(%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_y2_init,MAX_TERMS) (%o150) array_y2_init (%i151) array(array_y1_init,MAX_TERMS) (%o151) array_y1_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_y2,MAX_TERMS) (%o159) array_y2 (%i160) array(array_x,MAX_TERMS) (%o160) array_x (%i161) array(array_y1,MAX_TERMS) (%o161) array_y1 (%i162) array(array_tmp0,MAX_TERMS) (%o162) array_tmp0 (%i163) array(array_tmp1_g,MAX_TERMS) (%o163) array_tmp1_g (%i164) array(array_tmp1,MAX_TERMS) (%o164) array_tmp1 (%i165) array(array_tmp2,MAX_TERMS) (%o165) array_tmp2 (%i166) array(array_tmp3,MAX_TERMS) (%o166) array_tmp3 (%i167) array(array_tmp4,MAX_TERMS) (%o167) array_tmp4 (%i168) array(array_tmp5,MAX_TERMS) (%o168) array_tmp5 (%i169) array(array_m1,MAX_TERMS) (%o169) array_m1 (%i170) array(array_y2_higher,4,MAX_TERMS) (%o170) array_y2_higher (%i171) array(array_y2_higher_work,4,MAX_TERMS) (%o171) array_y2_higher_work (%i172) array(array_y2_higher_work2,4,MAX_TERMS) (%o172) array_y2_higher_work2 (%i173) array(array_y2_set_initial,3,MAX_TERMS) (%o173) array_y2_set_initial (%i174) array(array_y1_higher,2,MAX_TERMS) (%o174) array_y1_higher (%i175) array(array_y1_higher_work,2,MAX_TERMS) (%o175) array_y1_higher_work (%i176) array(array_y1_higher_work2,2,MAX_TERMS) (%o176) array_y1_higher_work2 (%i177) array(array_y1_set_initial,3,MAX_TERMS) (%o177) array_y1_set_initial (%i178) array(array_given_rad_poles,3,3) (%o178) array_given_rad_poles (%i179) array(array_given_ord_poles,3,3) (%o179) array_given_ord_poles (%i180) array(array_rad_test_poles,3,3) (%o180) array_rad_test_poles (%i181) array(array_ord_test_poles,3,3) (%o181) array_ord_test_poles (%i182) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o182) array_fact_2 (%i183) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o183) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i184) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o184) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i185) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o185) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i186) 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)) (%o186) 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)) (%i187) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o187) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i188) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o188) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i189) 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) (%o189) 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) (%i190) 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) (%o190) 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) (%i191) 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) (%o191) 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 (%i192) 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) (%o192) 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) (%i193) 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) (%o193) 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 (%i194) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o194) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i195) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o195) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i196) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o196) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i197) 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) (%o197) 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) (%i198) log_revs(file,revs):=printf(file,revs) (%o198) log_revs(file, revs) := printf(file, revs) (%i199) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o199) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i200) 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) (%o200) 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) (%i201) logstart(file):=(printf(file,""),0) (%o201) logstart(file) := (printf(file, ""), 0) (%i202) logend(file):=(printf(file,"~%"),0) (%o202) logend(file) := (printf(file, "~%"), 0) (%i203) 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) (%o203) 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) (%i204) 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) (%o204) 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 (%i205) 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) (%o205) 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) (%i206) 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) (%o206) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i207) 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) (%o207) 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) (%i208) 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) (%o208) 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 ! (%i209) 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) (%o209) 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) (%i210) 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) (%o210) 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) (%i211) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o211) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i212) factorial_2(nnn):=nnn! (%o212) factorial_2(nnn) := nnn! (%i213) 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) (%o213) 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 (%i214) 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) (%o214) 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) (%i215) log10(x):=log(x)/glob_log_10 log(x) (%o215) log10(x) := ----------- glob_log_10 (%i216) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o216) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i217) 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) (%o217) 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) (%i218) exact_soln_y2(x):=block(sin(x)) (%o218) exact_soln_y2(x) := block(sin(x)) (%i219) exact_soln_y2p(x):=block(cos(x)) (%o219) exact_soln_y2p(x) := block(cos(x)) (%i220) exact_soln_y2pp(x):=block(-sin(x)) (%o220) exact_soln_y2pp(x) := block(- sin(x)) (%i221) exact_soln_y1(x):=block(cos(x)) (%o221) exact_soln_y1(x) := block(cos(x)) (%i222) 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) (%o222) 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) (%i223) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o223) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i224) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y2[1]) < min_size then (min_size:abs(array_y2[1]), omniout_float(ALWAYS,"min_size",32,min_size, 32,"")), if abs(array_y1[1]) < min_size then (min_size:abs(array_y1[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) (%o224) est_size_answer() := block([min_size], min_size : glob_estimated_size_answer, if !array_y2 ! < min_size then (min_size : !array_y2 !, ! 1! ! 1! omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if !array_y1 ! < min_size then (min_size : !array_y1 !, ! 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) (%i225) 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_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, 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, omniout_float(ALWAYS,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%o225) 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_y2 hn_div_ho_3 + array_y2 hn_div_ho_2 no_terms no_terms - 1 + array_y2 hn_div_ho + array_y2 ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, est_tmp : mabs(array_y1 hn_div_ho_3 no_terms + array_y1 hn_div_ho_2 + array_y1 hn_div_ho no_terms - 1 no_terms - 2 + array_y1 ), 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) (%i226) 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)) (%o226) 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)) (%i227) 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_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[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_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[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) (%o227) 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_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 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_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 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) (%i228) 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_y2_higher[1,1]) > glob_small_float then (tmp:abs(array_y2_higher[1,1]), if tmp < glob_normmax then glob_normmax:tmp), 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 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) (%o228) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat, [sz2], convfloat, [tmp], convfloat]), hnew : h_param, glob_normmax : glob_small_float, 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 !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_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 (%i229) 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) (%o229) 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) (%i230) 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:-10-3+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[1,1] then ( array_rad_test_poles[1,1]: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[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_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[2,1] then ( array_rad_test_poles[2,1]: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[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:-10-3+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[1,2] then ( array_rad_test_poles[1,2]: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[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_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[2,2] then ( array_rad_test_poles[2,2]: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[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:-10-3+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[1,3] then ( array_rad_test_poles[1,3]: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[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_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[2,3] then ( array_rad_test_poles[2,3]: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[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_y2[term] :array_y2[term]*ratio, array_y2_higher[1,term] :array_y2_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, 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, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%o230) 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 - 3 + 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 1, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 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 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_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 2, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 2, 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 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 - 3 + 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 1, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 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 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_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 2, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 2, 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 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 - 3 + 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 1, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 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 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_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 2, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 2, 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 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_y2 : array_y2 ratio, term term array_y2_higher : array_y2_higher ratio, 1, term 1, term array_x : array_x ratio, array_y1 : array_y1 ratio, term term term term array_y1_higher : array_y1_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) (%i231) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]),array_tmp1[1]:cos(array_x[1]), array_tmp1_g[1]:sin(array_x[1]), array_tmp2[1]:array_m1[1]*array_tmp1[1], array_tmp3[1]:array_tmp2[1]+array_const_0D0[1], if not array_y2_set_initial[1,4] then (if 1 <= MAX_TERMS then ( temporary :array_tmp3[1]*expt(glob_h,3) *factorial_3(0,3), 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, temporary:temporary*2.0/glob_h, array_y2_higher[3,2]:temporary, temporary:temporary*1.0/glob_h, array_y2_higher[4,1]:temporary,0)),kkk:2, array_tmp5[1]:array_m1[1]*array_y2[1], if not array_y1_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_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_tmp1[2]:(-array_tmp1_g[1]*array_x[2])/1, array_tmp1_g[2]:array_tmp1[1]*array_x[2]/1, array_tmp2[2]:ats(2,array_m1,array_tmp1,1), array_tmp3[2]:array_tmp2[2], if not array_y2_set_initial[1,5] then (if 2 <= MAX_TERMS then ( temporary :array_tmp3[2]*expt(glob_h,3) *factorial_3(1,4), 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, temporary:temporary*3.0/glob_h, array_y2_higher[3,3]:temporary, temporary:temporary*2.0/glob_h, array_y2_higher[4,2]:temporary,0)),kkk:3, array_tmp5[2]:ats(2,array_m1,array_y2,1), if not array_y1_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_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_tmp1[3]:(-array_tmp1_g[2]*array_x[2])/2, array_tmp1_g[3]:array_tmp1[2]*array_x[2]/2, array_tmp2[3]:ats(3,array_m1,array_tmp1,1), array_tmp3[3]:array_tmp2[3], if not array_y2_set_initial[1,6] then (if 3 <= MAX_TERMS then ( temporary :array_tmp3[3]*expt(glob_h,3) *factorial_3(2,5), 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, temporary:temporary*4.0/glob_h, array_y2_higher[3,4]:temporary, temporary:temporary*3.0/glob_h, array_y2_higher[4,3]:temporary,0)),kkk:4, array_tmp5[3]:ats(3,array_m1,array_y2,1), if not array_y1_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_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_tmp1[4]:(-array_tmp1_g[3]*array_x[2])/3, array_tmp1_g[4]:array_tmp1[3]*array_x[2]/3, array_tmp2[4]:ats(4,array_m1,array_tmp1,1), array_tmp3[4]:array_tmp2[4], if not array_y2_set_initial[1,7] then (if 4 <= MAX_TERMS then ( temporary :array_tmp3[4]*expt(glob_h,3) *factorial_3(3,6), if 7 <= MAX_TERMS then (array_y2[7]:temporary, array_y2_higher[1,7]:temporary), temporary:temporary*6.0/glob_h, array_y2_higher[2,6]:temporary, temporary:temporary*5.0/glob_h, array_y2_higher[3,5]:temporary, temporary:temporary*4.0/glob_h, array_y2_higher[4,4]:temporary,0)),kkk:5, array_tmp5[4]:ats(4,array_m1,array_y2,1), if not array_y1_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_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_tmp1[5]:(-array_tmp1_g[4]*array_x[2])/4, array_tmp1_g[5]:array_tmp1[4]*array_x[2]/4, array_tmp2[5]:ats(5,array_m1,array_tmp1,1), array_tmp3[5]:array_tmp2[5], if not array_y2_set_initial[1,8] then (if 5 <= MAX_TERMS then ( temporary :array_tmp3[5]*expt(glob_h,3) *factorial_3(4,7), if 8 <= MAX_TERMS then (array_y2[8]:temporary, array_y2_higher[1,8]:temporary), temporary:temporary*7.0/glob_h, array_y2_higher[2,7]:temporary, temporary:temporary*6.0/glob_h, array_y2_higher[3,6]:temporary, temporary:temporary*5.0/glob_h, array_y2_higher[4,5]:temporary,0)),kkk:6, array_tmp5[5]:ats(5,array_m1,array_y2,1), if not array_y1_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_y1[6]:temporary, array_y1_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y1_higher[2,5]:temporary,0)),kkk:6, while kkk <= MAX_TERMS do (array_tmp1[kkk] :(-array_tmp1_g[kkk-1]*array_x[2])/(kkk-1), array_tmp1_g[kkk] :array_tmp1[kkk-1]*array_x[2]/(kkk-1), array_tmp2[kkk]:ats(kkk,array_m1,array_tmp1,1), array_tmp3[kkk]:array_tmp2[kkk],order_d:3, if order_d+kkk <= MAX_TERMS then (if not array_y2_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_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))), array_tmp5[kkk]:ats(kkk,array_m1,array_y2,1), order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y1_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_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))), kkk:1+kkk)),0) (%o231) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : cos(array_x ), array_tmp1_g : sin(array_x ), 1 1 1 1 array_tmp2 : array_m1 array_tmp1 , array_tmp3 : 1 1 1 1 array_tmp2 + array_const_0D0 , if not array_y2_set_initial 1 1 1, 4 then (if 1 <= MAX_TERMS then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(0, 3), 1 if 4 <= MAX_TERMS then (array_y2 : temporary, 4 temporary 3.0 array_y2_higher : temporary), temporary : -------------, 1, 4 glob_h temporary 2.0 array_y2_higher : temporary, temporary : -------------, 2, 3 glob_h temporary 1.0 array_y2_higher : temporary, temporary : -------------, 3, 2 glob_h array_y2_higher : temporary, 0)), kkk : 2, 4, 1 array_tmp5 : array_m1 array_y2 , if not array_y1_set_initial 1 1 1 2, 2 then (if 1 <= MAX_TERMS then (temporary : array_tmp5 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_tmp1_g array_x array_tmp1 array_x 1 2 1 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 2 1 2 1 array_tmp2 : ats(2, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 , 2 2 2 if not array_y2_set_initial then (if 2 <= MAX_TERMS 1, 5 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(1, 4), 2 if 5 <= MAX_TERMS then (array_y2 : temporary, 5 temporary 4.0 array_y2_higher : temporary), temporary : -------------, 1, 5 glob_h temporary 3.0 array_y2_higher : temporary, temporary : -------------, 2, 4 glob_h temporary 2.0 array_y2_higher : temporary, temporary : -------------, 3, 3 glob_h array_y2_higher : temporary, 0)), kkk : 3, 4, 2 array_tmp5 : ats(2, array_m1, array_y2, 1), 2 if not array_y1_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_y1 : temporary, 3 temporary 2.0 array_y1_higher : temporary), temporary : -------------, 1, 3 glob_h array_y1_higher : temporary, 0)), kkk : 3, 2, 2 - array_tmp1_g array_x array_tmp1 array_x 2 2 2 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 3 2 3 2 array_tmp2 : ats(3, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 , 3 3 3 if not array_y2_set_initial then (if 3 <= MAX_TERMS 1, 6 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(2, 5), 3 if 6 <= MAX_TERMS then (array_y2 : temporary, 6 temporary 5.0 array_y2_higher : temporary), temporary : -------------, 1, 6 glob_h temporary 4.0 array_y2_higher : temporary, temporary : -------------, 2, 5 glob_h temporary 3.0 array_y2_higher : temporary, temporary : -------------, 3, 4 glob_h array_y2_higher : temporary, 0)), kkk : 4, 4, 3 array_tmp5 : ats(3, array_m1, array_y2, 1), 3 if not array_y1_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_y1 : temporary, 4 temporary 3.0 array_y1_higher : temporary), temporary : -------------, 1, 4 glob_h array_y1_higher : temporary, 0)), kkk : 4, 2, 3 - array_tmp1_g array_x array_tmp1 array_x 3 2 3 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 4 3 4 3 array_tmp2 : ats(4, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 , 4 4 4 if not array_y2_set_initial then (if 4 <= MAX_TERMS 1, 7 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(3, 6), 4 if 7 <= MAX_TERMS then (array_y2 : temporary, 7 temporary 6.0 array_y2_higher : temporary), temporary : -------------, 1, 7 glob_h temporary 5.0 array_y2_higher : temporary, temporary : -------------, 2, 6 glob_h temporary 4.0 array_y2_higher : temporary, temporary : -------------, 3, 5 glob_h array_y2_higher : temporary, 0)), kkk : 5, 4, 4 array_tmp5 : ats(4, array_m1, array_y2, 1), 4 if not array_y1_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_y1 : temporary, 5 temporary 4.0 array_y1_higher : temporary), temporary : -------------, 1, 5 glob_h array_y1_higher : temporary, 0)), kkk : 5, 2, 4 - array_tmp1_g array_x array_tmp1 array_x 4 2 4 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 5 4 5 4 array_tmp2 : ats(5, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 , 5 5 5 if not array_y2_set_initial then (if 5 <= MAX_TERMS 1, 8 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(4, 7), 5 if 8 <= MAX_TERMS then (array_y2 : temporary, 8 temporary 7.0 array_y2_higher : temporary), temporary : -------------, 1, 8 glob_h temporary 6.0 array_y2_higher : temporary, temporary : -------------, 2, 7 glob_h temporary 5.0 array_y2_higher : temporary, temporary : -------------, 3, 6 glob_h array_y2_higher : temporary, 0)), kkk : 6, 4, 5 array_tmp5 : ats(5, array_m1, array_y2, 1), 5 if not array_y1_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_y1 : temporary, 6 temporary 5.0 array_y1_higher : temporary), temporary : -------------, 1, 6 glob_h array_y1_higher : temporary, 0)), kkk : 6, 2, 5 - array_tmp1_g array_x kkk - 1 2 while kkk <= MAX_TERMS do (array_tmp1 : ------------------------------, kkk kkk - 1 array_tmp1 array_x kkk - 1 2 array_tmp1_g : --------------------------, kkk kkk - 1 array_tmp2 : ats(kkk, array_m1, array_tmp1, 1), kkk array_tmp3 : array_tmp2 , order_d : 3, kkk kkk if order_d + kkk <= MAX_TERMS then (if not subscript(array_y2_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_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))), array_tmp5 : ats(kkk, array_m1, array_y2, 1), kkk order_d : 1, if order_d + kkk <= MAX_TERMS then (if not array_y1_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_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))), kkk : 1 + kkk)), 0) (%i232) exact_soln_y2(x):=block(sin(x)) (%o232) exact_soln_y2(x) := block(sin(x)) (%i233) exact_soln_y2p(x):=block(cos(x)) (%o233) exact_soln_y2p(x) := block(cos(x)) (%i234) exact_soln_y2pp(x):=block(-sin(x)) (%o234) exact_soln_y2pp(x) := block(- sin(x)) (%i235) exact_soln_y1(x):=block(cos(x)) (%o235) exact_soln_y1(x) := block(cos(x)) (%i236) 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_y2_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_y1_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_y2[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_y1[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_g[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 <= 4 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 <= 4 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 <= 4 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 <= 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 <= 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_y2), zero_ats_ar(array_x),zero_ats_ar(array_m1), zero_ats_ar(array_y1),zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1_g),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_3),array_const_3[1]:3, zero_ats_ar(array_const_0D0),array_const_0D0[1]:0.0, zero_ats_ar(array_const_1),array_const_1[1]:1, 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_y2_set_initial[1,1]:true, array_y2_set_initial[1,2]:true, array_y2_set_initial[1,3]:true, array_y2_set_initial[1,4]:false, array_y2_set_initial[1,5]:false, array_y2_set_initial[1,6]:false, array_y2_set_initial[1,7]:false, array_y2_set_initial[1,8]:false, array_y2_set_initial[1,9]:false, array_y2_set_initial[1,10]:false, array_y2_set_initial[1,11]:false, array_y2_set_initial[1,12]:false, array_y2_set_initial[1,13]:false, array_y2_set_initial[1,14]:false, array_y2_set_initial[1,15]:false, array_y2_set_initial[1,16]:false, array_y2_set_initial[1,17]:false, array_y2_set_initial[1,18]:false, array_y2_set_initial[1,19]:false, array_y2_set_initial[1,20]:false, array_y2_set_initial[1,21]:false, array_y2_set_initial[1,22]:false, array_y2_set_initial[1,23]:false, array_y2_set_initial[1,24]:false, array_y2_set_initial[1,25]:false, array_y2_set_initial[1,26]:false, array_y2_set_initial[1,27]:false, array_y2_set_initial[1,28]:false, array_y2_set_initial[1,29]:false, array_y2_set_initial[1,30]:false, array_y1_set_initial[2,1]:true, array_y1_set_initial[2,2]:false, array_y1_set_initial[2,3]:false, array_y1_set_initial[2,4]:false, array_y1_set_initial[2,5]:false, array_y1_set_initial[2,6]:false, array_y1_set_initial[2,7]:false, array_y1_set_initial[2,8]:false, array_y1_set_initial[2,9]:false, array_y1_set_initial[2,10]:false, array_y1_set_initial[2,11]:false, array_y1_set_initial[2,12]:false, array_y1_set_initial[2,13]:false, array_y1_set_initial[2,14]:false, array_y1_set_initial[2,15]:false, array_y1_set_initial[2,16]:false, array_y1_set_initial[2,17]:false, array_y1_set_initial[2,18]:false, array_y1_set_initial[2,19]:false, array_y1_set_initial[2,20]:false, array_y1_set_initial[2,21]:false, array_y1_set_initial[2,22]:false, array_y1_set_initial[2,23]:false, array_y1_set_initial[2,24]:false, array_y1_set_initial[2,25]:false, array_y1_set_initial[2,26]:false, array_y1_set_initial[2,27]:false, array_y1_set_initial[2,28]:false, array_y1_set_initial[2,29]:false, array_y1_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/mtest4postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos ( x ) ; "), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ; "), 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:5.0,"), 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, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS,"glob_max_iter:20,"), 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_y2 (x) := (block("), omniout_str(ALWAYS," (sin(x)) "),omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"exact_soln_y2p (x) := (block("), omniout_str(ALWAYS," ( cos(x)) "),omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"exact_soln_y2pp (x) := (block("), omniout_str(ALWAYS," ( -sin(x)) "), omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"exact_soln_y1 (x) := (block("), omniout_str(ALWAYS," ( cos(x)) "),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:5.0, array_y1_init[1+0]:exact_soln_y1(x_start), array_y2_init[1+0]:exact_soln_y2(x_start), array_y2_init[1+1]:exact_soln_y2p(x_start), array_y2_init[1+2]:exact_soln_y2pp(x_start), glob_max_iter:20,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:3,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), 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), if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter:1, while subiter <= 4 do (atomall(),subiter:1+subiter)) else (subiter:1, while subiter <= MAX_TERMS+4 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:3,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),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),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 <= 4 do (atomall(), subiter:1+subiter)) else (subiter:1, while subiter <= MAX_TERMS+4 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:4,ord:4, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y2_higher_work[4,iii] :array_y2_higher[4,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:4, 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:3, calc_term:2,iii:MAX_TERMS, while iii >= calc_term do ( array_y2_higher_work[3,iii] :array_y2_higher[3,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:3, 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:3, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y2_higher_work[3,iii] :array_y2_higher[3,iii] /expt(glob_h,calc_term-1) /factorial_3(iii-calc_term,iii-1), iii:iii-1),temp_sum:0.0,ord:3, 