(%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_y_init,MAX_TERMS) (%o150) array_y_init (%i151) array(array_norms,MAX_TERMS) (%o151) array_norms (%i152) array(array_fact_1,MAX_TERMS) (%o152) array_fact_1 (%i153) array(array_1st_rel_error,2) (%o153) array_1st_rel_error (%i154) array(array_last_rel_error,2) (%o154) array_last_rel_error (%i155) array(array_type_pole,2) (%o155) array_type_pole (%i156) array(array_type_real_pole,2) (%o156) array_type_real_pole (%i157) array(array_type_complex_pole,2) (%o157) array_type_complex_pole (%i158) array(array_y,MAX_TERMS) (%o158) array_y (%i159) array(array_x,MAX_TERMS) (%o159) array_x (%i160) array(array_tmp0,MAX_TERMS) (%o160) array_tmp0 (%i161) array(array_tmp1,MAX_TERMS) (%o161) array_tmp1 (%i162) array(array_tmp2,MAX_TERMS) (%o162) array_tmp2 (%i163) array(array_tmp3,MAX_TERMS) (%o163) array_tmp3 (%i164) array(array_tmp4,MAX_TERMS) (%o164) array_tmp4 (%i165) array(array_tmp5,MAX_TERMS) (%o165) array_tmp5 (%i166) array(array_tmp6,MAX_TERMS) (%o166) array_tmp6 (%i167) array(array_m1,MAX_TERMS) (%o167) array_m1 (%i168) array(array_y_higher,2,MAX_TERMS) (%o168) array_y_higher (%i169) array(array_y_higher_work,2,MAX_TERMS) (%o169) array_y_higher_work (%i170) array(array_y_higher_work2,2,MAX_TERMS) (%o170) array_y_higher_work2 (%i171) array(array_y_set_initial,2,MAX_TERMS) (%o171) array_y_set_initial (%i172) array(array_given_rad_poles,2,3) (%o172) array_given_rad_poles (%i173) array(array_given_ord_poles,2,3) (%o173) array_given_ord_poles (%i174) array(array_rad_test_poles,2,3) (%o174) array_rad_test_poles (%i175) array(array_ord_test_poles,2,3) (%o175) array_ord_test_poles (%i176) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o176) array_fact_2 (%i177) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o177) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i178) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o178) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i179) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o179) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i180) 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)) (%o180) 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)) (%i181) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o181) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i182) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o182) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i183) 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) (%o183) 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) (%i184) 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) (%o184) 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) (%i185) 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) (%o185) 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 (%i186) 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) (%o186) 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) (%i187) 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) (%o187) 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 (%i188) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o188) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i189) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o189) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i190) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o190) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i191) 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) (%o191) 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) (%i192) log_revs(file,revs):=printf(file,revs) (%o192) log_revs(file, revs) := printf(file, revs) (%i193) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o193) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i194) 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) (%o194) 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) (%i195) logstart(file):=(printf(file,""),0) (%o195) logstart(file) := (printf(file, ""), 0) (%i196) logend(file):=(printf(file,"~%"),0) (%o196) logend(file) := (printf(file, "~%"), 0) (%i197) 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) (%o197) 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) (%i198) 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) (%o198) 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 (%i199) 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) (%o199) 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) (%i200) 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) (%o200) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i201) 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) (%o201) 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) (%i202) 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) (%o202) 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 ! (%i203) 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) (%o203) 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) (%i204) 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) (%o204) 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) (%i205) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o205) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i206) factorial_2(nnn):=nnn! (%o206) factorial_2(nnn) := nnn! (%i207) 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) (%o207) 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 (%i208) 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) (%o208) 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) (%i209) log10(x):=log(x)/glob_log_10 log(x) (%o209) log10(x) := ----------- glob_log_10 (%i210) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o210) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i211) 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) (%o211) 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) (%i212) exact_soln_y(x):=block(0.25*log(3.0+2.0*x)+0.5*x) (%o212) exact_soln_y(x) := block(0.25 log(3.0 + 2.0 x) + 0.5 x) (%i213) 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")), 0) (%o213) 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")), 0) (%i214) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o214) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i215) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[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) (%o215) est_size_answer() := block([min_size], min_size : glob_estimated_size_answer, if !array_y ! < min_size then (min_size : !array_y !, ! 