 " " absolute error = 3.09197112358106100000000000000E-14 " " relative error = 2.88020892991774900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40236545463173345 " " Order of pole (three term test) = 22.79681987958861 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4023654546317335 " " Order of pole (three term test) = 22.203180120411385 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.189999999999934 " " y1[1] (analytic) = 1.4596588463464726 " " y1[1] (numeric) = 1.45965884634653 " " absolute error = 5.75095526755831100000000000000E-14 " " relative error = 3.939931088660174000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.11190442801721512 " " y2[1] (numeric) = 0.1119044280172467 " " absolute error = 3.158584505058570400000000000000E-14 " " relative error = 2.82257329850491800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40822098606305557 " " Order of pole (three term test) = 22.78871374497537 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4082209860630555 " " Order of pole (three term test) = 22.211286255024625 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.199999999999934 " " y1[1] (analytic) = 1.4685166713003182 " " y1[1] (numeric) = 1.4685166713003757 " " absolute error = 5.75095526755831100000000000000E-14 " " relative error = 3.916166142306065600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.11654534427981555 " " y2[1] (numeric) = 0.11654534427984788 " " absolute error = 3.23213678043998700000000000000E-14 " " relative error = 2.77328691284303800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41391323454282647 " " Order of pole (three term test) = 22.780492128713618 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41391323454282636 " " Order of pole (three term test) = 22.219507871286382 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.209999999999933 " " y1[1] (analytic) = 1.477327644977463 " " y1[1] (numeric) = 1.4773276449775203 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 3.877779466553746000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.12127460527177836 " " y2[1] (numeric) = 0.1212746052718113 " " absolute error = 3.29458682557515200000000000000E-14 " " relative error = 2.716633724094116300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4194399232475496 " " Order of pole (three term test) = 22.772158319340214 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41943992324754964 " " Order of pole (three term test) = 22.227841680659786 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.219999999999933 " " y1[1] (analytic) = 1.4860908862878819 " " y1[1] (numeric) = 1.486090886287939 " " absolute error = 5.70654634657330500000000000000E-14 " " relative error = 3.8399712959869714000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.1260917380709452 " " y2[1] (numeric) = 0.12609173807097884 " " absolute error = 3.363975764614224300000000000000E-14 " " relative error = 2.667879605816434500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4247988415754315 " " Order of pole (three term test) = 22.7637156502678 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4247988415754315 " " Order of pole (three term test) = 22.236284349732195 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.229999999999933 " " y1[1] (analytic) = 1.4948055189147464 " " y1[1] (numeric) = 1.4948055189148033 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.802730063645823300000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.1309962609680505 " " y2[1] (numeric) = 0.1309962609680848 " " absolute error = 3.43058914609173370000000000000E-14 " " relative error = 2.618845088203274300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4299878460305926 " " Order of pole (three term test) = 22.755167498451456 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4299878460305925 " " Order of pole (three term test) = 22.244832501548547 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.239999999999933 " " y1[1] (analytic) = 1.5034706714020558 " " y1[1] (numeric) = 1.5034706714021127 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.780813283693714700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.13598768351489166 " " y2[1] (numeric) = 0.1359876835149266 " " absolute error = 3.4944269700076800000000000000E-14 " " relative error = 2.569664310536634000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43500486108043607 " " Order of pole (three term test) = 22.746517283037903 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.435004861080436 " " Order of pole (three term test) = 22.253482716962097 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.2499999999999325 " " y1[1] (analytic) = 1.5120854772417827 " " y1[1] (numeric) = 1.5120854772418393 " " absolute error = 5.662137425588298000000000000000E-14 " " relative error = 3.744588193464225000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.14106550657337336 " " y2[1] (numeric) = 0.14106550657340905 " " absolute error = 3.56936702416987800000000000000E-14 " " relative error = 2.530290438019530700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4398478799858348 " " Order of pole (three term test) = 22.737768463998 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4398478799858348 " " Order of pole (three term test) = 22.262231536002 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.259999999999932 " " y1[1] (analytic) = 1.520649074960522 " " y1[1] (numeric) = 1.520649074960578 " " absolute error = 5.61772850460329200000000000000E-14 " " relative error = 3.69429646662504050000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.14622922236542146 " " y2[1] (numeric) = 0.1462292223654578 " " absolute error = 3.63320484808582500000000000000E-14 " " relative error = 2.484595615920448300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44451496560379933 " " Order of pole (three term test) = 22.728924540742696 