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:2, calc_term:3,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:3,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:2, calc_term:2,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: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: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:4,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:4,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:3,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:3,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),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)), 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 ( y2 , x , 3 ) = m1 * cos ( x ) ; "), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 ; "), 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, "2014-01-08T23:11:42-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "mtest4"), logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos ( x ) ; "), 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, "mtest4 diffeq.max"), logitem_str(html_log_file, "mtest4 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 ( y1 , x , 1 ) = m1 * y2 ; "), 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))) (%o236) 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_y2_init : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_y1_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_y2 : 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_y1 : 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_g : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 4 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 <= 4 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 <= 4 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 <= 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 <= 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_y2), zero_ats_ar(array_x), zero_ats_ar(array_m1), zero_ats_ar(array_y1), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1_g), 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_3), array_const_3 : 3, zero_ats_ar(array_const_0D0), 1 array_const_0D0 : 0.0, zero_ats_ar(array_const_1), array_const_1 : 1, 1 1 zero_ats_ar(array_m1), array_m1 : - 1.0, iiif : 0, 1 while iiif <= MAX_TERMS do (jjjf : 0, while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0, iiif iiif, jjjf jjjf : 1 + jjjf), iiif : 1 + iiif), array_y2_set_initial : true, 1, 1 array_y2_set_initial : true, array_y2_set_initial : true, 1, 2 1, 3 array_y2_set_initial : false, array_y2_set_initial : false, 1, 4 1, 5 array_y2_set_initial : false, array_y2_set_initial : false, 1, 6 1, 7 array_y2_set_initial : false, array_y2_set_initial : false, 1, 8 1, 9 array_y2_set_initial : false, array_y2_set_initial : false, 1, 10 1, 11 array_y2_set_initial : false, array_y2_set_initial : false, 1, 12 1, 13 array_y2_set_initial : false, array_y2_set_initial : false, 1, 14 1, 15 array_y2_set_initial : false, array_y2_set_initial : false, 1, 16 1, 17 array_y2_set_initial : false, array_y2_set_initial : false, 1, 18 1, 19 array_y2_set_initial : false, array_y2_set_initial : false, 1, 20 1, 21 array_y2_set_initial : false, array_y2_set_initial : false, 1, 22 1, 23 array_y2_set_initial : false, array_y2_set_initial : false, 1, 24 1, 25 array_y2_set_initial : false, array_y2_set_initial : false, 1, 26 1, 27 array_y2_set_initial : false, array_y2_set_initial : false, 1, 28 1, 29 array_y2_set_initial : false, array_y1_set_initial : true, 1, 30 2, 1 array_y1_set_initial : false, array_y1_set_initial : false, 2, 2 2, 3 array_y1_set_initial : false, array_y1_set_initial : false, 2, 4 2, 5 array_y1_set_initial : false, array_y1_set_initial : false, 2, 6 2, 7 array_y1_set_initial : false, array_y1_set_initial : false, 2, 8 2, 9 array_y1_set_initial : false, array_y1_set_initial : false, 2, 10 2, 11 array_y1_set_initial : false, array_y1_set_initial : false, 2, 12 2, 13 array_y1_set_initial : false, array_y1_set_initial : false, 2, 14 2, 15 array_y1_set_initial : false, array_y1_set_initial : false, 2, 16 2, 17 array_y1_set_initial : false, array_y1_set_initial : false, 2, 18 2, 19 array_y1_set_initial : false, array_y1_set_initial : false, 2, 20 2, 21 array_y1_set_initial : false, array_y1_set_initial : false, 2, 22 2, 23 array_y1_set_initial : false, array_y1_set_initial : false, 2, 24 2, 25 array_y1_set_initial : false, array_y1_set_initial : false, 2, 26 2, 27 array_y1_set_initial : false, array_y1_set_initial : false, 2, 28 2, 29 array_y1_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/mtest4postode.ode#################"), omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos ( x ) ; "), omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ; "), 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:5.0,"), 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, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "glob_max_iter:20,"), 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_y2 (x) := (block("), omniout_str(ALWAYS, " (sin(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_y2p (x) := (block("), omniout_str(ALWAYS, " ( cos(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := (block("), omniout_str(ALWAYS, " ( -sin(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_y1 (x) := (block("), omniout_str(ALWAYS, " ( cos(x)) "), 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 : 5.0, array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), glob_max_iter : 20, 1 + 2 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 : 3, 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), 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), if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 4 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= MAX_TERMS + 4 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 : 3, term_no : 1, 2 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), 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), 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 <= 4 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= MAX_TERMS + 4 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 : 4, ord : 4, calc_term : 1, iii : MAX_TERMS, 2 while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, calc_term : 2, iii : MAX_TERMS, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, calc_term : 1, iii : MAX_TERMS, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, calc_term : 3, 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 : 3, 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 : 2, calc_term : 2, 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 : 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 : 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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 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) -------------------------------------, 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 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 ( y2 , x , 3 ) = m1 * cos ( x ) ; "), omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 ; "), 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, "2014-01-08T23:11:42-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest4"), logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos ( x ) ; "), 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, "mtest4 diffeq.max"), logitem_str(html_log_file, "\ mtest4 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 ( y1 , x , 1 ) = m1 * y2 ; "), 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))) (%i237) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o237) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i238) 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_y2 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable array_y1 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_y2_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_y1_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_tmp1 in translation. warning: encountered undefined variable array_tmp1_g in translation. warning: encountered undefined variable array_m1 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_const_0D0 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_y2_set_initial in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_y1_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_y2_init in translation. warning: encountered undefined variable array_y1_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_y2_higher_work in translation. warning: encountered undefined variable array_y2_higher_work2 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_const_3 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/mtest4postode.ode#################" "diff ( y2 , x , 3 ) = m1 * cos ( x ) ; " "diff ( y1 , x , 1 ) = m1 * y2 ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "array_y2_init[1 + 1] : exact_soln_y2p(x_start)," "array_y2_init[2 + 1] : exact_soln_y2pp(x_start)," "glob_max_iter:20," "/* 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_y2 (x) := (block(" " (sin(x)) " "));" "exact_soln_y2p (x) := (block(" " ( cos(x)) " "));" "exact_soln_y2pp (x) := (block(" " ( -sin(x)) " "));" "exact_soln_y1 (x) := (block(" " ( cos(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 = 4.9 "" estimated_steps = 4900000. "" step_error = 2.040816326530612300000000000000000E-17 "" est_needed_step_err = 2.040816326530612300000000000000000E-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 = 2.467208605532302300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" estimated_step_error = 2.467208605532302300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 1.6557156646065660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" estimated_step_error = 1.6557156646065660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 1.111131969458435700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" estimated_step_error = 1.111131969458435700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 7.4566803670241880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" estimated_step_error = 7.4566803670241880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 5.00409341203781700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" estimated_step_error = 5.00409341203781700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 3.3581901424816246000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" estimated_step_error = 3.3581901424816246000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 2.25364312158092020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" estimated_step_error = 2.25364312158092020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 1.51239411765430700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" estimated_step_error = 1.51239411765430700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 1.0149502701580557000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" estimated_step_error = 1.0149502701580557000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 6.81121272440810900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" estimated_step_error = 6.81121272440810900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 4.570923134360029000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" estimated_step_error = 4.570923134360029000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 3.06748875023403760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 3.06748875023403760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 2.058549011618171800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" estimated_step_error = 2.058549011618171800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 1.381458319740679000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" estimated_step_error = 1.381458319740679000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 9.27066811845143100000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 9.27066811845143100000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 6.221249002141342000000000000000000000000000000000000000000000000000000000000000000E-66 "" estimated_step_error = 6.221249002141342000000000000000000000000000000000000000000000000000000000000000000E-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 = 4.1747508757515445000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 4.1747508757515445000000000000000000000000000000000000000000000000000000000E-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 = 2.801274758009002500000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 2.801274758009002500000000000000000000000000000000000000000000000000E-50 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y2[1] (analytic) = 9.98334166468281500E-2 " " y2[1] (numeric) = 9.98334166468281500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9950041652780258 " " y1[1] (numeric) = 0.9950041652780258 " " 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 = 9.93346653975306100E-2 " " Order of pole (three term test) = 22.990033288920618 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.93346653975306200E-2 " " Order of pole (three term test) = 22.00996671107938 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y2[1] (analytic) = 0.10977830083717481 " " y2[1] (numeric) = 0.10977830083717481 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9939560979566968 " " y1[1] (numeric) = 0.9939560979566969 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.116973905494893400000000000000E-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 = 0.1091148115404347 " " Order of pole (three term test) = 22.9879487246653 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10911481154043476 " " Order of pole (three term test) = 22.0120512753347 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y2[1] (analytic) = 0.11971220728891936 " " y2[1] (numeric) = 0.11971220728891936 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9928086358538663 " " y1[1] (numeric) = 0.9928086358538664 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.118264874549875200000000000000E-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 = 0.11885131321356734 " " Order of pole (three term test) = 22.985668987426013 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.01433101257398 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y2[1] (analytic) = 0.12963414261969486 " " y2[1] (numeric) = 0.12963414261969486 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9915618937147881 " " y1[1] (numeric) = 0.9915618937147882 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.119670926910892300000000000000E-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 = 0.12854027594607753 " " Order of pole (three term test) = 22.983194989067258 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1285402759460775 " " Order of pole (three term test) = 22.016805010932746 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y2[1] (analytic) = 0.1395431146442365 " " y2[1] (numeric) = 0.1395431146442365 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9902159962126371 " " y1[1] (numeric) = 0.9902159962126373 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.242385558042932800000000000000E-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 = 0.13817782428205685 " " Order of pole (three term test) = 22.980527719155386 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13817782428205688 " " Order of pole (three term test) = 22.019472280844617 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y2[1] (analytic) = 0.14943813247359924 " " y2[1] (numeric) = 0.14943813247359924 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9887710779360422 " " y1[1] (numeric) = 0.9887710779360425 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.245662417518588200000000000000E-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 = 0.14776010333066988 " " Order of pole (three term test) = 22.9776682445628 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14776010333066986 " " Order of pole (three term test) = 22.022331755437197 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y2[1] (analytic) = 0.159318206614246 " " y2[1] (numeric) = 0.15931820661424598 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.742147128409054800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9872272833756269 " " y1[1] (numeric) = 0.9872272833756272 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.249174112832397000000000000000E-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 = 0.15728328030805885 " " Order of pole (three term test) = 22.97461770904122 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.025382290958774 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y2[1] (analytic) = 0.16918234906699606 " " y2[1] (numeric) = 0.16918234906699603 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.64057159441838300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9855847669095607 " " y1[1] (numeric) = 0.9855847669095609 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.252922451523711500000000000000E-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 = 0.16674354607040717 " " Order of pole (three term test) = 22.971377332764177 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16674354607040723 " " Order of pole (three term test) = 22.028622667235826 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y2[1] (analytic) = 0.17902957342582423 " " y2[1] (numeric) = 0.1790295734258242 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.550334678484202600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9838436927881214 " " y1[1] (numeric) = 0.9838436927881216 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.128454685193831700000000000000E-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 = 0.17613711663754494 " " Order of pole (three term test) = 22.967948411838968 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.17613711663754494 " " Order of pole (three term test) = 22.032051588161035 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y2[1] (analytic) = 0.18885889497650063 " " y2[1] (numeric) = 0.1888588949765006 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.46964619374070200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9820042351172703 " " y1[1] (numeric) = 0.9820042351172704 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.130568468976688600000000000000E-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 = 0.18546023470649134 " " Order of pole (three term test) = 22.96433231778825 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18546023470649128 " " Order of pole (three term test) = 22.03566768221174 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y2[1] (analytic) = 0.19866933079506127 " " y2[1] (numeric) = 0.19866933079506124 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.397073997508975000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9800665778412416 " " y1[1] (numeric) = 0.9800665778412417 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.132803678573149600000000000000E-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 = 0.19470917115432543 " " Order of pole (three term test) = 22.96053049700145 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19470917115432534 " " Order of pole (three term test) = 22.039469502998557 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y2[1] (analytic) = 0.20845989984609964 " " y2[1] (numeric) = 0.2084598998460996 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.331458742718389000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9780309147241483 " " y1[1] (numeric) = 0.9780309147241484 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.135161484070565100000000000000E-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 = 0.20388022652978524 " " Order of pole (three term test) = 22.95654447015615 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.20388022652978527 " " Order of pole (three term test) = 22.043455529843847 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y2[1] (analytic) = 0.2182296230808694 " " y2[1] (numeric) = 0.21822962308086935 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.543703757884741600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9758974493306055 " " y1[1] (numeric) = 0.9758974493306056 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.13764312570617800000000000000E-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 = 0.21296973253299992 " " Order of pole (three term test) = 22.95237583160998 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21296973253299994 " " Order of pole (three term test) = 22.04762416839002 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y2[1] (analytic) = 0.2279775235351885 " " y2[1] (numeric) = 0.22797752353518844 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.4349396541580400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9736663950053748 " " y1[1] (numeric) = 0.973666395005375 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.28049983098991100000000000000E-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 = 0.2219740534827599 " " Order of pole (three term test) = 22.948026248762762 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.05197375123724 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y2[1] (analytic) = 0.2377026264271347 " " y2[1] (numeric) = 0.23770262642713463 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.33531922072700400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9713379748520296 " " y1[1] (numeric) = 0.9713379748520298 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.28596647792810600000000000000E-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 = 0.2308895877707414 " " Order of pole (three term test) = 22.94349746138964 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2308895877707415 " " Order of pole (three term test) = 22.05650253861036 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y2[1] (analytic) = 0.24740395925452305 " " y2[1] (numeric) = 0.247403959254523 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.243745467878682500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9689124217106447 " " y1[1] (numeric) = 0.968912421710645 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.291689113996543700000000000000E-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 = 0.23971276930210164 " " Order of pole (three term test) = 22.93879128094519 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23971276930210167 " " Order of pole (three term test) = 22.061208719054815 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y2[1] (analytic) = 0.25708055189215523 " " y2[1] (numeric) = 0.2570805518921552 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.1592901844455600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9663899781345132 " " y1[1] (numeric) = 0.9663899781345134 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.297670815602401000000000000000E-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 = 0.24844006892186843 " " Order of pole (three term test) = 22.933909589838823 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24844006892186846 " " Order of pole (three term test) = 22.066090410161177 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y2[1] (analytic) = 0.26673143668883126 " " y2[1] (numeric) = 0.2667314366888312 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.081162682598118300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9637708963658905 " " y1[1] (numeric) = 0.9637708963658908 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.303914817954133600000000000000E-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 = 0.2570679958265566 " " Order of pole (three term test) = 22.928854340681912 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2570679958265566 " " Order of pole (three term test) = 22.071145659318084 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y2[1] (analytic) = 0.2763556485641139 " " y2[1] (numeric) = 0.2763556485641138 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.008685240185324700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9610554383107709 " " y1[1] (numeric) = 0.9610554383107712 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.46563677921611300000000000000E-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) = 22.9236275555067 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2655930989604419 " " Order of pole (three term test) = 22.076372444493288 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y2[1] (analytic) = 0.2859522251048357 " " y2[1] (numeric) = 0.28595222510483564 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.941273623973597300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9582438755126971 " " y1[1] (numeric) = 0.9582438755126974 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.475805229742204000000000000000E-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 = 0.27401196839593706 " " Order of pole (three term test) = 22.918231324957596 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.274011968395937 " " Order of pole (three term test) = 22.081768675042408 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y2[1] (analytic) = 0.2955202066613397 " " y2[1] (numeric) = 0.2955202066613397 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.955336489125606 " " y1[1] (numeric) = 0.9553364891256062 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.3242554581816800000000000000E-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 = 0.28232123669751785 " " Order of pole (three term test) = 22.912667807454838 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2823212366975179 " " Order of pole (three term test) = 22.087332192545162 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y2[1] (analytic) = 0.30505863644344366 " " y2[1] (numeric) = 0.30505863644344366 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9523335698857134 " " y1[1] (numeric) = 0.9523335698857136 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.331584351811500400000000000000E-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 = 0.2905175802686526 " " Order of pole (three term test) = 22.906939228331265 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.29051758026865254 " " Order of pole (three term test) = 22.093060771668732 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y2[1] (analytic) = 0.31456656061611793 " " y2[1] (numeric) = 0.31456656061611793 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9492354180824408 " " y1[1] (numeric) = 0.949235418082441 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.33919426830475480000000000000E-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 = 0.29859772068119605 " " Order of pole (three term test) = 22.901047878942144 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2985977206811961 " " Order of pole (three term test) = 22.09895212105786 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y2[1] (analytic) = 0.32404302839486854 " " y2[1] (numeric) = 0.32404302839486854 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9460423435283869 " " y1[1] (numeric) = 0.9460423435283871 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.347089498096748300000000000000E-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 = 0.3065584259867171 " " Order of pole (three term test) = 22.89499611574868 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30655842598671706 " " Order of pole (three term test) = 22.105003884251317 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y2[1] (analytic) = 0.33348709214081457 " " y2[1] (numeric) = 0.3334870921408146 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.664566711560107600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9427546655283462 " " y1[1] (numeric) = 0.9427546655283464 