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) (%i216) 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_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[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) (%o216) 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_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 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) (%i217) 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)) (%o217) 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)) (%i218) 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_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y[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, " ")))),0) (%o218) 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_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : mabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[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, " ")))), 0) (%i219) 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_y_higher[1,1]) > glob_small_float then (tmp:abs(array_y_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) (%o219) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat, [sz2], convfloat, [tmp], convfloat]), hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_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 (%i220) 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) (%o220) 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) (%i221) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_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_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_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_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_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)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_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_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_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)), 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_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_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) (%o221) check_for_pole() := (block(mode_declare([cnt], fixnum, [dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat, [ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum, [h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad], convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 1 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 1 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad : comp_rad_from_ratio(array_y_higher , array_y_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_y_higher , 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 1 array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float, 1, 1 tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 2 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 2 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad : comp_rad_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_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_y_higher , 1, last_no - 2 array_y_higher , array_y_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 glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 3 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 3 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad : comp_rad_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 tmp_rad array_y_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_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 array_y_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)), if mabs(glob_min_pole_est) 1, 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_y : array_y ratio, term term array_y_higher : array_y_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) (%i222) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]), array_tmp1[1]:array_const_0D1[1]*array_x[1], array_tmp2[1]:array_const_0D2[1]+array_tmp1[1], array_tmp3[1]:array_const_0D2[1]*array_x[1], array_tmp4[1]:array_const_0D3[1]+array_tmp3[1], array_tmp5[1]:array_tmp2[1]/array_tmp4[1], array_tmp6[1]:array_tmp5[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp6[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:temporary*1.0/glob_h, array_y_higher[2,1]:temporary,0)),kkk:2, array_tmp1[2]:array_const_0D1[1]*array_x[2], array_tmp2[2]:array_tmp1[2], array_tmp3[2]:array_const_0D2[1]*array_x[2], array_tmp4[2]:array_tmp3[2], array_tmp5[2]:(array_tmp2[2] -array_tmp5[1]*array_tmp4[2]) /array_tmp4[1], array_tmp6[2]:array_tmp5[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp6[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y_higher[2,2]:temporary,0)),kkk:3, array_tmp5[3]:(-array_tmp5[2]*array_tmp4[2]) /array_tmp4[1], array_tmp6[3]:array_tmp5[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp6[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y_higher[2,3]:temporary,0)),kkk:4, array_tmp5[4]:(-array_tmp5[3]*array_tmp4[2]) /array_tmp4[1], array_tmp6[4]:array_tmp5[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp6[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y_higher[2,4]:temporary,0)),kkk:5, array_tmp5[5]:(-array_tmp5[4]*array_tmp4[2]) /array_tmp4[1], array_tmp6[5]:array_tmp5[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp6[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y_higher[2,5]:temporary,0)),kkk:6, while kkk <= MAX_TERMS do (array_tmp5[kkk] :(-array_tmp5[kkk-1]*array_tmp4[2]) /array_tmp4[1],array_tmp6[kkk]:array_tmp5[kkk], order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp6[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_y[order_d+kkk]:temporary, array_y_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_y_higher[adj3,term] :temporary),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%o222) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_const_0D2 array_x , 1 1 1 array_tmp2 1 array_tmp4 : array_const_0D3 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_0D2 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp2 - array_tmp5 array_tmp4 2 1 2 array_tmp5 : -------------------------------------, 2 array_tmp4 1 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= MAX_TERMS then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), 2 if 3 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 - array_tmp5 array_tmp4 2 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 3 array_tmp4 3 3 1 if not array_y_set_initial then (if 3 <= MAX_TERMS 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 if 4 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - array_tmp5 array_tmp4 3 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 4 array_tmp4 4 4 1 if not array_y_set_initial then (if 4 <= MAX_TERMS 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 if 5 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - array_tmp5 array_tmp4 4 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 5 array_tmp4 5 5 1 if not array_y_set_initial then (if 5 <= MAX_TERMS 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 if 6 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 - array_tmp5 array_tmp4 kkk - 1 2 while kkk <= MAX_TERMS do (array_tmp5 : -------------------------------, kkk array_tmp4 1 array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if order_d + kkk <= MAX_TERMS then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp6 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_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_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)), 0) (%i223) exact_soln_y(x):=block(0.25*log(3.0+2.0*x)+0.5*x) (%o223) exact_soln_y(x) := block(0.25 