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44451496560379933 " " Order of pole (three term test) = 22.271075459257307 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.269999999999932 " " y1[1] (analytic) = 1.5291606082056375 " " y1[1] (numeric) = 1.5291606082056937 " " absolute error = 5.61772850460329200000000000000E-14 " " relative error = 3.673733468190304400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.1514783145237597 " " y2[1] (numeric) = 0.1514783145237967 " " absolute error = 3.69981822956333400000000000000E-14 " " relative error = 2.442473855875264300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4490042511623095 " " Order of pole (three term test) = 22.719989050723374 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4490042511623097 " " Order of pole (three term test) = 22.280010949276626 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.279999999999932 " " y1[1] (analytic) = 1.5376192258308987 " " y1[1] (numeric) = 1.5376192258309545 " " absolute error = 5.57331958361828600000000000000E-14 " " relative error = 3.6246422326090355000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.1568122581435465 " " y2[1] (numeric) = 0.15681225814358418 " " absolute error = 3.769207168602406500000000000000E-14 " " relative error = 2.403643192965221600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4533139410069985 " " Order of pole (three term test) = 22.710965568016928 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4533139410069985 " " Order of pole (three term test) = 22.289034431983072 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.289999999999932 " " y1[1] (analytic) = 1.546024081981591 " " y1[1] (numeric) = 1.5460240819816466 " " absolute error = 5.57331958361828600000000000000E-14 " " relative error = 3.604937108401814000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.16223051983486492 " " y2[1] (numeric) = 0.1622305198349032 " " absolute error = 3.82749387739522700000000000000E-14 " " relative error = 2.359293356941251000000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45744231131939 " " Order of pole (three term test) = 22.701857701896103 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45744231131938995 " " Order of pole (three term test) = 22.2981422981039 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.299999999999931 " " y1[1] (analytic) = 1.5543743361791038 " " y1[1] (numeric) = 1.5543743361791593 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 3.571285882634485000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.16773255777606078 " " y2[1] (numeric) = 0.16773255777609983 " " absolute error = 3.90520948911898800000000000000E-14 " " relative error = 2.328235818315500200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.461387710806403 " " Order of pole (three term test) = 22.692669095385916 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46138771080640306 " " Order of pole (three term test) = 22.307330904614084 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.309999999999931 " " y1[1] (analytic) = 1.562669153404976 " " y1[1] (numeric) = 1.562669153405031 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.523910477238222000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.17331782176792532 " " y2[1] (numeric) = 0.17331782176796495 " " absolute error = 3.96349619791180900000000000000E-14 " " relative error = 2.28683707046525100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46514856136084765 " " Order of pole (three term test) = 22.683403423806464 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46514856136084765 " " Order of pole (three term test) = 22.316596576193536 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.319999999999931 " " y1[1] (analytic) = 1.5709077041843966 " " y1[1] (numeric) = 1.5709077041844517 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.505429496254089000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.17898575328871347 " " y2[1] (numeric) = 0.17898575328875377 " " absolute error = 4.03010957938931800000000000000E-14 " " relative error = 2.25163707464947700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4687233586926462 " " Order of pole (three term test) = 22.67406439330283 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46872335869264636 " " Order of pole (three term test) = 22.325935606697165 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.329999999999930 " " y1[1] (analytic) = 1.579089164669154 " " y1[1] (numeric) = 1.5790891646692087 " " absolute error = 5.4622972811557700000000000000E-14 " " relative error = 3.4591442987326265000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.18473578554999637 " " y2[1] (numeric) = 0.18473578555003745 " " absolute error = 4.10782519111307900000000000000E-14 " " relative error = 2.223621795248408600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4721106729305292 " " Order of pole (three term test) = 22.66465573936272 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47211067293052916 " " Order of pole (three term test) = 22.33534426063728 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.339999999999930 " " y1[1] (analytic) = 1.5872127167200172 " " y1[1] (numeric) = 1.5872127167200716 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 3.4274503747079630000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.19056734355333982 " " y2[1] (numeric) = 0.19056734355338154 " " absolute error = 4.17166301502902570000000000000E-14 " " relative error = 2.18907549281200800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4753091491939648 " " Order of pole (three term test) = 22.655181225322238 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47530914919396483 " " Order of pole (three term test) = 22.34481877467777 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.34999999999993 " " y1[1] (analytic) = 1.5952775479885504 " " y1[1] (numeric) = 1.5952775479886048 " " absolute error = 5.44009282066326700000000000000E-14 " " relative error = 3.4101231021038053000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.19647984414780295 " " y2[1] (numeric) = 0.19647984414784533 " " absolute error = 4.23827639650653500000000000000E-14 " " relative error = 2.157104925896760300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4783175081350939 " " Order of pole (three term test) = 22.645644640860677 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4783175081350937 " " Order of pole (three term test) = 22.354355359139326 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.35999999999993 " " y1[1] (analytic) = 1.603282851998348 " " y1[1] (numeric) = 1.603282851998402 " " absolute error = 5.39568389967826100000000000000E-14 " " relative error = 3.3653973738651455000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.20247269608825336 " " y2[1] (numeric) = 0.20247269608829643 " " absolute error = 4.307665335545607400000000000000E-14 " " relative error = 2.12752900453698300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48113454645045045 " " Order of pole (three term test) = 22.636049800484674 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48113454645045034 " " Order of pole (three term test) = 22.363950199515326 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.36999999999993 " " y1[1] (analytic) = 1.6112278282256796 " " y1[1] (numeric) = 1.6112278282257333 " " absolute error = 5.373479439185758000000000000000E-14 " " relative error = 3.3350214941999570000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.20854530009449113 " " y2[1] (numeric) = 0.20854530009453484 " " absolute error = 4.37150315946155400000000000000E-14 " " relative error = 2.09618876928937800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48375913736226883 " " Order of pole (three term test) = 22.62640054200245 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48375913736226867 " " Order of pole (three term test) = 22.373599457997546 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.37999999999993 " " y1[1] (analytic) = 1.6191116821795437 " " y1[1] (numeric) = 1.619111682179597 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.291354498182053000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.21469704891117602 " " y2[1] (numeric) = 0.2146970489112204 " " absolute error = 4.43811654093906300000000000000E-14 " " relative error = 2.067153024900305300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48619023106917786 " " Order of pole (three term test) = 22.616700724988746 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48619023106917775 " " Order of pole (three term test) = 22.38329927501125 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.3899999999999295 " " y1[1] (analytic) = 1.6269336254811142 " " y1[1] (numeric) = 1.6269336254811675 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.2755303810411120000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.2209273273685528 " " y2[1] (numeric) = 0.2209273273685979 " " absolute error = 4.510281037539698400000000000000E-14 " " relative error = 2.041522473141410300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48842685516610934 " " Order of pole (three term test) = 22.606954229241044 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4884268551661093 " " Order of pole (three term test) = 22.39304577075896 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.399999999999930 " " y1[1] (analytic) = 1.6346928759425796 " " y1[1] (numeric) = 1.6346928759426327 " " absolute error = 5.30686605770824800000000000000E-14 " " relative error = 3.2463994526484113000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.22723551244396778 " " y2[1] (numeric) = 0.2272355124440135 " " absolute error = 4.57134330389408200000000000000E-14 " " relative error = 2.011720463376644500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49046811503324544 " " Order of pole (three term test) = 22.59716495322766 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49046811503324556 " " Order of pole (three term test) = 22.40283504677233 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.409999999999929 " " y1[1] (analytic) = 1.64238865764536 " " y1[1] (numeric) = 1.6423886576454125 " " absolute error = 5.26245713672324200000000000000E-14 " " relative error = 3.2041484895955497000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.23362097332416998 " " y2[1] (numeric) = 0.2336209733242164 " " absolute error = 4.64350780049471700000000000000E-14 " " relative error = 1.987624541762111300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49231319419385616 " " Order of pole (three term test) = 22.58733681252852 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4923131941938562 " " Order of pole (three term test) = 22.412663187471477 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.419999999999929 " " y1[1] (analytic) = 1.6500202010176976 " " y1[1] (numeric) = 1.65002020101775 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 3.175871830537990700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.2400830714683928 " " y2[1] (numeric) = 0.24008307146843985 " " absolute error = 4.70457006684910100000000000000E-14 " " relative error = 1.959559263414564800000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4939613546408777 " " Order of pole (three term test) = 22.577473738268846 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49396135464087765 " " Order of pole (three term test) = 22.422526261731157 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.429999999999929 " " y1[1] (analytic) = 1.6575867429116156 " " y1[1] (numeric) = 1.6575867429116675 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 3.1345833196753436000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.24662116067220674 " " y2[1] (numeric) = 