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.355274527340485400000000000000E-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 = 0.3143965120092341 " " Order of pole (three term test) = 22.888786359375462 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.31439651200923424 " " Order of pole (three term test) = 22.111213640624534 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y2[1] (analytic) = 0.34289780745545156 " " y2[1] (numeric) = 0.34289780745545156 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9393727128473789 " " y1[1] (numeric) = 0.9393727128473791 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.363754044462085500000000000000E-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 = 0.3221088436188456 " " Order of pole (three term test) = 22.88242109364224 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3221088436188457 " " Order of pole (three term test) = 22.117578906357757 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y2[1] (analytic) = 0.35227423327509017 " " y2[1] (numeric) = 0.3522742332750902 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.575793685367538300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9358968236779348 " " y1[1] (numeric) = 0.935896823677935 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.372532947087363500000000000000E-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 = 0.3296923359857367 " " Order of pole (three term test) = 22.875902864570445 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3296923359857368 " " Order of pole (three term test) = 22.12409713542955 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y2[1] (analytic) = 0.3616154319649622 " " y2[1] (numeric) = 0.3616154319649622 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9323273456060344 " " y1[1] (numeric) = 0.9323273456060346 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.381616349359539400000000000000E-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 = 0.33714395581407275 " " Order of pole (three term test) = 22.869234279364793 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33714395581407275 " " Order of pole (three term test) = 22.130765720635207 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y2[1] (analytic) = 0.3709204694129829 " " y2[1] (numeric) = 0.3709204694129829 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.9286646355765101 " " y1[1] (numeric) = 0.9286646355765104 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.391009589669441400000000000000E-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 = 0.3444607225552757 " " Order of pole (three term test) = 22.862418005370447 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3444607225552758 " " Order of pole (three term test) = 22.13758199462955 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y2[1] (analytic) = 0.38018841512316165 " " y2[1] (numeric) = 0.38018841512316165 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.924909059857313 " " y1[1] (numeric) = 0.9249090598573132 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.40071823882108400000000000000E-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 = 0.3516397096002052 " " Order of pole (three term test) = 22.855456769006135 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3516397096002053 " " Order of pole (three term test) = 22.144543230993865 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y2[1] (analytic) = 0.3894183423086507 " " y2[1] (numeric) = 0.38941834230865074 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.425488868915681700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.921060994002885 " " y1[1] (numeric) = 0.9210609940028852 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.410748108657132200000000000000E-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 = 0.35867804544976156 " " Order of pole (three term test) = 22.848353354673577 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35867804544976173 " " Order of pole (three term test) = 22.151646645326416 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y2[1] (analytic) = 0.3986093279844231 " " y2[1] (numeric) = 0.39860932798442317 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.39262047659424300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.917120822816605 " " y1[1] (numeric) = 0.9171208228166052 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.421105261170514200000000000000E-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 = 0.36557291486344806 " " Order of pole (three term test) = 22.841110603643806 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36557291486344806 " " Order of pole (three term test) = 22.15888939635619 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y2[1] (analytic) = 0.4077604530595704 " " y2[1] (numeric) = 0.4077604530595705 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.36136672437795500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9130889403123081 " " y1[1] (numeric) = 0.9130889403123084 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.431796018130329700000000000000E-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 = 0.3723215599854299 " " Order of pole (three term test) = 22.83373141292065 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3723215599854298 " " Order of pole (three term test) = 22.166268587079347 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y2[1] (analytic) = 0.416870802429211 " " y2[1] (numeric) = 0.4168708024292111 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.663230473699783600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.908965749674885 " " y1[1] (numeric) = 0.9089657496748852 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.442826971252231300000000000000E-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 = 0.37892128144763854 " " Order of pole (three term test) = 22.82621873408202 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37892128144763865 " " Order of pole (three term test) = 22.173781265917974 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y2[1] (analytic) = 0.42593946506599983 " " y2[1] (numeric) = 0.42593946506599994 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.606527724434095600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9047516632199633 " " y1[1] (numeric) = 0.9047516632199635 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.45420499294564780000000000000E-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 = 0.3853694394494849 " " Order of pole (three term test) = 22.818575572099284 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3853694394494848 " " Order of pole (three term test) = 22.18142442790071 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y2[1] (analytic) = 0.43496553411123046 " " y2[1] (numeric) = 0.43496553411123057 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.552439072888123600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.9004471023526768 " " y1[1] (numeric) = 0.900447102352677 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.465937247672583800000000000000E-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 = 0.3916634548137418 " " Order of pole (three term test) = 22.81080498413533 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3916634548137419 " " Order of pole (three term test) = 22.18919501586467 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y2[1] (analytic) = 0.44394810696552 " " y2[1] (numeric) = 0.4439481069655201 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.500794591092566000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8960524975255251 " " y1[1] (numeric) = 0.8960524975255253 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.478031203955280700000000000000E-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 = 0.3978008100181832 " " Order of pole (three term test) = 22.802910078321734 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3978008100181832 " " Order of pole (three term test) = 22.19708992167827 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y2[1] (analytic) = 0.45288628537906855 " " y2[1] (numeric) = 0.45288628537906866 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.45143882795190700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8915682881953289 " " y1[1] (numeric) = 0.891568288195329 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.245247323536392700000000000000E-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 = 0.40377905020255705 " " Order of pole (three term test) = 22.794894012515545 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4037790502025572 " " Order of pole (three term test) = 22.205105987484455 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y2[1] (analytic) = 0.4617791755414832 " " y2[1] (numeric) = 0.4617791755414833 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.404229301425961600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.886994922779284 " " y1[1] (numeric) = 0.8869949227792843 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.503335692489458400000000000000E-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 = 0.40959578415049913 " " Order of pole (three term test) = 22.786759993036224 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40959578415049924 " " Order of pole (three term test) = 22.213240006963773 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y2[1] (analytic) = 0.4706258881711583 " " y2[1] (numeric) = 0.47062588817115847 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.53855276302199930000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8823328586101213 " " y1[1] (numeric) = 0.8823328586101216 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.516562800061679700000000000000E-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 = 0.41524868524598535 " " Order of pole (three term test) = 22.778511273383106 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41524868524598546 " " Order of pole (three term test) = 22.221488726616897 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y2[1] (analytic) = 0.4794255386042033 " " y2[1] (numeric) = 0.47942553860420345 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.47360414254563900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8775825618903725 " " y1[1] (numeric) = 0.8775825618903728 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.530184789072519300000000000000E-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 = 0.42073549240394825 " " Order of pole (three term test) = 22.77015115293407 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4207354924039482 " " Order of pole (three term test) = 22.22984884706593 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y2[1] (analytic) = 0.4881772468829078 " " y2[1] (numeric) = 0.488177246882908 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.411331739795679400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8727445076457511 " " y1[1] (numeric) = 0.8727445076457513 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.54421085414793200000000000000E-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 = 0.42605401097468165 " " Order of pole (three term test) = 22.761682975625828 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42605401097468154 " " Order of pole (three term test) = 22.238317024374176 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y2[1] (analytic) = 0.496880137843737 " " y2[1] (numeric) = 0.4968801378437372 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.35158202170170600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8678191796776498 " " y1[1] (numeric) = 0.8678191796776499 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.279325291056078500000000000000E-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 = 0.4312021136216693 " " Order of pole (three term test) = 22.753110128616388 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4312021136216693 " " Order of pole (three term test) = 22.246889871383612 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y2[1] (analytic) = 0.5055333412048473 " " y2[1] (numeric) = 0.5055333412048475 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.39228408547353500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8628070705147608 " " y1[1] (numeric) = 0.862807070514761 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.573513969844462600000000000000E-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 = 0.43617774117249314 " " Order of pole (three term test) = 22.74443604093026 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4361777411724933 " " Order of pole (three term test) = 22.25556395906974 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y2[1] (analytic) = 0.5141359916531134 " " y2[1] (numeric) = 0.5141359916531136 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.318791302882455400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8577086813638239 " " y1[1] (numeric) = 0.8577086813638242 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.588811443204271000000000000000E-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 = 0.440978903442474 " " Order of pole (three term test) = 22.735664182086868 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4409789034424741 " " Order of pole (three term test) = 22.26433581791314 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y2[1] (analytic) = 0.5226872289306594 " " y2[1] (numeric) = 0.5226872289306597 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.248135263976157700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8525245220595056 " " y1[1] (numeric) = 0.8525245220595058 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.604553877096954500000000000000E-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 = 0.4456036800307177 " " Order of pole (three term test) = 22.72679806071279 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44560368003071776 " " Order of pole (three term test) = 22.273201939287212 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y2[1] (analytic) = 0.5311861979208837 " " y2[1] (numeric) = 0.531186197920884 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.18016518113867100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8472551110134159 " " y1[1] (numeric) = 0.8472551110134162 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.93112892513755530000000000000E-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 = 0.4500502210882527 " " Order of pole (three term test) = 22.717841223138354 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45005022108825277 " " Order of pole (three term test) = 22.282158776861642 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y2[1] (analytic) = 0.5396320487339695 " " y2[1] (numeric) = 0.5396320487339697 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.11474087660230800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8419009751622685 " " y1[1] (numeric) = 0.8419009751622688 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.95612925051371360000000000000E-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 = 0.4543167480579418 " " Order of pole (three term test) = 22.708797251979178 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45431674805794187 " " Order of pole (three term test) = 22.291202748020822 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y2[1] (analytic) = 0.5480239367918739 " " y2[1] (numeric) = 0.5480239367918741 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.05173186822601230000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8364626499151867 " " y1[1] (numeric) = 0.836462649915187 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.981850324354809000000000000000E-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 = 0.45840155438588365 " " Order of pole (three term test) = 22.69966976470314 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45840155438588354 " " Order of pole (three term test) = 22.30033023529686 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y2[1] (analytic) = 0.5563610229127841 " " y2[1] (numeric) = 0.5563610229127843 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.99101654825735900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8309406791001632 " " y1[1] (numeric) = 0.8309406791001636 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.0083114928039100000000000000E-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 = 0.46230300620401044 " " Order of pole (three term test) = 22.69046241218344 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4623030062040104 " " Order of pole (three term test) = 22.309537587816557 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y2[1] (analytic) = 0.5646424733950357 " " y2[1] (numeric) = 0.5646424733950359 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.93248144423036100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8253356149096781 " " y1[1] (numeric) = 0.8253356149096783 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.6903553041186900000000000000E-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 = 0.4660195429836133 " " Order of pole (three term test) = 22.681178877238338 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4660195429836133 " " Order of pole (three term test) = 22.318821122761666 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y2[1] (analytic) = 0.5728674601004816 " " y2[1] (numeric) = 0.5728674601004818 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.87602055257396600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8196480178454792 " " y1[1] (numeric) = 0.8196480178454796 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.06353581215317450000000000000E-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 = 0.469549678159534 " " Order of pole (three term test) = 22.67182287315803 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46954967815953397 " " Order of pole (three term test) = 22.328177126841975 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y2[1] (analytic) = 0.5810351605373054 " " y2[1] (numeric) = 0.5810351605373056 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.821534736722269600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8138784566625337 " " y1[1] (numeric) = 0.813878456662534 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.092342101710768600000000000000E-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 = 0.47289199972476975 " " Order of pole (three term test) = 22.662398142219384 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47289199972476975 " " Order of pole (three term test) = 22.33760185778061 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y2[1] (analytic) = 0.5891447579422698 " " y2[1] (numeric) = 0.5891447579422701 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.768931182559879000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8080275083121516 " " y1[1] (numeric) = 0.808027508312152 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.12197485804999200000000000000E-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 = 0.476045170795258 " " Order of pole (three term test) = 22.652908454189145 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.34709154581085 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y2[1] (analytic) = 0.5971954413623924 " " y2[1] (numeric) = 0.5971954413623926 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.859061452465854700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.8020957578842923 " " y1[1] (numeric) = 0.8020957578842927 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.15245815868775700000000000000E-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 = 0.47900793014461235 " " Order of pole (three term test) = 22.643357604815975 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47900793014461257 " " Order of pole (three term test) = 22.356642395184025 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y2[1] (analytic) = 0.6051864057360399 " " y2[1] (numeric) = 0.6051864057360401 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.66902829971826940000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7960837985490555 " " y1[1] (numeric) = 0.7960837985490559 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.18381718098767450000000000000E-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 = 0.4817790927085966 " " Order of pole (three term test) = 22.633749414312298 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48177909270859653 " " Order of pole (three term test) = 22.366250585687705 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y2[1] (analytic) = 0.6131168519734341 " " y2[1] (numeric) = 0.6131168519734344 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.62157073664405360000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7899922314973647 " " y1[1] (numeric) = 0.7899922314973651 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.21607826138044760000000000000E-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 = 0.48435755005913256 " " Order of pole (three term test) = 22.624087725826186 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4843575500591328 " " Order of pole (three term test) = 22.375912274173817 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y2[1] (analytic) = 0.62098598703656 " " y2[1] (numeric) = 0.6209859870365603 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.575678188563675700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.783821665880849 " " y1[1] (numeric) = 0.7838216658808492 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.832845972374345400000000000000E-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 = 0.48674227084765975 " " Order of pole (three term test) = 22.614376403904227 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4867422708476599 " " Order of pole (three term test) = 22.385623596095776 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y2[1] (analytic) = 0.6287930240184689 " " y2[1] (numeric) = 0.6287930240184691 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.531282893470990600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7775727187509276 " " y1[1] (numeric) = 0.7775727187509279 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.28341812097750630000000000000E-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 = 0.4889323012176582 " " Order of pole (three term test) = 22.60461933294571 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4889323012176584 " " Order of pole (three term test) = 22.395380667054294 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y2[1] (analytic) = 0.6365371822219683 " " y2[1] (numeric) = 0.6365371822219685 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.48832104591184200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7712460149971063 " " y1[1] (numeric) = 0.7712460149971065 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.87903730596085370000000000000E-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 = 0.49092676518617995 " " Order of pole (three term test) = 22.594820415648915 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49092676518617984 " " Order of pole (three term test) = 22.40517958435108 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y2[1] (analytic) = 0.6442176872376915 " " y2[1] (numeric) = 0.6442176872376917 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.44673251486039100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.764842187284488 " " y1[1] (numeric) = 0.7648421872844884 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.354714121746798300000000000000E-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 = 0.4927248649942302 " " Order of pole (three term test) = 22.584983571450124 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49272486499423024 " " Order of pole (three term test) = 22.415016428549883 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y2[1] (analytic) = 0.6518337710215371 " " y2[1] (numeric) = 0.6518337710215373 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.40646058545031700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7583618759905079 " " y1[1] (numeric) = 0.7583618759905081 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.92795052012623350000000000000E-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 = 0.4943258814258599 " " Order of pole (three term test) = 22.57511273495584 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49432588142586 " " Order of pole (three term test) = 22.42488726504416 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y2[1] (analytic) = 0.6593846719714735 " " y2[1] (numeric) = 0.6593846719714738 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.367451722241997500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7518057291408946 " " y1[1] (numeric) = 0.7518057291408949 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.43022571493502770000000000000E-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 = 0.4957291740958434 " " Order of pole (three term test) = 22.565211854369075 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4957291740958434 " " Order of pole (three term test) = 22.43478814563093 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y2[1] (analytic) = 0.6668696350036982 " " y2[1] (numeric) = 0.6668696350036984 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.32965535196095600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.74517440234487 " " y1[1] (numeric) = 0.7451744023448703 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.46965041122550750000000000000E-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 = 0.49693418170582254 " " Order of pole (three term test) = 22.555284889910038 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49693418170582254 " " Order of pole (three term test) = 22.444715110089962 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y2[1] (analytic) = 0.6742879116281455 " " y2[1] (numeric) = 0.6742879116281456 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.646511831933032700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7384685587295875 " " y1[1] (numeric) = 0.7384685587295878 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.51023816045104550000000000000E-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 = 0.49794042226882 " " Order of pole (three term test) = 22.545335812232153 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4979404222688202 " " Order of pole (three term test) = 22.45466418776785 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y2[1] (analytic) = 0.6816387600233346 " " y2[1] (numeric) = 0.6816387600233347 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.628755713051221200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7316888688738205 " " y1[1] (numeric) = 0.7316888688738208 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.55202916917660900000000000000E-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) = 22.53536860083385 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4987474933020273 " " Order of pole (three term test) = 22.464631399166155 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y2[1] (analytic) = 0.6889214451105518 " " y2[1] (numeric) = 0.6889214451105519 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.611537908283575400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7248360107409048 " " y1[1] (numeric) = 0.7248360107409051 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.59506567626374400000000000000E-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 = 0.49935507198779155 " " Order of pole (three term test) = 22.525387242466792 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4993550719877916 " " Order of pole (three term test) = 22.47461275753321 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y2[1] (analytic) = 0.6961352386273572 " " y2[1] (numeric) = 0.6961352386273573 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.594838133484378400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.717910669610943 " " y1[1] (numeric) = 0.7179106696109433 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.63939207879506500000000000000E-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) = 22.515395729541233 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.484604270458764 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y2[1] (analytic) = 0.7032794192004106 " " y2[1] (numeric) = 0.7032794192004107 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.57863715944854180000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.710913538012277 " " y1[1] (numeric) = 0.7109135380122773 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.68505506757975300000000000000E-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) = 22.50539805852913 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999708601149832 " " Order of pole (three term test) = 22.494601941470865 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y2[1] (analytic) = 0.7103532724176083 " " y2[1] (numeric) = 0.7103532724176084 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.562916745419692400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.7038453156522356 " " y1[1] (numeric) = 0.7038453156522361 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.30947169746432700000000000000E-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) = 22.4953982283656 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4999788232493701 " " Order of pole (three term test) = 22.504601771634402 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y2[1] (analytic) = 0.7173560908995231 " " y2[1] (numeric) = 0.7173560908995233 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.09531915518553900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6967067093471649 " " y1[1] (numeric) = 0.6967067093471654 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.3741198971111890000000000000E-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 = 0.4997868015207526 " " Order of pole (three term test) = 22.485400238849355 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.514599761150645 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y2[1] (analytic) = 0.7242871743701429 " " y2[1] (numeric) = 0.7242871743701431 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.065698424359460400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6894984329517466 " " y1[1] (numeric) = 0.689498432951747 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.83056801103500240000000000000E-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 = 0.499394871735262 " " Order of pole (three term test) = 22.475408089042915 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49939487173526204 " " Order of pole (three term test) = 22.52459191095709 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y2[1] (analytic) = 0.7311458297268963 " " y2[1] (numeric) = 0.7311458297268965 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.51847002264904720000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6822212072876132 " " y1[1] (numeric) = 0.6822212072876135 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.88209548207626300000000000000E-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 = 0.4988031906595868 " " Order of pole (three term test) = 22.46542577567297 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.53457422432703 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y2[1] (analytic) = 0.7379313711099631 " " y2[1] (numeric) = 0.7379313711099633 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.00901430157443800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6748757600712666 " " y1[1] (numeric) = 0.674875760071267 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.58031057158086300000000000000E-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 = 0.49801199495826814 " " Order of pole (three term test) = 22.45545729153177 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49801199495826826 " " Order of pole (three term test) = 22.544542708468228 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y2[1] (analytic) = 0.7446431199708597 " " y2[1] (numeric) = 0.74464311997086 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.98189292252805100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6674628258413077 " " y1[1] (numeric) = 0.667462825841308 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.99004430647850300000000000000E-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 = 0.4970216010990379 " " Order of pole (three term test) = 22.44550662388006 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.497021601099038 " " Order of pole (three term test) = 22.55449337611994 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y2[1] (analytic) = 0.7512804051402932 " " y2[1] (numeric) = 0.7512804051402934 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.95554899882643660000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6599831458849816 " " y1[1] (numeric) = 0.6599831458849821 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.728796221827400000000000000E-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 = 0.4958324052262342 " " Order of pole (three term test) = 22.435577752852232 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49583240522623423 " " Order of pole (three term test) = 22.564422247147764 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y2[1] (analytic) = 0.7578425628952774 " " y2[1] (numeric) = 0.7578425628952776 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.92995690393434100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6524374681640513 " " y1[1] (numeric) = 0.6524374681640518 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.80661720884489600000000000000E-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 = 0.4944448830023505 " " Order of pole (three term test) = 22.425674649864312 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4944448830023507 " " Order of pole (three term test) = 22.574325350135684 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y2[1] (analytic) = 0.7643289370255055 " " y2[1] (numeric) = 0.7643289370255058 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.905092221016116000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6448265472400007 " " y1[1] (numeric) = 0.6448265472400011 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.88695606207377900000000000000E-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 = 0.4928595894177767 " " Order of pole (three term test) = 22.415801276025462 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49285958941777663 " " Order of pole (three term test) = 22.584198723974538 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y2[1] (analytic) = 0.7707388788989697 " " y2[1] (numeric) = 0.77073887889897 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.88093167483948200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6371511441985797 " " y1[1] (numeric) = 0.6371511441985801 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.96991936518682900000000000000E-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 = 0.49107715856880907 " " Order of pole (three term test) = 22.40596158055356 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49107715856880907 " " Order of pole (three term test) = 22.594038419446434 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y2[1] (analytic) = 0.7770717475268243 " " y2[1] (numeric) = 0.7770717475268245 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.85745306828783400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6294120265736963 " " y1[1] (numeric) = 0.6294120265736968 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.05562002473216500000000000000E-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 = 0.48909830340402205 " " Order of pole (three term test) = 22.396159499195605 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4890983034040224 " " Order of pole (three term test) = 22.603840500804395 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y2[1] (analytic) = 0.7833269096274839 " " y2[1] (numeric) = 0.7833269096274841 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.834635223123204700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.621609968270664 " " y1[1] (numeric) = 0.6216099682706644 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.14417774035270200000000000000E-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 = 0.48692381543909746 " " Order of pole (three term test) = 22.386398952653455 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.613601047346545 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y2[1] (analytic) = 0.7895037396899508 " " y2[1] (numeric) = 0.7895037396899511 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.21868688701014900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.613745749488811 " " y1[1] (numeric) = 0.6137457494888114 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.23571951773099300000000000000E-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) = 22.37668384501558 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4845545644402281 " " Order of pole (three term test) = 22.623316154984423 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y2[1] (analytic) = 0.7956016200363665 " " y2[1] (numeric) = 0.7956016200363668 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.186352805218303600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.6058201566434622 " " y1[1] (numeric) = 0.6058201566434628 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.16297528606782400000000000000E-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 = 0.48199149807622377 " " Order of pole (three term test) = 22.367018062195513 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4819914980762238 " " Order of pole (three term test) = 22.632981937804487 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y2[1] (analytic) = 0.8016199408837775 " " y2[1] (numeric) = 0.801619940883778 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.53989724058584400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5978339822872977 " " y1[1] (numeric) = 0.5978339822872982 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.28537903095999500000000000000E-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 = 0.47923564153945675 " " Order of pole (three term test) = 22.357405470377483 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.479235641539457 " " Order of pole (three term test) = 22.64259452962251 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y2[1] (analytic) = 0.8075581004051147 " " y2[1] (numeric) = 0.8075581004051151 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.499161108374537000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5897880250310976 " " y1[1] (numeric) = 0.5897880250310982 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.4120512583026600000000000000E-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 = 0.4762880971357975 " " Order of pole (three term test) = 22.347849914470086 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47628809713579756 " " Order of pole (three term test) = 22.652150085529918 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y2[1] (analytic) = 0.8134155047893742 " " y2[1] (numeric) = 0.8134155047893746 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.45956165373384500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5816830894638829 " " y1[1] (numeric) = 0.5816830894638835 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.54319495215522300000000000000E-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 = 0.473150043843707 " " Order of pole (three term test) = 22.338355216568246 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47315004384370696 " " Order of pole (three term test) = 22.661644783431747 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y2[1] (analytic) = 0.8191915683009987 " " y2[1] (numeric) = 0.8191915683009992 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.421066659305376000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.573519986072456 " " y1[1] (numeric) = 0.5735199860724566 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.67902646451884700000000000000E-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 = 0.46982273684266207 " " Order of pole (three term test) = 22.32892517442455 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4698227368426621 " " Order of pole (three term test) = 22.67107482557545 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y2[1] (analytic) = 0.8248857133384505 " " y2[1] (numeric) = 0.824885713338451 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.383645305878304000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5652995311603537 " " y1[1] (numeric) = 0.5652995311603543 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.81977662661663400000000000000E-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 = 0.46630750701109996 " " Order of pole (three term test) = 22.319563559930117 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.46630750701109996 " " Order of pole (three term test) = 22.680436440069883 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y2[1] (analytic) = 0.8304973704919709 " " y2[1] (numeric) = 0.8304973704919714 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.34726810257078200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5570225467662167 " " y1[1] (numeric) = 0.5570225467662172 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.96569197306764500000000000000E-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 = 0.4626057603940837 " " Order of pole (three term test) = 22.31027411760592 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4626057603940838 " " Order of pole (three term test) = 22.689725882394086 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y2[1] (analytic) = 0.836025978600521 " " y2[1] (numeric) = 0.8360259786005214 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.311906821286257000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.548689860581587 " " y1[1] (numeric) = 0.5486898605815875 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.0117036092560280000000000000E-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 = 0.45871897764090463 " " Order of pole (three term test) = 22.30106056310504 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4587189776409045 " " Order of pole (three term test) = 22.698939436894957 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y2[1] (analytic) = 0.8414709848078968 " " y2[1] (numeric) = 0.8414709848078974 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.5969180439335910000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5403023058681392 " " y1[1] (numeric) = 0.5403023058681397 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.21927289642999700000000000000E-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 = 0.4546487134128403 " " Order of pole (three term test) = 22.291926581726425 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45464871341284063 " " Order of pole (three term test) = 22.70807341827357 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y2[1] (analytic) = 0.8468318446180155 " " y2[1] (numeric) = 0.8468318446180161 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.55515632578714700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5318607213743549 " " y1[1] (numeric) = 0.5318607213743554 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.34972751329546800000000000000E-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 = 0.45039659576131336 " " Order of pole (three term test) = 22.28287582694085 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45039659576131347 " " Order of pole (three term test) = 22.71712417305915 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y2[1] (analytic) = 0.8521080219493633 " " y2[1] (numeric) = 0.8521080219493639 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.51456737894160800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.523365951251649 " " y1[1] (numeric) = 0.5233659512516494 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.48525221765013300000000000000E-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 = 0.44596432547668935 " " Order of pole (three term test) = 22.27391191892954 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4459643254766894 " " Order of pole (three term test) = 22.726088081070454 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y2[1] (analytic) = 0.8572989891886037 " " y2[1] (numeric) = 0.8572989891886044 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.77014580882173600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5148188449699548 " " y1[1] (numeric) = 0.5148188449699552 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.6261257564489500000000000000E-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 = 0.4413536754079866 " " Order of pole (three term test) = 22.2650384431362 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4413536754079866 " " Order of pole (three term test) = 22.7349615568638 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y2[1] (analytic) = 0.8624042272433388 " " y2[1] (numeric) = 0.8624042272433394 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.72414830229183800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.5062202572327777 " " y1[1] (numeric) = 0.5062202572327783 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.09658099292008120000000000000E-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 = 0.4365664897537578 " " Order of pole (three term test) = 22.25625894883282 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43656648975375806 " " Order of pole (three term test) = 22.74374105116718 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y2[1] (analytic) = 0.8674232255940173 " " y2[1] (numeric) = 0.867423225594018 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.67945560045295000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.49757104789172635 " " y1[1] (numeric) = 0.4975710478917269 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.11564271005047110000000000000E-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 = 0.4316046833244363 " " Order of pole (three term test) = 22.24757694770007 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43160468332443647 " " Order of pole (three term test) = 22.752423052299925 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y2[1] (analytic) = 0.8723554823449866 " " y2[1] (numeric) = 0.8723554823449874 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.90870904082048400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.48887208186052694 " " y1[1] (numeric) = 0.48887208186052744 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.02194496192125410000000000000E-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 = 0.42647024077643764 " " Order of pole (three term test) = 22.23899591242265 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42647024077643764 " " Order of pole (three term test) = 22.761004087577355 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y2[1] (analytic) = 0.877200504274682 " " y2[1] (numeric) = 0.8772005042746828 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.85950376738788400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.48012422902853347 " " y1[1] (numeric) = 0.48012422902853397 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.04056477652084810000000000000E-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 = 0.4211652158183223 " " Order of pole (three term test) = 22.230519275300246 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4211652158183224 " " Order of pole (three term test) = 22.769480724699754 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y2[1] (analytic) = 0.8819578068849478 " " y2[1] (numeric) = 0.8819578068849486 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.8117153810623300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.47132836417373936 " " y1[1] (numeric) = 0.47132836417373986 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.05998365270705320000000000000E-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 = 0.41569173038934115 " " Order of pole (three term test) = 22.22215042687469 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41569173038934126 " " Order of pole (three term test) = 22.77784957312531 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y2[1] (analytic) = 0.8866269144494876 " " y2[1] (numeric) = 0.8866269144494884 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.76531159354835200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.46248536687530023 " " y1[1] (numeric) = 0.4624853668753007 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.60223266847277900000000000000E-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 = 0.4100519738106868 " " Order of pole (three term test) = 22.213892714573785 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41005197381068664 " " Order of pole (three term test) = 22.786107285426215 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y2[1] (analytic) = 0.8912073600614356 " " y2[1] (numeric) = 0.8912073600614365 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.96601306837163400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.4535961214255767 " " y1[1] (numeric) = 0.45359612142557715 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.79041021017473800000000000000E-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 = 0.4042482019097947 " " Order of pole (three term test) = 22.205749441372323 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40424820190979466 " " Order of pole (three term test) = 22.79425055862767 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y2[1] (analytic) = 0.895698685680048 " " y2[1] (numeric) = 0.8956986856800488 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.91604022535532700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.4446615167417062 " " y1[1] (numeric) = 0.4446615167417066 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.98712938111134200000000000000E-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 = 0.3982827361180429 " " Order of pole (three term test) = 22.197723864471033 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3982827361180429 " " Order of pole (three term test) = 22.80227613552897 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y2[1] (analytic) = 0.9001004421765053 " " y2[1] (numeric) = 0.9001004421765062 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.86754786557429300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.4356824462767115 " " y1[1] (numeric) = 0.43568244627671193 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.01929562149036380000000000000E-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 = 0.3921579625422095 " " Order of pole (three term test) = 22.189819193993657 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.39215796254220975 " " Order of pole (three term test) = 22.810180806006347 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y2[1] (analytic) = 0.9044121893788263 " " y2[1] (numeric) = 0.9044121893788272 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.82050474474641100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.4266598079301566 " " y1[1] (numeric) = 0.42665980793015706 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.0408508174333571000000000000E-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 = 0.3858763310100624 " " Order of pole (three term test) = 22.182038591703 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3858763310100624 " " Order of pole (three term test) = 22.817961408297002 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y2[1] (analytic) = 0.9086334961158836 " " y2[1] (numeric) = 0.9086334961158845 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.77488088978452600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.4175945039583574 " " y1[1] (numeric) = 0.41759450395835784 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.06344601195792400000000000000E-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 = 0.37944035409046045 " " Order of pole (three term test) = 22.174385169736226 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3794403540904605 " " Order of pole (three term test) = 22.82561483026377 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y2[1] (analytic) = 0.9127639402605214 " " y2[1] (numeric) = 0.9127639402605223 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.73064754778350400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.40848744088415656 " " y1[1] (numeric) = 0.40848744088415706 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.22304950184013790000000000000E-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 = 0.37285260608835946 " " Order of pole (three term test) = 22.166861989360086 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3728526060883596 " " Order of pole (three term test) = 22.833138010639917 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y2[1] (analytic) = 0.9168031087717673 " " y2[1] (numeric) = 0.9168031087717682 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.68777713777617600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.39933952940627243 " " y1[1] (numeric) = 0.39933952940627293 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.2510666345105210000000000000E-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 = 0.36611572201512516 " " Order of pole (three term test) = 22.15947205974642 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36611572201512516 " " Order of pole (three term test) = 22.84052794025358 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y2[1] (analytic) = 0.920750597736136 " " y2[1] (numeric) = 0.9207505977361369 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.64624320509705400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.39015168430822944 " " y1[1] (numeric) = 0.39015168430823 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.42280947292803830000000000000E-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 = 0.3592323965345627 " " Order of pole (three term test) = 22.15221833676855 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3592323965345626 " " Order of pole (three term test) = 22.847781663231444 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y2[1] (analytic) = 0.9246060124080206 " " y2[1] (numeric) = 0.9246060124080215 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.60602037820385400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.380924824366881 " " y1[1] (numeric) = 0.3809248243668815 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.3115458198653370000000000000E-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 = 0.3522053828850873 " " Order of pole (three term test) = 22.145103721818934 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3522053828850874 " " Order of pole (three term test) = 22.85489627818106 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y2[1] (analytic) = 0.928368967249167 " " y2[1] (numeric) = 0.9283689672491678 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.56708432781710100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.37165987226053215 " " y1[1] (numeric) = 0.37165987226053265 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.34424079210548300000000000000E-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 = 0.34503749177846765 " " Order of pole (three term test) = 22.13813106064871 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3450374917784677 " " Order of pole (three term test) = 22.861868939351282 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y2[1] (analytic) = 0.9320390859672266 " " y2[1] (numeric) = 0.9320390859672275 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.5294117282475900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.3623577544766728 " " y1[1] (numeric) = 0.3623577544766733 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.37874891570309350000000000000E-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 = 0.33773159027557503 " " Order of pole (three term test) = 22.131303142229378 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33773159027557503 " " Order of pole (three term test) = 22.868696857770622 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y2[1] (analytic) = 0.9356160015533862 " " y2[1] (numeric) = 0.9356160015533871 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.49298022079035500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.35301940121932956 " " y1[1] (numeric) = 0.35301940121933006 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.4152206914285728000000000000E-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 = 0.33029060063959964 " " Order of pole (three term test) = 22.12462269763725 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.33029060063959975 " " Order of pole (three term test) = 22.875377302362747 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y2[1] (analytic) = 0.9390993563190678 " " y2[1] (numeric) = 0.9390993563190687 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.45776837907189900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.3436457463160462 " " y1[1] (numeric) = 0.3436457463160467 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.45382378928632180000000000000E-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 = 0.32271749916718456 " " Order of pole (three term test) = 22.11809239896111 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3227174991671846 " " Order of pole (three term test) = 22.881907601038883 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y2[1] (analytic) = 0.9424888019316978 " " y2[1] (numeric) = 0.9424888019316986 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.24578621671443500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.3342377271245018 " " y1[1] (numeric) = 0.3342377271245023 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.49474556741232860000000000000E-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 = 0.31501531499794516 " " Order of pole (three term test) = 22.111714858233352 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3150153149979453 " " Order of pole (three term test) = 22.88828514176664 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y2[1] (analytic) = 0.9457839994495393 " " y2[1] (numeric) = 0.9457839994495401 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.21705714719139100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.3247962844387754 " " y1[1] (numeric) = 0.3247962844387759 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.5381960478537920000000000000E-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 = 0.3071871289028553 " " Order of pole (three term test) = 22.10549262638524 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30718712890285527 " " Order of pole (three term test) = 22.89450737361477 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y2[1] (analytic) = 0.9489846193555865 " " y2[1] (numeric) = 0.9489846193555873 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.18934365622639800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.31532236239526784 " " y1[1] (numeric) = 0.31532236239526834 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.58441144892557150000000000000E-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 = 0.29923607205197755 " " Order of pole (three term test) = 22.09942819222653 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2992360720519778 " " Order of pole (three term test) = 22.90057180777347 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y2[1] (analytic) = 0.9520903415905161 " " y2[1] (numeric) = 0.9520903415905169 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.16262998676501800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.30581690837828845 " " y1[1] (numeric) = 0.305816908378289 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.8151759994444720000000000000E-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 = 0.2911653247620401 " " Order of pole (three term test) = 22.093523981450055 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2911653247620401 " " Order of pole (three term test) = 22.90647601854994 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y2[1] (analytic) = 0.9551008555846925 " " y2[1] (numeric) = 0.9551008555846934 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.29931550690949100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.29628087292531785 " " y1[1] (numeric) = 0.2962808729253184 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.87359888214080780000000000000E-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 = 0.2829781152243507 " " Order of pole (three term test) = 22.087782355661385 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.28297811522435073 " " Order of pole (three term test) = 22.91221764433861 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y2[1] (analytic) = 0.9580158602892253 " " y2[1] (numeric) = 0.9580158602892261 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.2710199957648300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.2867152096319546 " " y1[1] (numeric) = 0.2867152096319552 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.9361076554855730000000000000E-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 = 0.2746777182135626 " " Order of pole (three term test) = 22.082205611434294 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2746777182135628 " " Order of pole (three term test) = 22.917794388565706 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y2[1] (analytic) = 0.9608350642060729 " " y2[1] (numeric) = 0.9608350642060738 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.24381772467907300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.27712087505655675 " " y1[1] (numeric) = 0.2771208750565573 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.00313856615560730000000000000E-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 = 0.26626745377780997 " " Order of pole (three term test) = 22.076795979392113 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2662674537778099 " " Order of pole (three term test) = 22.92320402060789 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y2[1] (analytic) = 0.9635581854171932 " " y2[1] (numeric) = 0.9635581854171941 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.21769368100556800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.2674988286245865 " " y1[1] (numeric) = 0.26749882862458707 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.07519231081057710000000000000E-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 = 0.2577506859107313 " " Order of pole (three term test) = 22.071555623315525 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.25775068591073125 " " Order of pole (three term test) = 22.928444376684464 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y2[1] (analytic) = 0.9661849516127343 " " y2[1] (numeric) = 0.9661849516127351 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.04355435199438800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.25785003253266875 " " y1[1] (numeric) = 0.2578500325326693 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.15284639237828100000000000000E-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 = 0.2491308212059187 " " Order of pole (three term test) = 22.0664866392771 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24913082120591865 " " Order of pole (three term test) = 22.933513360722902 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y2[1] (analytic) = 0.9687151001182654 " " y2[1] (numeric) = 0.9687151001182663 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.16862367058892900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.24817545165237204 " " y1[1] (numeric) = 0.2481754516523726 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.2367704324364130000000000000E-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 = 0.24041130749432327 " " Order of pole (three term test) = 22.061591054802857 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24041130749432335 " " Order of pole (three term test) = 22.93840894519714 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y2[1] (analytic) = 0.9711483779210448 " " y2[1] (numeric) = 0.9711483779210456 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.00244468205035700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.23847605343372227 " " y1[1] (numeric) = 0.23847605343372283 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.3277452990342112000000000000E-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 = 0.23159563246517184 " " Order of pole (three term test) = 22.056870828061324 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2315956324651719 " " Order of pole (three term test) = 22.94312917193868 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y2[1] (analytic) = 0.9734845416953196 " " y2[1] (numeric) = 0.9734845416953204 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.98324045170964100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.22875280780845852 " " y1[1] (numeric) = 0.22875280780845908 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.4266872071681390000000000000E-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 = 0.2226873222709348 " " Order of pole (three term test) = 22.052327847080257 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22268732227093482 " " Order of pole (three term test) = 22.947672152919743 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y2[1] (analytic) = 0.9757233578266593 " " y2[1] (numeric) = 0.9757233578266601 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.96492275196382200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.21900668709304064 " " y1[1] (numeric) = 0.2190066870930412 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.53467836841324460000000000000E-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 = 0.2136899401169141 " " Order of pole (three term test) = 22.04796392899147 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2136899401169141 " " Order of pole (three term test) = 22.95203607100853 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y2[1] (analytic) = 0.9778646024353164 " " y2[1] (numeric) = 0.9778646024353173 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.08283639154303400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.2092386658914184 " " y1[1] (numeric) = 0.20923866589141896 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.65300636451508400000000000000E-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 = 0.20460708483600784 " " Order of pole (three term test) = 22.043780819304022 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.20460708483600787 " " Order of pole (three term test) = 22.956219180695985 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y2[1] (analytic) = 0.9799080613986144 " " y2[1] (numeric) = 0.9799080613986153 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.0638954274183200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.199449720997572 " " y1[1] (numeric) = 0.19944972099757255 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.78321528621910700000000000000E-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 = 0.19544238944922526 " " Order of pole (three term test) = 22.03978019120601 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19544238944922535 " " Order of pole (three term test) = 22.960219808793997 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y2[1] (analytic) = 0.9818535303723599 " " y2[1] (numeric) = 0.9818535303723608 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.0459359998765900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.18964083129783338 " " y1[1] (numeric) = 0.18964083129783393 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.9271729538074454000000000000E-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 = 0.18619951971252685 " " Order of pole (three term test) = 22.03596364489533 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18619951971252685 " " Order of pole (three term test) = 22.964036355104664 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y2[1] (analytic) = 0.9837008148112767 " " y2[1] (numeric) = 0.9837008148112776 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.0289487039870200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.17981297767299848 " " y1[1] (numeric) = 0.17981297767299903 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 3.0871604457943210000000000000E-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 = 0.17688217265057044 " " Order of pole (three term test) = 22.032332706939627 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1768821726505705 " " Order of pole (three term test) = 22.967667293060373 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y2[1] (analytic) = 0.9854497299884604 " " y2[1] (numeric) = 0.9854497299884613 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.01292468475815600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.16996714290023993 " " y1[1] (numeric) = 0.16996714290024048 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 3.26599307866458630000000000000E-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 = 0.16749407507795158 " " Order of pole (three term test) = 22.02888882966567 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16749407507795155 " " Order of pole (three term test) = 22.97111117033433 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y2[1] (analytic) = 0.9871001010138505 " " y2[1] (numeric) = 0.9871001010138514 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.99785562566427700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.16010431155483018 " " y1[1] (numeric) = 0.16010431155483074 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 3.4671865293426020000000000000E-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 = 0.15803898210852585 " " Order of pole (three term test) = 22.025633390578445 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.15803898210852596 " " Order of pole (three term test) = 22.97436660942156 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y2[1] (analytic) = 0.98865176285172 " " y2[1] (numeric) = 0.9886517628517209 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.98373373793635800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.15022546991168476 " " y1[1] (numeric) = 0.1502254699116853 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 3.69518905575013270000000000000E-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 = 0.14852067565341512 " " Order of pole (three term test) = 22.022567691810185 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14852067565341517 " " Order of pole (three term test) = 22.97743230818981 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y2[1] (analytic) = 0.990104560337178 " " y2[1] (numeric) = 0.9901045603371789 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.97055175059145300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = 0.14033160584673562 " " y1[1] (numeric) = 0.14033160584673618 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 3.9557126775763410000000000000E-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 = 0.1389429629082924 " " Order of pole (three term test) = 22.019692959599517 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.13894296290829242 " " Order of pole (three term test) = 22.980307040400472 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y2[1] (analytic) = 0.9914583481916865 " " y2[1] (numeric) = 0.9914583481916875 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.0078090763823570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.13042370873814443 " " y1[1] (numeric) = 0.130423708738145 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 4.25621627910529800000000000000E-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 = 0.1293096748305543 " " Order of pole (three term test) = 22.017010343801008 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1293096748305543 " " Order of pole (three term test) = 22.982989656198985 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y2[1] (analytic) = 0.9927129910375886 " " y2[1] (numeric) = 0.9927129910375896 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00653535431048530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.12050276936736551 " " y1[1] (numeric) = 0.12050276936736605 " " absolute error = 5.4123372450476380000000000000000E-16 " " relative error = 4.4914629543056833000000000000E-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 = 0.11962466460699016 " " Order of pole (three term test) = 22.01452091742521 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11962466460699016 " " Order of pole (three term test) = 22.985479082574795 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y2[1] (analytic) = 0.993868363411645 " " y2[1] (numeric) = 0.993868363411646 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00536525655439080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.11056977982006848 " " y1[1] (numeric) = 0.11056977982006902 " " absolute error = 5.4123372450476380000000000000000E-16 " " relative error = 4.8949516349360550000000000000E-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 = 0.10989180611255746 " " Order of pole (three term test) = 22.01222567620946 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10989180611255747 " " Order of pole (three term test) = 22.987774323790543 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y2[1] (analytic) = 0.994924349777581 " " y2[1] (numeric) = 0.994924349777582 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00429818848640680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 0.10062573338693062 " " y1[1] (numeric) = 0.10062573338693116 " " absolute error = 5.4123372450476380000000000000000E-16 " " relative error = 5.378681041991390000000000000E-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 = 0.10011499236088425 " " Order of pole (three term test) = 22.010125538219665 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10011499236088427 " " Order of pole (three term test) = 22.989874461780346 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y2[1] (analytic) = 0.9958808445376401 " " y2[1] (numeric) = 0.9958808445376411 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00333360927987540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 9.06716244643085600E-2 " " y1[1] (numeric) = 9.06716244643091100E-2 " " absolute error = 5.4123372450476380000000000000000E-16 " " relative error = 5.9691632051636160000000000000E-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 = 9.02981339471153700E-2 " " Order of pole (three term test) = 22.008221343482997 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.02981339471153700E-2 " " Order of pole (three term test) = 22.991778656517 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y2[1] (analytic) = 0.9967377520431435 " " y2[1] (numeric) = 0.9967377520431445 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00247103123609880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 8.07084484547995200E-2 " " y1[1] (numeric) = 8.07084484548000600E-2 " " absolute error = 5.4123372450476380000000000000000E-16 " " relative error = 6.7060355497712220000000000000E-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 = 8.04451574837267600E-2 " " Order of pole (three term test) = 22.006513853651985 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.04451574837267700E-2 " " Order of pole (three term test) = 22.99348614634802 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y2[1] (analytic) = 0.9974949866040546 " " y2[1] (numeric) = 0.9974949866040556 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00171001917953850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 7.0737201667701800E-2 " " y1[1] (numeric) = 7.07372016677023400E-2 " " absolute error = 5.4123372450476380000000000000000E-16 " " relative error = 7.6513307247760130000000000000E-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 = 7.0560004029932500E-2 " " Order of pole (three term test) = 22.005003751699782 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.05600040299325100E-2 " " Order of pole (three term test) = 22.994996248300218 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y2[1] (analytic) = 0.9981524724975482 " " y2[1] (numeric) = 0.9981524724975492 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00105018991985250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 6.07588812193847900E-2 " " y1[1] (numeric) = 6.07588812193853200E-2 " " absolute error = 5.3429483060085660000000000000000E-16 " " relative error = 8.7936910601045220000000000000E-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 = 6.06466275153138200E-2 " " Order of pole (three term test) = 22.003691641647034 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.0646627515313800E-2 " " Order of pole (three term test) = 22.99630835835297 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y2[1] (analytic) = 0.9987101439755831 " " y2[1] (numeric) = 0.9987101439755841 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.00049121177953090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 5.07744849335780700E-2 " " y1[1] (numeric) = 5.0774484933578600E-2 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 1.0386239021170247000000000000E-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 = 5.07089931582998400E-2 " " Order of pole (three term test) = 22.00257804832027 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.070899315829984000E-2 " " Order of pole (three term test) = 22.997421951679733 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y2[1] (analytic) = 0.999167945271476 " " y2[1] (numeric) = 0.9991679452714771 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11114756020671430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 4.078501124158992500E-2 " " y1[1] (numeric) = 4.07850112415904500E-2 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 1.2930140770911097000000000000E-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 = 4.07510758801334400E-2 " " Order of pole (three term test) = 22.001663417141977 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.075107588013343600E-2 " " Order of pole (three term test) = 22.99833658285802 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y2[1] (analytic) = 0.9995258306054791 " " y2[1] (numeric) = 0.9995258306054802 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11074970814173060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 3.079145908246501000E-2 " " y1[1] (numeric) = 3.07914590824655440E-2 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 1.7126695272367450000000000000E-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 = 3.07768587149554700E-2 " " Order of pole (three term test) = 22.00094811395243 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.07768587149554600E-2 " " Order of pole (three term test) = 22.999051886047564 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y2[1] (analytic) = 0.999783764189357 " " y2[1] (numeric) = 0.9997837641893581 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11046314652383430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 2.07948278030913200E-2 " " y1[1] (numeric) = 2.079482780309184500E-2 " " absolute error = 5.2388648974499570000000000000000E-16 " " relative error = 2.519311507196591000000000000E-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 = 2.079033121664414200E-2 " " Order of pole (three term test) = 22.00043242486336 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.07903312166441400E-2 " " Order of pole (three term test) = 22.999567575136634 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y2[1] (analytic) = 0.9999417202299663 " " y2[1] (numeric) = 0.9999417202299674 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11028773193884530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 1.079611705826628200E-2 " " y1[1] (numeric) = 1.079611705826680500E-2 " " absolute error = 5.2388648974499570000000000000000E-16 " " relative error = 4.852545474614604000000000000E-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 = 1.079548786304687400E-2 " " Order of pole (three term test) = 22.000116556143535 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.079548786304687100E-2 " " Order of pole (three term test) = 22.999883443856465 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y2[1] (analytic) = 0.9999996829318346 " " y2[1] (numeric) = 0.9999996829318357 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11022337664164570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = 7.9632671073215310000E-4 " " y1[1] (numeric) = 7.9632671073267410000E-4 " " absolute error = 5.2095914387928490000000000000000E-16 " " relative error = 6.54202774889100800000000000E-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 = 7.9632645824230360000E-4 " " Order of pole (three term test) = 22.000000634136228 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.9632645824230430000E-4 " " Order of pole (three term test) = 22.999999365863776 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y2[1] (analytic) = 0.9999576464987401 " " y2[1] (numeric) = 0.9999576464987412 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11027004844905240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -9.203543268809447000E-3 " " y1[1] (numeric) = -9.203543268808928000E-3 " " absolute error = 5.1868231931706530000000000000000E-16 " " relative error = 5.635680782583653000000000000E-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 = 9.203153466528015000E-3 " " Order of pole (three term test) = 22.0000847052087 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.203153466528015000E-3 " " Order of pole (three term test) = 22.999915294791297 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y2[1] (analytic) = 0.9998156151342908 " " y2[1] (numeric) = 0.999815615134292 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11042777070053680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -1.92024929016937600E-2 " " y1[1] (numeric) = -1.920249290169324000E-2 " " absolute error = 5.1694759584108850000000000000000E-16 " " relative error = 2.692085858266304000000000000E-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 = 1.919895225261880600E-2 " " Order of pole (three term test) = 22.00036873573364 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 1.919895225261881200E-2 " " Order of pole (three term test) = 22.99963126426636 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y2[1] (analytic) = 0.9995736030415051 " " y2[1] (numeric) = 0.9995736030415062 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11069662228671010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -2.919952230128992600E-2 " " y1[1] (numeric) = -2.919952230128941000E-2 " " absolute error = 5.1347814888913490000000000000000E-16 " " relative error = 1.7585155797786847000000000000E-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 = 2.918707171379118000E-2 " " Order of pole (three term test) = 22.000852612102623 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 2.91870717137911700E-2 " " Order of pole (three term test) = 22.999147387897384 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y2[1] (analytic) = 0.9992316344213905 " " y2[1] (numeric) = 0.9992316344213916 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.1110767377456340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -3.91936317729888200E-2 " " y1[1] (numeric) = -3.919363177298830000E-2 " " absolute error = 5.1347814888913490000000000000000E-16 " " relative error = 1.3101060699432554000000000000E-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 = 3.91635167354337570E-2 " " Order of pole (three term test) = 22.00153614077156 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 3.916351673543377000E-2 " " Order of pole (three term test) = 22.998463859228444 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y2[1] (analytic) = 0.998789743470524 " " y2[1] (numeric) = 0.9987897434705251 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11156830742717890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -4.91838219141716550E-2 " " y1[1] (numeric) = -4.91838219141711500E-2 " " absolute error = 5.0653925498522770000000000000000E-16 " " relative error = 1.0298899826637409000000000000E-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 = 4.91242968725554600E-2 " " Order of pole (three term test) = 22.002419048338083 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 4.91242968725554730E-2 " " Order of pole (three term test) = 22.997580951661917 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y2[1] (analytic) = 0.9982479743776324 " " y2[1] (numeric) = 0.9982479743776335 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11217157772580120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -5.91690937141494700E-2 " " y1[1] (numeric) = -5.91690937141489600E-2 " " absolute error = 5.0653925498522770000000000000000E-16 " " relative error = 8.5608756732418210000000000000E-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 = 5.906542794591001000E-2 " " Order of pole (three term test) = 22.00350098165095 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 5.906542794591001000E-2 " " Order of pole (three term test) = 22.996499018349045 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y2[1] (analytic) = 0.9976063813191736 " " y2[1] (numeric) = 0.9976063813191747 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11288685138227140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -6.91484486540632800E-2 " " y1[1] (numeric) = -6.91484486540627800E-2 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 7.2250407754008670000000000000E-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 = 6.89829336356147600E-2 " " Order of pole (three term test) = 22.004781507951268 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 6.89829336356147500E-2 " " Order of pole (three term test) = 22.995218492048735 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y2[1] (analytic) = 0.9968650284539188 " " y2[1] (numeric) = 0.9968650284539199 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11371448785504050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -7.91208888067351900E-2 " " y1[1] (numeric) = -7.9120888806734690E-2 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 6.3143926795573580000000000000E-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 = 7.88728470716254300E-2 " " Order of pole (three term test) = 22.006260115045563 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 7.88728470716254300E-2 " " Order of pole (three term test) = 22.99373988495443 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y2[1] (analytic) = 0.9960239899165366 " " y2[1] (numeric) = 0.9960239899165377 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11465490376209660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -8.90854169364602800E-2 " " y1[1] (numeric) = -8.9085416936459790E-2 " " absolute error = 4.857225732735060000000000000000E-16 " " relative error = 5.4523241847758890000000000000E-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 = 8.87312124204313800E-2 " " Order of pole (three term test) = 22.00793621151074 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 8.87312124204314200E-2 " " Order of pole (three term test) = 22.99206378848926 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y2[1] (analytic) = 0.9950833498101801 " " y2[1] (numeric) = 0.9950833498101812 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11570857339431940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -9.90410365987293400E-2 " " y1[1] (numeric) = -9.90410365987288600E-2 " " absolute error = 4.857225732735060000000000000000E-16 " " relative error = 4.9042557504869410000000000000E-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 = 9.85540864673362300E-2 " " Order of pole (three term test) = 22.009809126930552 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 9.85540864673362300E-2 " " Order of pole (three term test) = 22.990190873069448 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y2[1] (analytic) = 0.9940432021980758 " " y2[1] (numeric) = 0.994043202198077 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11687602930152160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.10898675223987243 " " y1[1] (numeric) = -0.10898675223987196 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 4.3293774313706790000000000000E-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 = 0.10833754019369098 " " Order of pole (three term test) = 22.011878112163792 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.10833754019369105 " " Order of pole (three term test) = 22.988121887836204 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y2[1] (analytic) = 0.9929036510941184 " " y2[1] (numeric) = 0.9929036510941195 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11815786295252270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.11892156929661354 " " y1[1] (numeric) = -0.11892156929661307 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 3.9676972668332250000000000000E-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 = 0.11807766034844974 " " Order of pole (three term test) = 22.014142339643964 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.11807766034844976 " " Order of pole (three term test) = 22.98585766035603 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y2[1] (analytic) = 0.9916648104524685 " " y2[1] (numeric) = 0.9916648104524696 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.11955472547079020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.12884449429552597 " " y1[1] (numeric) = -0.1288444942955255 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 3.6621261005025030000000000000E-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 = 0.1277705510134168 " " Order of pole (three term test) = 22.01660090371027 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.12777055101341683 " " Order of pole (three term test) = 22.98339909628973 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y2[1] (analytic) = 0.9903268041561579 " " y2[1] (numeric) = 0.990326804156159 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.12106732844736070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.13875453495237888 " " y1[1] (numeric) = -0.1387545349523784 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 3.4005719930352590000000000000E-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 = 0.13741233516156331 " " Order of pole (three term test) = 22.019252820969857 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1374123351615633 " " Order of pole (three term test) = 22.98074717903015 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y2[1] (analytic) = 0.9888897660047012 " " y2[1] (numeric) = 0.9888897660047025 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.23496608931623450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.14865070027136496 " " y1[1] (numeric) = -0.14865070027136448 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 3.17418474722506560000000000000E-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 = 0.1469991562077852 " " Order of pole (three term test) = 22.022097030691167 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.14699915620778517 " " Order of pole (three term test) = 22.977902969308833 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y2[1] (analytic) = 0.9873538397007162 " " y2[1] (numeric) = 0.9873538397007174 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.23688720090241650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.15853200064419906 " " y1[1] (numeric) = -0.1585320006441986 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.9763377964596266000000000000E-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 = 0.15652717955148637 " " Order of pole (three term test) = 22.02513239522825 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.15652717955148643 " " Order of pole (three term test) = 22.974867604771752 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y2[1] (analytic) = 0.9857191788355533 " " y2[1] (numeric) = 0.9857191788355545 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.23893838459179620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.16839744794907832 " " y1[1] (numeric) = -0.16839744794907785 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.8019711178068010000000000000E-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 = 0.16599259411036824 " " Order of pole (three term test) = 22.028357700475762 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.16599259411036832 " " Order of pole (three term test) = 22.971642299524238 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y2[1] (analytic) = 0.9839859468739367 " " y2[1] (numeric) = 0.9839859468739379 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.24112069991191870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.1782460556494934 " " y1[1] (numeric) = -0.17824605564949295 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.4914391975288840000000000000E-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 = 0.17539161384481128 " " Order of pole (three term test) = 22.031771656354604 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.1753916138448113 " " Order of pole (three term test) = 22.9682283436454 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y2[1] (analytic) = 0.9821543171376182 " " y2[1] (numeric) = 0.9821543171376195 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.24343527873181730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.18807683889288143 " " y1[1] (numeric) = -0.18807683889288096 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.5087873033341934000000000000E-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 = 0.1847204792722396 " " Order of pole (three term test) = 22.035372897327935 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.18472047927223964 " " Order of pole (three term test) = 22.96462710267206 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y2[1] (analytic) = 0.9802244727880453 " " y2[1] (numeric) = 0.9802244727880465 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.24588332671810690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.19788881460911031 " " y1[1] (numeric) = -0.19788881460910987 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24413497411297300000000000000E-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 = 0.19397545897086627 " " Order of pole (three term test) = 22.0391599829474 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.19397545897086627 " " Order of pole (three term test) = 22.9608400170526 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y2[1] (analytic) = 0.9781966068080444 " " y2[1] (numeric) = 0.9781966068080457 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.24846612489560820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.2076810016087851 " " y1[1] (numeric) = -0.20768100160878467 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.13832370996845800000000000000E-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 = 0.2031528510722095 " " Order of pole (three term test) = 22.04313139842923 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.20315285107220957 " " Order of pole (three term test) = 22.956868601570772 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y2[1] (analytic) = 0.9760709219825239 " " y2[1] (numeric) = 0.9760709219825252 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.36492912507237020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.21745242068136594 " " y1[1] (numeric) = -0.2174524206813655 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.04223622095607130000000000000E-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 = 0.2122489847417924 " " Order of pole (three term test) = 22.04728555526019 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.21224898474179238 " " Order of pole (three term test) = 22.95271444473981 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y2[1] (analytic) = 0.9738476308781949 " " y2[1] (numeric) = 0.9738476308781961 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.25404148284098570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.22720209469308839 " " y1[1] (numeric) = -0.22720209469308794 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.95459998047092000000000000000E-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 = 0.2212602216474273 " " Order of pole (three term test) = 22.051620791832928 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.22126022164742737 " " Order of pole (three term test) = 22.948379208167065 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y2[1] (analytic) = 0.971526955822315 " " y2[1] (numeric) = 0.9715269558223163 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.37131308767705430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.23692904868467599 " " y1[1] (numeric) = -0.23692904868467554 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.87435526506963630000000000000E-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 = 0.23018295741450043 " " Order of pole (three term test) = 22.056135374110625 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23018295741450043 " " Order of pole (three term test) = 22.943864625889375 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y2[1] (analytic) = 0.9691091288804561 " " y2[1] (numeric) = 0.9691091288804573 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.2601731742001970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.2466323099688353 " " y1[1] (numeric) = -0.24663230996883487 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.80061245789806760000000000000E-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 = 0.23901362306767268 " " Order of pole (three term test) = 22.060827496320563 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.23901362306767263 " " Order of pole (three term test) = 22.939172503679437 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y2[1] (analytic) = 0.9665943918332972 " " y2[1] (numeric) = 0.9665943918332985 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.37831094490765080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.256310908227524 " " y1[1] (numeric) = -0.25631090822752356 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.7326192354476389000000000000E-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 = 0.24774868645842363 " " Order of pole (three term test) = 22.065695281676422 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.24774868645842363 " " Order of pole (three term test) = 22.93430471832358 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y2[1] (analytic) = 0.9639829961524478 " " y2[1] (numeric) = 0.9639829961524491 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.382044740278280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.26596387560898166 " " y1[1] (numeric) = -0.2659638756089812 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.66973506771633780000000000000E-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 = 0.2563846536778632 " " Order of pole (three term test) = 22.070736783128947 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2563846536778632 " " Order of pole (three term test) = 22.929263216871053 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y2[1] (analytic) = 0.9612752029752996 " " y2[1] (numeric) = 0.9612752029753009 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.38593778912283140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.2755902468245142 " " y1[1] (numeric) = -0.2755902468245138 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.6114111982084850000000000000E-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 = 0.26491807045424787 " " Order of pole (three term test) = 22.0759499841448 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.26491807045424787 " " Order of pole (three term test) = 22.924050015855205 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y2[1] (analytic) = 0.9584712830789138 " " y2[1] (numeric) = 0.9584712830789152 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.3899922231060710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.28518905924502214 " " y1[1] (numeric) = -0.2851890592450217 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.55717477741150050000000000000E-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 = 0.2733455235346447 " " Order of pole (three term test) = 22.08133279951306 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.27334552353464475 " " Order of pole (three term test) = 22.91866720048694 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y2[1] (analytic) = 0.9555715168529435 " " y2[1] (numeric) = 0.955571516852945 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.51039446714150730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.29475935299726225 " " y1[1] (numeric) = -0.29475935299726186 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.31828915577248520000000000000E-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 = 0.2816636420501861 " " Order of pole (three term test) = 22.086883076179365 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2816636420501862 " " Order of pole (three term test) = 22.913116923820635 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y2[1] (analytic) = 0.9525761942715949 " " y2[1] (numeric) = 0.9525761942715963 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.5151438180925170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3043001710598347 " " y1[1] (numeric) = -0.30430017105983426 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.45937877163644800000000000000E-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 = 0.28986909886437257 " " Order of pole (three term test) = 22.092598594107052 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.2898690988643726 " " Order of pole (three term test) = 22.90740140589295 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y2[1] (analytic) = 0.94948561486463 " " y2[1] (numeric) = 0.9494856148646315 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.52007561717349030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.31381055935888374 " " y1[1] (numeric) = -0.3138105593588833 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.41515062704498760000000000000E-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 = 0.2979586119038833 " " Order of pole (three term test) = 22.09847706716514 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.29795861190388323 " " Order of pole (three term test) = 22.90152293283486 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y2[1] (analytic) = 0.946300087687414 " " y2[1] (numeric) = 0.9463000876874155 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.52519264321304530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3232895668635048 " " y1[1] (numeric) = -0.3232895668635044 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.20195050644138250000000000000E-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 = 0.3059289454713607 " " Order of pole (three term test) = 22.10451614404279 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30592894547136057 " " Order of pole (three term test) = 22.89548385595721 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y2[1] (analytic) = 0.94301993129001 " " y2[1] (numeric) = 0.9430199312900115 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.5304978019269921000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.33273624568084664 " " y1[1] (numeric) = -0.3327362456808462 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.33465835361989170000000000000E-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 = 0.3137769115396478 " " Order of pole (three term test) = 22.110713409189785 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3137769115396477 " " Order of pole (three term test) = 22.889286590810215 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y2[1] (analytic) = 0.9396454736853244 " " y2[1] (numeric) = 0.9396454736853258 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.5359941301606730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3421496511508996 " " y1[1] (numeric) = -0.34214965115089924 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.13569619992810890000000000000E-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 = 0.3214993710269556 " " Order of pole (three term test) = 22.117066383782678 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3214993710269556 " " Order of pole (three term test) = 22.88293361621732 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y2[1] (analytic) = 0.9361770523163055 " " y2[1] (numeric) = 0.9361770523163069 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.42309366188144440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3515288419409613 " " y1[1] (numeric) = -0.3515288419409609 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.10539452886220320000000000000E-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 = 0.3290932350524536 " " Order of pole (three term test) = 22.12357252671635 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3290932350524536 " " Order of pole (three term test) = 22.87642747328365 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y2[1] (analytic) = 0.9326150140221999 " " y2[1] (numeric) = 0.9326150140222013 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.42852903879850530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3608728801397686 " " y1[1] (numeric) = -0.3608728801397682 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.07677268091829400000000000000E-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 = 0.3365554661717819 " " Order of pole (three term test) = 22.130229235620376 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3365554661717818 " " Order of pole (three term test) = 22.869770764379624 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y2[1] (analytic) = 0.9289597150038688 " " y2[1] (numeric) = 0.9289597150038701 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.43415005842814140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3701808313512883 " " y1[1] (numeric) = -0.37018083135128793 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.04969794681253540000000000000E-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 = 0.3438830795919879 " " Order of pole (three term test) = 22.13703384789993 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.34388307959198794 " " Order of pole (three term test) = 22.86296615210007 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y2[1] (analytic) = 0.9252115207881677 " " y2[1] (numeric) = 0.925211520788169 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.43996005196223440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3794517647881559 " " y1[1] (numeric) = -0.3794517647881555 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.02405126205103850000000000000E-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 = 0.35107314436540377 " " Order of pole (three term test) = 22.143983641800844 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3510731443654039 " " Order of pole (three term test) = 22.85601635819915 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y2[1] (analytic) = 0.9213708061913948 " " y2[1] (numeric) = 0.9213708061913961 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.44596249479326170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.38868475336475344 " " y1[1] (numeric) = -0.38868475336475306 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.99725497990273400000000000000E-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 = 0.35812278456198626 " " Order of pole (three term test) = 22.151075837498215 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3581227845619863 " " Order of pole (three term test) = 22.848924162501778 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y2[1] (analytic) = 0.9174379552818093 " " y2[1] (numeric) = 0.9174379552818105 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.33114759429431130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.3978788737899174 " " y1[1] (numeric) = -0.397878873789917 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.76624003474928200000000000000E-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 = 0.36502918041965066 " " Order of pole (three term test) = 22.158307598208335 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3650291804196506 " " Order of pole (three term test) = 22.841692401791665 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y2[1] (analytic) = 0.9134133613412245 " " y2[1] (numeric) = 0.9134133613412259 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.45855938388500470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.40703320665926696 " " y1[1] (numeric) = -0.40703320665926657 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.54659355211008200000000000000E-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 = 0.3717895694721383 " " Order of pole (three term test) = 22.165676031323322 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37178956947213837 " " Order of pole (three term test) = 22.83432396867667 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y2[1] (analytic) = 0.9092974268256812 " " y2[1] (numeric) = 0.9092974268256824 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 1.3430647564361730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.4161468365471436 " " y1[1] (numeric) = -0.4161468365471434 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.00179549784725100000000000000E-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 = 0.37840124765396516 " " Order of pole (three term test) = 22.173178189568198 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37840124765396516 " " Order of pole (three term test) = 22.826821810431806 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y2[1] (analytic) = 0.9050905633252004 " " y2[1] (numeric) = 0.9050905633252015 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.22664302293277990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.4252188520981534 " " y1[1] (numeric) = -0.4252188520981534 " " 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 = 