log(3.0 + 2.0 x) + 0.5 x) (%i224) 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_y_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 <= 2 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= MAX_TERMS do (array_y[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_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp4[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp5[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp6[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term), ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_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_y_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_y_higher_work2[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 do (term:1, while term <= MAX_TERMS do (array_y_set_initial[ord,term]:0.0, term:1+term),ord:1+ord),ord:1, while ord <= 2 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 <= 2 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 <= 2 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 <= 2 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_y),zero_ats_ar(array_x), zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5), zero_ats_ar(array_tmp6),zero_ats_ar(array_m1), zero_ats_ar(array_const_1),array_const_1[1]:1, zero_ats_ar(array_const_0D0),array_const_0D0[1]:0.0, zero_ats_ar(array_const_0D1),array_const_0D1[1]:0.1, zero_ats_ar(array_const_0D2),array_const_0D2[1]:0.2, zero_ats_ar(array_const_0D3),array_const_0D3[1]:0.3, 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_y_set_initial[1,1]:true, array_y_set_initial[1,2]:false, array_y_set_initial[1,3]:false, array_y_set_initial[1,4]:false, array_y_set_initial[1,5]:false, array_y_set_initial[1,6]:false, array_y_set_initial[1,7]:false, array_y_set_initial[1,8]:false, array_y_set_initial[1,9]:false, array_y_set_initial[1,10]:false, array_y_set_initial[1,11]:false, array_y_set_initial[1,12]:false, array_y_set_initial[1,13]:false, array_y_set_initial[1,14]:false, array_y_set_initial[1,15]:false, array_y_set_initial[1,16]:false, array_y_set_initial[1,17]:false, array_y_set_initial[1,18]:false, array_y_set_initial[1,19]:false, array_y_set_initial[1,20]:false, array_y_set_initial[1,21]:false, array_y_set_initial[1,22]:false, array_y_set_initial[1,23]:false, array_y_set_initial[1,24]:false, array_y_set_initial[1,25]:false, array_y_set_initial[1,26]:false, array_y_set_initial[1,27]:false, array_y_set_initial[1,28]:false, array_y_set_initial[1,29]:false, array_y_set_initial[1,30]: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:1,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/div_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), 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_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000,"), omniout_str(ALWAYS,"glob_display_interval:0.1,"), omniout_str(ALWAYS,"glob_max_minutes:10,"), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_desired_digits_correct:10,"), omniout_str(ALWAYS,"glob_display_interval:0.01,"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:1000000000,"), omniout_str(ALWAYS,"glob_max_minutes:10.0,"), omniout_str(ALWAYS,"glob_subiter_method:3,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.5 * x + 0.25 * ln(2.0 * x + 3.0)) "), 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_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_max_iter:1000000, glob_display_interval:0.1,glob_max_minutes:10, glob_desired_digits_correct:10,glob_display_interval:0.01, glob_look_poles:true,glob_max_iter:1000000000, glob_max_minutes:10.0,glob_subiter_method:3, glob_last_good_h:glob_h, glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes, omniout_str(ALWAYS,"START of Optimize"), glob_check_sign:my_check_sign(x_start,x_end),found_h:false, glob_h:glob_min_h*glob_check_sign, if abs(glob_max_h) < abs(glob_h) then glob_h:abs(glob_max_h)*glob_check_sign, if abs(glob_display_interval) < abs(glob_h) then glob_h:abs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h:false, glob_display_interval:abs(glob_display_interval)) else (glob_neg_h:true, glob_display_interval :-abs(glob_display_interval)),chk_data(), best_h:glob_h,min_value:glob_larger_float, est_answer:est_size_answer(),opt_iter:1, est_needed_step_err:estimated_needed_step_error( x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err",32, est_needed_step_err,16,""), estimated_step_error:0.0, while opt_iter <= 100 and not found_h do (omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_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_y_higher[ r_order,term_no] :array_y_init[it] *expt(glob_h,term_no-1) /factorial_1(term_no-1), term_no:1+term_no),r_order:1+r_order), atomall(),estimated_step_error:test_suggested_h(), omniout_float(ALWAYS,"estimated_step_error",32, estimated_step_error,32,""), if estimated_step_error > est_needed_step_err and opt_iter = 1 or glob_check_sign*glob_h >= glob_check_sign*glob_max_h then (found_h:true, glob_h:glob_check_sign*glob_max_h, best_h:glob_h) elseif estimated_step_error > est_needed_step_err and not found_h then (glob_h:glob_h/2.0,best_h:glob_h, found_h:true) else (glob_h:glob_h*2.0,best_h:glob_h), omniout_float(ALWAYS,"best_h",32,best_h,32,""), opt_iter:1+opt_iter), if not found_h and opt_iter = 1 then (omniout_str(ALWAYS,"Beginning glob_h too large."), found_h:false), if opt_iter > 100 then (glob_h:glob_check_sign*glob_max_h,found_h:false), if glob_check_sign*glob_display_interval < glob_check_sign*glob_h then glob_h:glob_check_sign*glob_display_interval, if glob_html_log then html_log_file:openw("entry.html"), if found_h then (omniout_str(ALWAYS,"START of Soultion"), array_x[1]:x_start,array_x[2]:glob_h, glob_next_display:x_start,order_diff:1,term_no:1, while term_no <= order_diff do (array_y[term_no] :array_y_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_y_higher[ r_order,term_no] :array_y_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, atomall(),display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display :glob_display_interval +glob_next_display, array_x[1]:glob_h+array_x[1], array_x[2]:glob_h,order_diff:2,ord:2, calc_term:1,iii:MAX_TERMS, while iii >= calc_term do ( array_y_higher_work[2,iii] :array_y_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_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_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_y_higher_work[1,iii] :array_y_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_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_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_y_higher_work[1,iii] :array_y_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_y_higher_work[ord,iii] +temp_sum,iii:iii-1), array_y_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_y[term_no] :array_y_higher_work2[1,term_no], ord:1, while ord <= order_diff do ( array_y_higher[ord,term_no] :array_y_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 ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), 