0.24662116067225445 " " absolute error = 4.7711834483266100000000000000E-14 " " relative error = 1.93462046619274700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4954119371321064 " " Order of pole (three term test) = 22.567579675546828 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4954119371321065 " " Order of pole (three term test) = 22.432420324453176 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.4399999999999284 " " y1[1] (analytic) = 1.665087526679229 " " y1[1] (numeric) = 1.6650875266792808 " " absolute error = 5.173639294753230000000000000000E-14 " " relative error = 3.1071275304495780000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.25323458713213987 " " y2[1] (numeric) = 0.2532345871321882 " " absolute error = 4.83502127224255700000000000000E-14 " " relative error = 1.9093052520979700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49666436145388676 " " Order of pole (three term test) = 22.557658581855637 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4966643614538867 " " Order of pole (three term test) = 22.442341418144366 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.449999999999928 " " y1[1] (analytic) = 1.6725218022484127 " " y1[1] (numeric) = 1.672521802248464 " " absolute error = 5.12923037376822300000000000000E-14 " " relative error = 3.0667644313352870000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.25992268951105724 " " y2[1] (numeric) = 0.2599226895111063 " " absolute error = 4.90718576884319200000000000000E-14 " " relative error = 1.8879405172646300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4977181266531887 " " Order of pole (three term test) = 22.547714425500484 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49771812665318865 " " Order of pole (three term test) = 22.452285574499523 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.459999999999928 " " y1[1] (analytic) = 1.6798888261978044 " " y1[1] (numeric) = 1.6798888261978553 " " absolute error = 5.08482145278321700000000000000E-14 " " relative error = 3.026879739590866400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.26668479900429454 " " y2[1] (numeric) = 0.2666847990043443 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 1.865047865079331200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4985728112379824 " " Order of pole (three term test) = 22.5377511840113 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49857281123798247 " " Order of pole (three term test) = 22.462248815988698 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.469999999999928 " " y1[1] (analytic) = 1.6871878618311484 " " y1[1] (numeric) = 1.6871878618311988 " " absolute error = 5.04041253179821100000000000000E-14 " " relative error = 2.9874637234099827000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.27352023940653747 " " y2[1] (numeric) = 0.2735202394065878 " " absolute error = 5.03486141667508500000000000000E-14 " " relative error = 1.840763750280172400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4992280733458299 " " Order of pole (three term test) = 22.527772842551858 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49922807334583 " " Order of pole (three term test) = 22.472227157448135 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.479999999999928 " " y1[1] (analytic) = 1.6944181792509638 " " y1[1] (numeric) = 1.694418179251014 " " absolute error = 5.018208071305708000000000000000E-14 " " relative error = 2.961611326387009000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.280428327179442 " " y2[1] (numeric) = 0.28042832717949295 " " absolute error = 5.095923683029469000000000000000E-14 " " relative error = 1.8171929113882500000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49968365088062466 " " Order of pole (three term test) = 22.5177833923257 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4996836508806247 " " Order of pole (three term test) = 22.482216607674296 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.489999999999927 " " y1[1] (analytic) = 1.7015790554315342 " " y1[1] (numeric) = 1.701579055431584 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 2.92304911396509000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.28740837151998744 " " y2[1] (numeric) = 0.28740837152003906 " " absolute error = 5.16253706450697800000000000000E-14 " " relative error = 1.796237540752342300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999393616174271 " " Order of pole (three term test) = 22.507786828979725 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999393616174271 " " Order of pole (three term test) = 22.492213171020275 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 5.499999999999927 " " y1[1] (analytic) = 1.7086697742912085 " " y1[1] (numeric) = 1.708669774291258 " " absolute error = 4.95159468982819800000000000000E-14 " " relative error = 2.8979237324439840000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y2[1] (analytic) = 0.29445967442955645 " " y2[1] (numeric) = 0.2944596744296088 " " absolute error = 5.23470156110761300000000000000E-14 " " relative error = 1.777731219478037600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999951032753517 " " Order of pole (three term test) = 22.497787151005976 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999951032753518 " " Order of pole (three term test) = 22.50221284899402 " " "NO COMPLEX POLE (six term test) for Equation 2" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y1 , x , 1 ) = m1 * y2 + 1.0 ; " "diff ( y2 , x , 1 ) = y1 - 1.0 ; " Iterations = 541 "Total Elapsed Time "= 10 Minutes 1 Seconds "Elapsed Time(since restart) "= 9 Minutes 45 Seconds "Expected Time Remaining "= 8 Minutes 17 Seconds "Optimized Time Remaining "= 8 Minutes 3 Seconds "Expected Total Time "= 18 Minutes 4 Seconds "Time to Timeout "= 0.0 Seconds Percent Done = 54.74747474747401 "%" (%o233) true (%o233) diffeq.max