0.3848615703820129 " " Order of pole (three term test) = 22.180811072179672 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.384861570382013 " " Order of pole (three term test) = 22.81918892782033 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y2[1] (analytic) = 0.9007931915226269 " " y2[1] (numeric) = 0.9007931915226278 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.8599592898656500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.43424834611830126 " " y1[1] (numeric) = -0.4342483461183015 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.11330916766555100000000000000E-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 = 0.39116795361332685 " " Order of pole (three term test) = 22.18857162610648 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3911679536133269 " " Order of pole (three term test) = 22.811428373893516 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y2[1] (analytic) = 0.8964057411515596 " " y2[1] (numeric) = 0.8964057411515604 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.66969143057074700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.4432344156657097 " " y1[1] (numeric) = -0.44323441566571015 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.00192853748296840000000000000E-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 = 0.397317874878699 " " Order of pole (three term test) = 22.196456747230524 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.397317874878699 " " Order of pole (three term test) = 22.803543252769472 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y2[1] (analytic) = 0.8919286509533794 " " y2[1] (numeric) = 0.89192865095338 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.46846526415611600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.4521761621409124 " " y1[1] (numeric) = -0.452176162140913 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.35040878902755350000000000000E-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 = 0.40330887429162043 " " Order of pole (three term test) = 22.204463281608486 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4033088742916205 " " Order of pole (three term test) = 22.795536718391514 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y2[1] (analytic) = 0.8873623686333753 " " y2[1] (numeric) = 0.8873623686333758 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.25574772984236600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.46107269137671314 " " y1[1] (numeric) = -0.461072691376714 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 1.80593490796996240000000000000E-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 = 0.4091385555322053 " " Order of pole (three term test) = 22.212588026733364 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.40913855553220546 " " Order of pole (three term test) = 22.787411973266636 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y2[1] (analytic) = 0.8827073508159741 " " y2[1] (numeric) = 0.8827073508159744 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.773242706992982500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.4699231137276022 " " y1[1] (numeric) = -0.46992311372760326 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 2.2444349779425360000000000000E-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 = 0.4148045868056853 " " Order of pole (three term test) = 22.220827732815447 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.779172267184553 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y2[1] (analytic) = 0.8779640629990781 " " y2[1] (numeric) = 0.8779640629990784 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.529085349650176400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.4787265441587198 " " y1[1] (numeric) = -0.47872654415872107 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 2.6669849288649990000000000000E-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 = 0.4203047017750973 " " Order of pole (three term test) = 22.229179104082153 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42030470177509743 " " Order of pole (three term test) = 22.77082089591785 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y2[1] (analytic) = 0.8731329795075167 " " y2[1] (numeric) = 0.8731329795075168 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.27153944551649900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.487482102334359 " " y1[1] (numeric) = -0.48748210233436046 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 2.96070342911331300000000000000E-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 = 0.42563670046778723 " " Order of pole (three term test) = 22.237638800096324 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.762361199903673 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y2[1] (analytic) = 0.8682145834456129 " " y2[1] (numeric) = 0.8682145834456128 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.27874265854773400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.49618891270599846 " " y1[1] (numeric) = -0.49618891270600013 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 3.3562510049967154000000000000E-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 = 0.4307984501553699 " " Order of pole (three term test) = 22.246203437092355 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43079845015537 " " Order of pole (three term test) = 22.753796562907635 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y2[1] (analytic) = 0.8632093666488742 " " y2[1] (numeric) = 0.8632093666488739 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.572314591384084500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.5048461045998568 " " y1[1] (numeric) = -0.5048461045998586 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.5186105690727250000000000000E-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 = 0.43578788620679343 " " Order of pole (three term test) = 22.25486958932964 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.43578788620679365 " " Order of pole (three term test) = 22.745130410670356 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y2[1] (analytic) = 0.8581178296348094 " " y2[1] (numeric) = 0.858117829634809 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.17515420975525400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.5134528123039588 " " y1[1] (numeric) = -0.5134528123039607 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 3.67585705372562470000000000000E-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 = 0.44060301291416215 " " Order of pole (three term test) = 22.263633790462844 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.73636620953716 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y2[1] (analytic) = 0.8529404815528769 " " y2[1] (numeric) = 0.8529404815528764 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.5082092398983500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.5220081751547062 " " y1[1] (numeric) = -0.5220081751547083 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 4.04097837387821100000000000000E-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 = 0.44524190429099375 " " Order of pole (three term test) = 22.272492534928343 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44524190429099364 " " Order of pole (three term test) = 22.727507465071653 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y2[1] (analytic) = 0.8476778401335705 " " y2[1] (numeric) = 0.8476778401335698 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.85833701480422900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.5305113376229437 " " y1[1] (numeric) = -0.5305113376229459 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 4.1854827442509360000000000000E-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 = 0.4497027048425882 " " Order of pole (three term test) = 22.281442279346482 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.44970270484258823 " " Order of pole (three term test) = 22.718557720653514 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y2[1] (analytic) = 0.8423304316366466 " " y2[1] (numeric) = 0.8423304316366458 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.22626190445947300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " y1[1] (analytic) = -0.5389614493995101 " " y1[1] (numeric) = -0.5389614493995125 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 4.53184667826738400000000000000E-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 = 0.453983630308202 " " Order of pole (three term test) = 22.290479443938825 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.453983630308202 " " Order of pole (three term test) = 22.70952055606118 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y2[1] (analytic) = 0.8368987907984987 " " y2[1] (numeric) = 0.8368987907984977 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 1.19393256765168380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5473576654802695 " " y1[1] (numeric) = -0.5473576654802722 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.8679966083281680000000000000E-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 = 0.45808296837472673 " " Order of pole (three term test) = 22.299600413960007 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4580829683747267 " " Order of pole (three term test) = 22.70039958603999 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y2[1] (analytic) = 0.8313834607786843 " " y2[1] (numeric) = 0.8313834607786832 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.335392243171770200000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5556991462506109 " " y1[1] (numeric) = -0.5556991462506137 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 4.9947126611404974000000000000E-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 = 0.46199907936159323 " " Order of pole (three term test) = 22.30880154114366 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4619990793615933 " " Order of pole (three term test) = 22.691198458856345 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y2[1] (analytic) = 0.8257849931056094 " " y2[1] (numeric) = 0.825784993105608 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.61333475501873740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5639850575694082 " " y1[1] (numeric) = -0.5639850575694112 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 5.3150382731886750000000000000E-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 = 0.4657303968766202 " " Order of pole (three term test) = 22.318079145161565 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4657303968766205 " " Order of pole (three term test) = 22.681920854838435 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y2[1] (analytic) = 0.8201039476213756 " " y2[1] (numeric) = 0.8201039476213742 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 1.75988658047411230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5722145708524347 " " y1[1] (numeric) = -0.5722145708524378 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 5.4326202569771760000000000000E-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 = 0.46927542844255304 " " Order of pole (three term test) = 22.327429515095833 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4692754284425531 " " Order of pole (three term test) = 22.672570484904163 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y2[1] (analytic) = 0.8143408924257975 " " y2[1] (numeric) = 0.8143408924257958 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.18134304186635350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5803868631552197 " " y1[1] (numeric) = -0.5803868631552229 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 5.5474149671645590000000000000E-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 = 0.47263275609403094 " " Order of pole (three term test) = 22.33684891092316 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4726327560940308 " " Order of pole (three term test) = 22.66315108907684 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y2[1] (analytic) = 0.8084964038195919 " " y2[1] (numeric) = 0.80849640381959 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 2.33443109078307870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5885011172553434 " " y1[1] (numeric) = -0.5885011172553467 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 5.6595798652160130000000000000E-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 = 0.4758010369447571 " " Order of pole (three term test) = 22.346333565010788 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47580103694475717 " " Order of pole (three term test) = 22.65366643498921 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y2[1] (analytic) = 0.8025710662467491 " " y2[1] (numeric) = 0.802571066246747 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 2.62833266174494650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.5965565217341574 " " y1[1] (numeric) = -0.596556521734161 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.9553680990243060000000000000E-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 = 0.4787790037246346 " " Order of pole (three term test) = 22.355879683623552 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4787790037246346 " " Order of pole (three term test) = 22.64412031637644 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y2[1] (analytic) = 0.7965654722360886 " " y2[1] (numeric) = 0.7965654722360863 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 2.9269010934757420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6045522710579269 " " y1[1] (numeric) = -0.6045522710579305 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 6.060246825062321000000000000E-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 = 0.48156546528665733 " " Order of pole (three term test) = 22.3654834484413 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48156546528665733 " " Order of pole (three term test) = 22.6345165515587 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y2[1] (analytic) = 0.790480222342007 " " y2[1] (numeric) = 0.7904802223420044 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 3.23033123975246530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6124875656583824 " " y1[1] (numeric) = -0.6124875656583862 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 6.3442603638999580000000000000E-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 = 0.48415930708335253 " " Order of pole (three term test) = 22.37514101808613 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4841593070833527 " " Order of pole (three term test) = 22.624858981913867 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y2[1] (analytic) = 0.7843159250844224 " " y2[1] (numeric) = 0.7843159250844196 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 3.5388259664167027000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6203616120126767 " " y1[1] (numeric) = -0.6203616120126807 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 6.4426985991017300000000000000E-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 = 0.486559491612586 " " Order of pole (three term test) = 22.384848529658964 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48655949161258594 " " Order of pole (three term test) = 22.615151470341036 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y2[1] (analytic) = 0.7780731968879238 " " y2[1] (numeric) = 0.7780731968879208 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 3.8525966174872710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.628173622722736 " " y1[1] (numeric) = -0.6281736227227401 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 6.5393149959214310000000000000E-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 = 0.4887650588325476 " " Order of pole (three term test) = 22.394602100284605 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4887650588325476 " " Order of pole (three term test) = 22.605397899715395 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y2[1] (analytic) = 0.7717526620201285 " " y2[1] (numeric) = 0.7717526620201253 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 4.1718635125731257000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6359228165939993 " " y1[1] (numeric) = -0.6359228165940036 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 6.8087976764678460000000000000E-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 = 0.4907751265457569 " " Order of pole (three term test) = 22.404397828664845 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4907751265457569 " " Order of pole (three term test) = 22.59560217133515 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y2[1] (analytic) = 0.7653549525292563 " " y2[1] (numeric) = 0.7653549525292529 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 4.49685647811421700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6436084187135371 " " y1[1] (numeric) = -0.6436084187135416 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.8999906921311070000000000000E-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 = 0.49258889075192897 " " Order of pole (three term test) = 22.414231796638934 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49258889075192897 " " Order of pole (three term test) = 22.58576820336106 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y2[1] (analytic) = 0.7588807081809249 " " y2[1] (numeric) = 0.7588807081809212 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 4.8278154152121955000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6512296605275422 " " y1[1] (numeric) = -0.6512296605275467 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 6.9897221776965260000000000000E-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 = 0.49420562596956463 " " Order of pole (three term test) = 22.424100070750814 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49420562596956447 " " Order of pole (three term test) = 22.57589992924918 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y2[1] (analytic) = 0.7523305763941739 " " y2[1] (numeric) = 0.75233057639417 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 5.1649909070718710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6587857799181841 " " y1[1] (numeric) = -0.6587857799181887 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 6.9095516930077840000000000000E-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 = 0.4956246855261329 " " Order of pole (three term test) = 22.43399870382241 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49562468552613287 " " Order of pole (three term test) = 22.566001296177593 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y2[1] (analytic) = 0.7457052121767236 " " y2[1] (numeric) = 0.7457052121767194 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 5.6575271631275350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6662760212798204 " " y1[1] (numeric) = -0.6662760212798251 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 6.9985059562384170000000000000E-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 = 0.4968455018167317 " " Order of pole (three term test) = 22.44392373653247 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49684550181673154 " " Order of pole (three term test) = 22.55607626346753 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y2[1] (analytic) = 0.7390052780594745 " " y2[1] (numeric) = 0.73900527805947 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.0092833303732200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.673699635594557 " " y1[1] (numeric) = -0.6736996355945618 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 7.0861831499656860000000000000E-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 = 0.4978675865311221 " " Order of pole (three term test) = 22.453871199000236 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4978675865311222 " " Order of pole (three term test) = 22.546128800999767 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y2[1] (analytic) = 0.7322314440302551 " " y2[1] (numeric) = 0.7322314440302504 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 6.3681186344040540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6810558805071486 " " y1[1] (numeric) = -0.6810558805071535 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 7.1726585852442600000000000000E-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 = 0.4986905308490462 " " Order of pole (three term test) = 22.463837112373366 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49869053084904624 " " Order of pole (three term test) = 22.536162887626634 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y2[1] (analytic) = 0.7253843874668235 " " y2[1] (numeric) = 0.7253843874668187 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 6.7343347785716020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6883440203992341 " " y1[1] (numeric) = -0.6883440203992391 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 7.2580039380825320000000000000E-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 = 0.49931400560374917 " " Order of pole (three term test) = 22.473817490419382 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49931400560374917 " " Order of pole (three term test) = 22.526182509580625 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y2[1] (analytic) = 0.7184647930691302 " " y2[1] (numeric) = 0.7184647930691251 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 7.1082479789435220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.6955633264628979 " " y1[1] (numeric) = -0.695563326462903 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 7.3422874941468540000000000000E-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 = 0.4997377614136418 " " Order of pole (three term test) = 22.483808341120138 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4997377614136419 " " Order of pole (three term test) = 22.516191658879873 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y2[1] (analytic) = 0.7114733527908488 " " y2[1] (numeric) = 0.7114733527908433 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 7.6462355186231220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.7027130767735495 " " y1[1] (numeric) = -0.7027130767735547 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 7.2675834306716170000000000000E-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 = 0.49996162878205036 " " Order of pole (three term test) = 22.49380566826855 " " "NO COMPLEX POLE (six term test) for Equation 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) = 22.506194331731454 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y2[1] (analytic) = 0.7044107657701806 " " y2[1] (numeric) = 0.7044107657701749 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 8.0381188089842660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.7097925563621161 " " y1[1] (numeric) = -0.7097925563621214 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 7.3515116057037580000000000000E-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 = 0.49998551816501224 " " Order of pole (three term test) = 22.503805473067068 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49998551816501247 " " Order of pole (three term test) = 22.496194526932936 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y2[1] (analytic) = 0.6972777382599425 " " y2[1] (numeric) = 0.6972777382599366 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 8.5980148282618130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.7168010572865383 " " y1[1] (numeric) = -0.7168010572865436 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 7.4345182167755620000000000000E-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 = 0.4998094200070928 " " Order of pole (three term test) = 22.513803755727096 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4998094200070929 " " Order of pole (three term test) = 22.4861962442729 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y2[1] (analytic) = 0.6900749835569413 " " y2[1] (numeric) = 0.6900749835569351 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 9.0095266254320930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.723737878702564 " " y1[1] (numeric) = -0.7237378787025694 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 7.5166617372793230000000000000E-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 = 0.49943340474520737 " " Order of pole (three term test) = 22.52379651706888 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49943340474520753 " " Order of pole (three term test) = 22.476203482931112 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y2[1] (analytic) = 0.6828032219306449 " " y2[1] (numeric) = 0.6828032219306385 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 9.4306724631712020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " y1[1] (analytic) = -0.7306023269338324 " " y1[1] (numeric) = -0.7306023269338379 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 7.4460381798865440000000000000E-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 = 0.4988576227804471 " " Order of pole (three term test) = 22.533779760121128 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4988576227804471 " " Order of pole (three term test) = 22.46622023987887 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y2[1] (analytic) = 0.6754631805511563 " " y2[1] (numeric) = 0.6754631805511495 " " absolute error = 6.772360450213455000000000000000E-15 " " relative error = 1.0026246648540378000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7373937155412407 " " y1[1] (numeric) = -0.7373937155412462 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 7.528020657256770000000000000E-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 = 0.49808230441792095 " " Order of pole (three term test) = 22.543749491719716 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4980823044179209 " " Order of pole (three term test) = 22.45625050828028 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y2[1] (analytic) = 0.6680555934164966 " " y2[1] (numeric) = 0.6680555934164896 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 1.0469794915372936000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7441113653915875 " " y1[1] (numeric) = -0.7441113653915932 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 7.6092607759170660000000000000E-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 = 0.4971077597746363 " " Order of pole (three term test) = 22.553701724104933 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49710775977463667 " " Order of pole (three term test) = 22.44629827589507 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y2[1] (analytic) = 0.6605812012792064 " " y2[1] (numeric) = 0.6605812012791992 " " absolute error = 7.216449660063518000000000000000E-15 " " relative error = 1.0924394527257153000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7507546047254859 " " y1[1] (numeric) = -0.7507546047254917 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 7.6898092821712030000000000000E-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 = 0.4959343786554572 " " Order of pole (three term test) = 22.563632476516517 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49593437865545736 " " Order of pole (three term test) = 22.436367523483476 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y2[1] (analytic) = 0.6530407515722708 " " y2[1] (numeric) = 0.6530407515722633 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 1.1560559657685579000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7573227692245386 " " y1[1] (numeric) = -0.7573227692245444 