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, "2014-01-08T20:34:59-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "div_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), 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, "div_lin_lin diffeq.max"), logitem_str(html_log_file, "div_lin_lin maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o224) 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_y_init : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_complex_pole : 0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp4 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp5 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp6 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_m1 : 0.0, term term : 1 + term), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_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_y_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_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 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 <= 2 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 <= 2 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 <= 2 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_y), zero_ats_ar(array_x), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5), zero_ats_ar(array_tmp6), zero_ats_ar(array_m1), zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0), array_const_0D0 : 0.0, 1 1 zero_ats_ar(array_const_0D1), array_const_0D1 : 0.1, 1 zero_ats_ar(array_const_0D2), array_const_0D2 : 0.2, 1 zero_ats_ar(array_const_0D3), array_const_0D3 : 0.3, zero_ats_ar(array_m1), 1 array_m1 : - 1.0, iiif : 0, while iiif <= MAX_TERMS do (jjjf : 0, 1 while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0, iiif iiif, jjjf jjjf : 1 + jjjf), iiif : 1 + iiif), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, ALWAYS : 1, INFO : 2, DEBUGL : 3, 1, 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 : 1, 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/div_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) /\ ( 0.2 * x + 0.3 ) ; "), 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_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.01,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000000,"), omniout_str(ALWAYS, "glob_max_minutes:10.0,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.5 * x + 0.25 * ln(2.0 * x + 3.0)) "), 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_y_init : exact_soln_y(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.01, glob_look_poles : true, glob_max_iter : 1000000000, glob_max_minutes : 10.0, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_sec : 3600.0 glob_max_hours + 60.0 glob_max_minutes, omniout_str(ALWAYS, "START of Optimize"), glob_check_sign : my_check_sign(x_start, x_end), found_h : false, glob_h : glob_min_h glob_check_sign, if mabs(glob_max_h) < mabs(glob_h) then glob_h : mabs(glob_max_h) glob_check_sign, if mabs(glob_display_interval) < mabs(glob_h) then glob_h : mabs(glob_display_interval), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : mabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - mabs(glob_display_interval)), chk_data(), best_h : glob_h, min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), estimated_step_error : 0.0, while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_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_y_higher : r_order, term_no array_y_init expt(glob_h, term_no - 1) it ----------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_check_sign glob_h >= glob_check_sign glob_max_h) then (found_h : true, glob_h : glob_check_sign glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) and (not found_h) glob_h then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_check_sign glob_max_h, found_h : false), if glob_check_sign glob_display_interval < glob_check_sign glob_h then glob_h : glob_check_sign glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_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_y_higher : r_order, term_no array_y_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, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS, 2 while iii >= calc_term do (array_y_higher_work : 2, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, iii : MAX_TERMS, factorial_1(calc_term - 1) while iii >= calc_term do (array_y_higher_work : 1, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, iii : MAX_TERMS, factorial_1(calc_term - 1) while iii >= calc_term do (array_y_higher_work : 1, iii array_y_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_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : MAX_TERMS, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_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 ( y , x \ , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; "), 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, "2014-01-08T20:34:59-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ( 0.1 * x + 0.\ 2 ) / ( 0.2 * x + 0.3 ) ; "), 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, "div_lin_lin diffeq.max"), logitem_str(html_log_file, "div_lin_lin maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i225) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o225) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i226) 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_y in translation. warning: encountered undefined variable ALWAYS 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_y_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 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_const_0D1 in translation. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_const_0D2 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_0D3 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable array_tmp5 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp6 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_y_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_y_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_m1 in translation. warning: encountered undefined variable ord in translation. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable jjjf in translation. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable x_start in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable est_answer in translation. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: encountered undefined variable order_diff in translation. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: encountered undefined variable it in translation. warning: encountered undefined variable 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_SUBITER_METHOD 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/div_lin_linpostode.ode#################" "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; " "!" "/* 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_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:1000000000," "glob_max_minutes:10.0," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (0.5 * x + 0.25 * ln(2.0 * x + 3.0)) " "));" "/* 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 = 4.740749205723465700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-164 "" estimated_step_error = 4.740749205723465700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-164 "" 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 = 3.181461979665938000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-156 "" estimated_step_error = 3.181461979665938000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-156 "" 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 = 2.1350417081676928000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-148 "" estimated_step_error = 2.1350417081676928000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-148 "" 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 = 1.43280051161233600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-140 "" estimated_step_error = 1.43280051161233600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-140 "" 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 = 9.6153383193115280000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-133 "" estimated_step_error = 9.6153383193115280000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-133 "" 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 = 6.45271324737752600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-125 "" estimated_step_error = 6.45271324737752600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-125 "" 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 = 4.3303008587023120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-117 "" estimated_step_error = 4.3303008587023120000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-117 "" 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 = 2.90595974850746950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-109 "" estimated_step_error = 2.90595974850746950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-109 "" 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 = 1.950081464176728600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-101 "" estimated_step_error = 1.950081464176728600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-101 "" 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 = 1.3085767166079987000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-93 "" estimated_step_error = 1.3085767166079987000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-93 "" 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 = 8.78035707471655200000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" estimated_step_error = 8.78035707471655200000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" 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 = 5.890583277128918000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" estimated_step_error = 5.890583277128918000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" 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 = 3.950670242602179500000000000000000000000000000000000000000000000000000000000000000000E-70 "" estimated_step_error = 3.950670242602179500000000000000000000000000000000000000000000000000000000000000000000E-70 "" 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 = 2.6479900617729796000000000000000000000000000000000000000000000000000000000000E-62 "" estimated_step_error = 2.6479900617729796000000000000000000000000000000000000000000000000000000000000E-62 "" 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 = 1.772676861880178000000000000000000000000000000000000000000000000000000E-54 "" estimated_step_error = 1.772676861880178000000000000000000000000000000000000000000000000000000E-54 "" 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 = 1.18381539762186880000000000000000000000000000000000000000000000E-46 "" estimated_step_error = 1.18381539762186880000000000000000000000000000000000000000000000E-46 "" 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 = 7.867629441166445000000000000000000000000000000000000000E-39 "" estimated_step_error = 7.867629441166445000000000000000000000000000000000000000E-39 "" 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 = 5.179696741806790000000000000000000000000000000E-31 "" estimated_step_error = 5.179696741806790000000000000000000000000000000E-31 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 0.3407877024514202 " " y[1] (numeric) = 0.3407877024514202 " " 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 = 1.6000000000000063 " " Order of pole (three term test) = 9.8401429081179390000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 0.34734533988907923 " " y[1] (numeric) = 0.34734533988907923 " " 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 = 1.610000000000007 " " Order of pole (three term test) = 1.3106070537381330000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 0.35389333245105953 " " y[1] (numeric) = 0.3538933324510595 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.568584263704220800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6199999999999881 " " Order of pole (three term test) = 1.74250034401911340000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 0.36043179884465404 " " y[1] (numeric) = 0.36043179884465404 " " 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 = 1.6299999999999941 " " Order of pole (three term test) = 2.3126611570292321000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 0.3669608555990131 " " y[1] (numeric) = 0.36696085559901304 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.512726776828648700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6399999999999944 " " Order of pole (three term test) = 7.66018436636269800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 0.37348061711810865 " " y[1] (numeric) = 0.3734806171181086 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.48631946845324800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6499999999999981 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 0.37999119573209933 " " y[1] (numeric) = 0.3799911957320993 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.460853615945201800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6600000000000086 " " Order of pole (three term test) = 6.68904729119830900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 0.3864927017471523 " " y[1] (numeric) = 0.3864927017471522 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.436279416928649400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6700000000000055 " " Order of pole (three term test) = 8.81758976038676900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 0.3929852434937783 " " y[1] (numeric) = 0.39298524349377817 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.82510105151755800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6799999999999873 " " Order of pole (three term test) = 2.320861218861210000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 0.39946892737373185 " " y[1] (numeric) = 0.3994689273737318 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.389623758628995000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6900000000000086 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 