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 7.769714934807049000000000000E-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 = 0.49456263039718595 " " Order of pole (three term test) = 22.57353777678592 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.494562630397186 " " Order of pole (three term test) = 22.426462223214077 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y2[1] (analytic) = 0.6454349983343768 " " y2[1] (numeric) = 0.645434998334369 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 1.2040811533975615000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7638152020777689 " " y1[1] (numeric) = -0.7638152020777749 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 7.8490246288204080000000000000E-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 = 0.4929930636808364 " " Order of pole (three term test) = 22.583413662925103 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49299306368083634 " " Order of pole (three term test) = 22.416586337074893 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y2[1] (analytic) = 0.6377647021345101 " " y2[1] (numeric) = 0.637764702134502 " " absolute error = 8.104628079763643000000000000000E-15 " " relative error = 1.2707865538244084000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7702312540473021 " " y1[1] (numeric) = -0.7702312540473081 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 7.7836419925484650000000000000E-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 = 0.49122630631216785 " " Order of pole (three term test) = 22.59325618471128 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.49122630631216785 " " Order of pole (three term test) = 22.406743815288724 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y2[1] (analytic) = 0.6300306299958988 " " y2[1] (numeric) = 0.6300306299958903 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 1.339251551500935000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7765702835332877 " " y1[1] (numeric) = -0.7765702835332938 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 7.8630701752530010000000000E-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 = 0.4892630649705709 " " Order of pole (three term test) = 22.60306140526697 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4892630649705709 " " Order of pole (three term test) = 22.396938594733026 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y2[1] (analytic) = 0.6222335553193116 " " y2[1] (numeric) = 0.6222335553193029 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 1.3917185143819996000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7828316566380599 " " y1[1] (numeric) = -0.782831656638066 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 7.8001784721661540000000000000E-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 = 0.4871041249264066 " " Order of pole (three term test) = 22.612825402634694 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48710412492640653 " " Order of pole (three term test) = 22.38717459736531 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y2[1] (analytic) = 0.6143742578057187 " " y2[1] (numeric) = 0.6143742578057098 " " absolute error = 8.992806499463768000000000000000E-15 " " relative error = 1.4637342605437628000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7890147472295257 " " y1[1] (numeric) = -0.7890147472295318 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 7.7390526056442010000000000000E-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 = 0.48475034972690645 " " Order of pole (three term test) = 22.62254427134567 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.48475034972690656 " " Order of pole (three term test) = 22.377455728654326 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y2[1] (analytic) = 0.6064535233783221 " " y2[1] (numeric) = 0.6064535233783128 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 1.5377721535692330000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.7951189370037787 " " y1[1] (numeric) = -0.7951189370037848 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 7.6796392983020370000000000000E-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 = 0.4822026808507676 " " Order of pole (three term test) = 22.632214123982017 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4822026808507676 " " Order of pole (three term test) = 22.367785876017976 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y2[1] (analytic) = 0.598472144103964 " " y2[1] (numeric) = 0.5984721441039543 " " absolute error = 9.658940314238862000000000000000E-15 " " relative error = 1.6139331478326838000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8011436155469281 " " y1[1] (numeric) = -0.8011436155469344 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 7.7604674333658120000000000000E-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 = 0.4794621373315719 " " Order of pole (three term test) = 22.641831092731604 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47946213733157195 " " Order of pole (three term test) = 22.358168907268393 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y2[1] (analytic) = 0.5904309181139206 " " y2[1] (numeric) = 0.5904309181139106 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 1.6923245235098788000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8070881803961404 " " y1[1] (numeric) = -0.8070881803961467 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.8408671989934330000000000000E-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 = 0.4765298153501867 " " Order of pole (three term test) = 22.651391330935155 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4765298153501867 " " Order of pole (three term test) = 22.348608669064845 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y2[1] (analytic) = 0.5823306495240899 " " y2[1] (numeric) = 0.5823306495240795 " " absolute error = 1.032507412901395600000000000000E-14 " " relative error = 1.7730603974652767000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8129520370998843 " " y1[1] (numeric) = -0.8129520370998906 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.7843106992373060000000000000E-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 = 0.47340688779630763 " " Order of pole (three term test) = 22.660891014624852 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.47340688779630763 " " Order of pole (three term test) = 22.339108985375145 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y2[1] (analytic) = 0.5741721483545806 " " y2[1] (numeric) = 0.5741721483545701 " " absolute error = 1.054711873393898700000000000000E-14 " " relative error = 1.8369262187593263000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.818734599277376 " " y1[1] (numeric) = -0.8187345992773823 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.7293316368317560000000000000E-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 = 0.47009460379931756 " " Order of pole (three term test) = 22.670326344053887 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4700946037993175 " " Order of pole (three term test) = 22.329673655946113 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y2[1] (analytic) = 0.5659562304487112 " " y2[1] (numeric) = 0.5659562304487004 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 1.92244294805277020000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8244352886772165 " " y1[1] (numeric) = -0.8244352886772228 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.6758859394737060000000000000E-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 = 0.4665942882286524 " " Order of pole (three term test) = 22.679693545216278 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4665942882286526 " " Order of pole (three term test) = 22.32030645478372 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y2[1] (analytic) = 0.5576837173914255 " " y2[1] (numeric) = 0.5576837173914143 " " absolute error = 1.121325254871408100000000000000E-14 " " relative error = 2.010683152300779000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8300535352352164 " " y1[1] (numeric) = -0.8300535352352227 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.6239314354225580000000000000E-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 = 0.4629073411638701 " " Order of pole (three term test) = 22.68898887135648 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4629073411638702 " " Order of pole (three term test) = 22.311011128643525 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y2[1] (analytic) = 0.5493554364271356 " " y2[1] (numeric) = 0.549355436427124 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 2.101793973533033200000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8355887771314018 " " y1[1] (numeric) = -0.8355887771314081 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.5734277596313750000000000000E-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 = 0.45903523733463786 " " Order of pole (three term test) = 22.698208604467958 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45903523733463786 " " Order of pole (three term test) = 22.301791395532053 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y2[1] (analytic) = 0.5409722203769975 " " y2[1] (numeric) = 0.5409722203769857 " " absolute error = 1.187938636348917500000000000000E-14 " " relative error = 2.195932788417594200000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8410404608461957 " " y1[1] (numeric) = -0.841040460846202 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.5243362655779160000000000000E-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 = 0.4549795255308599 " " Order of pole (three term test) = 22.70734905678038 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45497952553085985 " " Order of pole (three term test) = 22.292650943219623 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y2[1] (analytic) = 0.5325349075556305 " " y2[1] (numeric) = 0.5325349075556183 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 2.293268121508254000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8464080412157696 " " y1[1] (numeric) = -0.846408041215776 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.4766199424021830000000000000E-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 = 0.4507418279831823 " " Order of pole (three term test) = 22.71640657223472 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.45074182798318213 " " Order of pole (three term test) = 22.28359342776528 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y2[1] (analytic) = 0.5240443416872855 " " y2[1] (numeric) = 0.524044341687273 " " absolute error = 1.254552017826427000000000000000E-14 " " relative error = 2.3939806577952885000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8516909814865598 " " y1[1] (numeric) = -0.8516909814865661 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.4302433369881320000000000000E-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 = 0.4463238397141224 " " Order of pole (three term test) = 22.72537752794554 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4463238397141224 " " Order of pole (three term test) = 22.27462247205446 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y2[1] (analytic) = 0.515501371821474 " " y2[1] (numeric) = 0.5155013718214612 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 2.498264367395683000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8568887533689413 " " y1[1] (numeric) = -0.8568887533689477 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.3851724806553710000000000000E-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 = 0.44172732786008195 " " Order of pole (three term test) = 22.734258335650175 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4417273278600821 " " Order of pole (three term test) = 22.265741664349825 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y2[1] (analytic) = 0.5069068522480634 " " y2[1] (numeric) = 0.5069068522480502 " " absolute error = 1.321165399303936300000000000000E-14 " " relative error = 2.606327757150542000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8620008370900576 " " y1[1] (numeric) = -0.8620008370900639 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 7.3413748201525760000000000000E-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 = 0.43695413096451685 " " Order of pole (three term test) = 22.743045443143956 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4369541309645167 " " Order of pole (three term test) = 22.256954556856034 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y2[1] (analytic) = 0.49826164241184895 " " y2[1] (numeric) = 0.4982616424118354 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 2.7183952661624367000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8670267214457965 " " y1[1] (numeric) = -0.8670267214458027 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 7.1707696938491150000000000000E-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 = 0.43200615824254324 " " Order of pole (three term test) = 22.751735335701046 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4320061582425432 " " Order of pole (three term test) = 22.24826466429895 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y2[1] (analytic) = 0.48956660682660996 " " y2[1] (numeric) = 0.4895666068265961 " " absolute error = 1.387778780781445700000000000000E-14 " " relative error = 2.8347088249688485000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8719659038519106 " " y1[1] (numeric) = -0.8719659038519169 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 7.1301514318807310000000000000E-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 = 0.4268853888172779 " " Order of pole (three term test) = 22.760324537480276 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.426885388817278 " " Order of pole (three term test) = 22.239675462519724 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y2[1] (analytic) = 0.48082261498865914 " " y2[1] (numeric) = 0.4808226149886449 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 2.9555296011892424000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8768178903942755 " " y1[1] (numeric) = -0.8768178903942816 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 6.9640762378748880000000000000E-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 = 0.42159387092821515 " " Order of pole (three term test) = 22.768809612915472 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.42159387092821493 " " Order of pole (three term test) = 22.231190387084528 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y2[1] (analytic) = 0.47203054128989363 " " y2[1] (numeric) = 0.47203054128987904 " " absolute error = 1.45994327738208090000000000000E-14 " " relative error = 3.0929000343760993000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.88158219587828 " " y1[1] (numeric) = -0.8815821958782861 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 6.9264405111482620000000000000E-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 = 0.41613372111195746 " " Order of pole (three term test) = 22.77718716808957 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41613372111195734 " " Order of pole (three term test) = 22.222812831910428 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y2[1] (analytic) = 0.46319126493035656 " " y2[1] (numeric) = 0.46319126493034163 " " absolute error = 1.493249968120835500000000000000E-14 " " relative error = 3.2238301565236865000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.886258343877346 " " y1[1] (numeric) = -0.8862583438773521 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 6.8898946651648480000000000000E-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 = 0.410507123355631 " " Order of pole (three term test) = 22.785453852092218 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.41050712335563105 " " Order of pole (three term test) = 22.214546147907786 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y2[1] (analytic) = 0.45430566983031795 " " y2[1] (numeric) = 0.4543056698303026 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 3.372416141218212000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8908458667805706 " " y1[1] (numeric) = -0.8908458667805766 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 6.7297885712170660000000000000E-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 = 0.40471632822331727 " " Order of pole (three term test) = 22.793606358360023 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.4047163282233174 " " Order of pole (three term test) = 22.206393641639973 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y2[1] (analytic) = 0.4453746445418831 " " y2[1] (numeric) = 0.4453746445418674 " " absolute error = 1.565414464721470700000000000000E-14 " " relative error = 3.5148261893796673000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8953443058394861 " " y1[1] (numeric) = -0.8953443058394921 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 6.6959763901716740000000000000E-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 = 0.3987636519558602 " " Order of pole (three term test) = 22.801641425999193 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3987636519558602 " " Order of pole (three term test) = 22.19835857400081 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y2[1] (analytic) = 0.4363990821601383 " " y2[1] (numeric) = 0.4363990821601223 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 3.663438400343767600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.8997532112139355 " " y1[1] (numeric) = -0.8997532112139414 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 6.5397733035867330000000000000E-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 = 0.39265147554439855 " " Order of pole (three term test) = 22.80955584108979 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3926514755443986 " " Order of pole (three term test) = 22.19044415891021 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y2[1] (analytic) = 0.4273798802338422 " " y2[1] (numeric) = 0.42737988023382584 " " absolute error = 1.63757896132210600000000000000E-14 " " relative error = 3.831670691718337000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9040721420170553 " " y1[1] (numeric) = -0.9040721420170611 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 6.3857290361479830000000000000E-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 = 0.38638224377800245 " " Order of pole (three term test) = 22.817346437971313 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.38638224377800234 " " Order of pole (three term test) = 22.18265356202869 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y2[1] (analytic) = 0.41831794067567146 " " y2[1] (numeric) = 0.4183179406756547 " " absolute error = 1.676436767183986400000000000000E-14 " " relative error = 4.007566026157493000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9083006663593644 " " y1[1] (numeric) = -0.9083006663593701 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 6.3560007626006680000000000000E-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 = 0.3799584642657894 " " Order of pole (three term test) = 22.825010100508866 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.37995846426578944 " " Order of pole (three term test) = 22.174989899491138 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y2[1] (analytic) = 0.4092141696720303 " " y2[1] (numeric) = 0.40921416967201313 " " absolute error = 1.71529457304586690000000000000E-14 " " relative error = 4.1916793214189310000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9124383613919522 " " y1[1] (numeric) = -0.9124383613919579 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 6.2055012866299670000000000000E-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 = 0.37338270643391563 " " Order of pole (three term test) = 22.83254376333963 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3733827064339157 " " Order of pole (three term test) = 22.16745623666037 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y2[1] (analytic) = 0.40006947759243255 " " y2[1] (numeric) = 0.400069477592415 " " absolute error = 1.754152378907747300000000000000E-14 " " relative error = 4.384619365276287000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9164848133487636 " " y1[1] (numeric) = -0.9164848133487692 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 6.0569635658690770000000000000E-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 = 0.3666576004978378 " " Order of pole (three term test) = 22.83994441309892 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.36665760049783774 " " Order of pole (three term test) = 22.16005558690108 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y2[1] (analytic) = 0.3908847788984657 " " y2[1] (numeric) = 0.3908847788984478 " " absolute error = 1.78745906964650200000000000000E-14 " " relative error = 4.572854114922708700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.920439617587975 " " y1[1] (numeric) = -0.9204396175879804 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 5.9103201521454570000000000000E-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 = 0.3597858364102641 " " Order of pole (three term test) = 22.847209089625498 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.35978583641026407 " " Order of pole (three term test) = 22.1527909103745 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y2[1] (analytic) = 0.38166099205234527 " " y2[1] (numeric) = 0.38166099205232695 " " absolute error = 1.831867990631508300000000000000E-14 " " relative error = 4.799725486172466000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9243023786324579 " " y1[1] (numeric) = -0.9243023786324633 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 5.8856202758150430000000000000E-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 = 0.3527701627852064 " " Order of pole (three term test) = 22.854334887145622 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3527701627852063 " " Order of pole (three term test) = 22.145665112854378 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y2[1] (analytic) = 0.3723990394250693 " " y2[1] (numeric) = 0.37239903942505065 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 5.008537842229198000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9280727102093271 " " y1[1] (numeric) = -0.9280727102093324 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 5.6224562562143470000000000000E-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 = 0.34561338579857404 " " Order of pole (three term test) = 22.861318955435287 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.34561338579857404 " " Order of pole (three term test) = 22.138681044564713 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y2[1] (analytic) = 0.36309984720418237 " " y2[1] (numeric) = 0.36309984720416333 " " absolute error = 1.904032487232143500000000000000E-14 " " relative error = 5.243826186909538000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9317502352885667 " " y1[1] (numeric) = -0.9317502352885718 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 5.4811104090508270000000000000E-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 = 0.33831836806573956 " " Order of pole (three term test) = 22.868158500960302 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3383183680657395 " " Order of pole (three term test) = 22.1318414990397 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y2[1] (analytic) = 0.35376434530115725 " " y2[1] (numeric) = 0.3537643453011378 " " absolute error = 1.94289029309402400000000000000E-14 " " relative error = 5.492046665810977000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9353345861207334 " " y1[1] (numeric) = -0.9353345861207384 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 5.3414079677454770000000000000E-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 = 0.3308880274965302 " " Order of pole (three term test) = 22.874850787993648 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3308880274965301 " " Order of pole (three term test) = 22.125149212006352 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y2[1] (analytic) = 0.3443934672584046 " " y2[1] (numeric) = 0.3443934672583848 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 5.73819532514536000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9388254042737308 " " y1[1] (numeric) = -0.9388254042737357 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 5.2032905012084520000000000000E-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 = 0.3233253361281034 " " Order of pole (three term test) = 22.88139313970973 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.32332533612810344 " " Order of pole (three term test) = 22.118606860290267 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y2[1] (analytic) = 0.3349881501559197 " " y2[1] (numeric) = 0.33498815015589956 " " absolute error = 2.01505478969465900000000000000E-14 " " relative error = 6.015301701737077000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9422223406686528 " " y1[1] (numeric) = -0.9422223406686576 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 5.0667011381839110000000000000E-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 = 0.31563331893617297 " " Order of pole (three term test) = 22.887782939255118 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.3156333189361729 " " Order of pole (three term test) = 22.112217060744886 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y2[1] (analytic) = 0.3255493345175751 " " y2[1] (numeric) = 0.3255493345175546 " " absolute error = 2.053912595556539600000000000000E-14 " " relative error = 6.309067099154696000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.9455250556146907 " " y1[1] (numeric) = -0.9455250556146954 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 4.9315844944947110000000000000E-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 = 0.3078150526250559 " " Order of pole (three term test) = 22.894017630795158 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.30781505262505593 " " Order of pole (three term test) = 22.10598236920484 " " "NO COMPLEX POLE (six term test) for Equation 2" " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y2[1] (analytic) = 0.31607796421706896 " " y2[1] (numeric) = 0.31607796421704804 " " absolute error = 2.0927704014184200000000000000E-14 " " relative error = 6.62105758179711000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " y1[1] (analytic) = -0.948733218843102 " " y1[1] (numeric) = -0.9487332188431065 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 4.6808649790042234000000000000E-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 = 0.29987366439703445 " " Order of pole (three term test) = 22.90009472053639 " " "NO COMPLEX POLE (six term test) for Equation 1" "NO INFO (given) for Equation 2" "NO POLE (ratio test) for Equation 2" Radius of convergence (three term test) for eq 2 = 0.29987366439703456 " " Order of pole (three term test) = 22.09990527946361 " " "NO COMPLEX POLE (six term test) for Equation 2" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y2 , x , 3 ) = m1 * cos ( x ) ; " "diff ( y1 , x , 1 ) = m1 * y2 ; " Iterations = 273 "Total Elapsed Time "= 10 Minutes 2 Seconds "Elapsed Time(since restart) "= 9 Minutes 30 Seconds "Expected Time Remaining "= 7 Minutes 54 Seconds "Optimized Time Remaining "= 7 Minutes 29 Seconds "Expected Total Time "= 17 Minutes 32 Seconds "Time to Timeout "= 0.0 Seconds Percent Done = 55.91836734693843 "%" (%o238) true (%o238) diffeq.max