0.405943857905529 " " y[1] (numeric) = 0.4059438579055289 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.734917656725642000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6999999999999857 " " Order of pole (three term test) = 1.0000290228847440000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 0.4124101377686285 " " y[1] (numeric) = 0.4124101377686284 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.692036210923643400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7100000000000117 " " Order of pole (three term test) = 1.30973459476882550000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 0.4188678678463268 " " y[1] (numeric) = 0.4188678678463267 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.650532804852131500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7199999999999844 " " Order of pole (three term test) = 2.5689877755730960000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 0.42531714726740827 " " y[1] (numeric) = 0.42531714726740816 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.61034155748987400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7300000000000204 " " Order of pole (three term test) = 3.354086231631950300000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 0.43175807344659584 " " y[1] (numeric) = 0.43175807344659567 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.85710109285013700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7400000000000015 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 0.43819074212384207 " " y[1] (numeric) = 0.4381907421238419 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.800478597211156600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7499999999999887 " " Order of pole (three term test) = 1.89706610613914640000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 0.4446152474025015 " " y[1] (numeric) = 0.44461524740250136 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.745563263218771000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7599999999999862 " " Order of pole (three term test) = 1.23277820892745530000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 0.45103168178642083 " " y[1] (numeric) = 0.4510316817864207 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.461518934164109400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7699999999999987 " " Order of pole (three term test) = 7.99912505730532900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 0.4574401362159849 " " y[1] (numeric) = 0.4574401362159847 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.64055185606063800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7800000000000027 " " Order of pole (three term test) = 1.03655497432277310000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 0.4638407001031523 " " y[1] (numeric) = 0.4638407001031522 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.39354378427390500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.790000000000011 " " Order of pole (three term test) = 6.70627970998516500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 0.4702334613655162 " " y[1] (numeric) = 0.470233461365516 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.54150581309494950000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.7999999999999936 " " Order of pole (three term test) = 8.66517769227285200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 0.47661850645942 " " y[1] (numeric) = 0.4766185064594199 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.32937456179050480000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8100000000000096 " " Order of pole (three term test) = 1.11803830267297890000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 0.48299592041216244 " " y[1] (numeric) = 0.48299592041216227 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.44792671440501800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8199999999999945 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 0.48936578685331883 " " y[1] (numeric) = 0.48936578685331866 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.4030465179146200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8299999999999927 " " Order of pole (three term test) = 9.2674952087824100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 0.49572818804521 " " y[1] (numeric) = 0.49572818804520985 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.359370270035678000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8399999999999863 " " Order of pole (three term test) = 1.1907815608496831000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 0.5020832049125448 " " y[1] (numeric) = 0.5020832049125447 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.21123314574631220000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8499999999999992 " " Order of pole (three term test) = 7.63979584825548100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 0.508430917071264 " " y[1] (numeric) = 0.5084309170712638 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.36725221597624670000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8600000000000048 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 0.5147714028566103 " " y[1] (numeric) = 0.51477140285661 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.313460376641821700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8699999999999983 " " Order of pole (three term test) = 1.25284154835831050000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 0.5211047393504509 " " y[1] (numeric) = 0.5211047393504507 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.26103599061114900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.880000000000014 " " Order of pole (three term test) = 2.40178745503092760000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 0.5274310024078742 " " y[1] (numeric) = 0.527431002407874 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.20992705986818800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.8900000000000037 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 0.5337502666830851 " " y[1] (numeric) = 0.5337502666830849 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.16008419639573800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9000000000000048 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 0.5400626056546212 " " y[1] (numeric) = 0.5400626056546208 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.16719069049095900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.910000000000003 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 0.5463680916499091 " " y[1] (numeric) = 0.5463680916499087 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.09601681499663800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9200000000000064 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 0.5526667958691851 " " y[1] (numeric) = 0.5526667958691848 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.02654094432666300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9300000000000044 " " Order of pole (three term test) = 6.69465921032839900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 0.5589587884087956 " " y[1] (numeric) = 0.5589587884087954 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.97246826652698600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9400000000000006 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 0.5652441382839004 " " y[1] (numeric) = 0.5652441382839001 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.89244336790026500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9500000000000182 " " Order of pole (three term test) = 1.07568319187626910000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 0.571522913450593 " " y[1] (numeric) = 0.5715229134505927 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.82770873308721500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.960000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 0.5777951808274608 " " y[1] (numeric) = 0.5777951808274605 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.76444592200581500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9700000000000117 " " Order of pole (three term test) = 1.72004046215868480000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 0.5840610063165975 " " y[1] (numeric) = 0.5840610063165972 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.70260475850024300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9800000000000055 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 0.5903204548240868 " " y[1] (numeric) = 0.5903204548240865 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.642137328390554000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.9899999999999889 " " Order of pole (three term test) = 6.8434292771979100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 0.5965735902799729 " " y[1] (numeric) = 0.5965735902799725 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.4439971377487700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.999999999999985 " " Order of pole (three term test) = 2.5854332148529450000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 0.6028204756577327 " " y[1] (numeric) = 0.6028204756577322 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.3668567638735300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.010000000000007 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 0.6090611729932649 " " y[1] (numeric) = 0.6090611729932645 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.29137284630313200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0199999999999907 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 0.6152957434034105 " " y[1] (numeric) = 0.6152957434034101 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.21749198838356800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0300000000000082 " " Order of pole (three term test) = 8.54712424150182200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 0.6215242471040179 " " y[1] (numeric) = 0.6215242471040173 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.93145383947788500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0400000000000214 " " Order of pole (three term test) = 1.07149457001037910000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 0.6277467434275658 " " y[1] (numeric) = 0.6277467434275653 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.07433713515241900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0499999999999976 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 0.633963290840359 " " y[1] (numeric) = 0.6339632908403585 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.00496726334728100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0599999999999885 " " Order of pole (three term test) = 1.67839589982997970000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 0.640173946959306 " " y[1] (numeric) = 0.6401739469593055 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.93700847963892800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0699999999999945 " " Order of pole (three term test) = 1.04859593135909500000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 0.6463787685682932 " " y[1] (numeric) = 0.6463787685682928 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.87041764743766200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0799999999999828 " " Order of pole (three term test) = 1.30883736712227360000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 0.6525778116341665 " " y[1] (numeric) = 0.6525778116341661 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.80515337685152400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.089999999999993 " " Order of pole (three term test) = 8.15964835002438900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 0.658771131322331 " " y[1] (numeric) = 0.6587711313223304 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.42646992132639400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.0999999999999903 " " Order of pole (three term test) = 1.01631851934414170000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 0.6649587820119804 " " y[1] (numeric) = 0.6649587820119799 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.34805896739892800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.110000000000004 " " Order of pole (three term test) = 1.26454772702976560000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 0.6711408173109669 " " y[1] (numeric) = 0.6711408173109664 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.61693043241472200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.119999999999988 " " Order of pole (three term test) = 2.35767068400988930000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 0.67731729007032 " " y[1] (numeric) = 0.6773172900703196 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.5565904836706100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.1299999999999817 " " Order of pole (three term test) = 9.75829727210657700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 0.6834882523984267 " " y[1] (numeric) = 0.6834882523984261 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.12174182020887800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.140000000000003 " " Order of pole (three term test) = 1.21044722741954450000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 0.6896537556748794 " " y[1] (numeric) = 0.689653755674879 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.43930677090980300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.1499999999999972 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 0.695813850564005 " " y[1] (numeric) = 0.6958138505640045 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.97787385034980600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.160000000000012 " " Order of pole (three term test) = 9.2844213847534510000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 0.7019685870280787 " " y[1] (numeric) = 0.7019685870280781 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.48951031548721700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.1700000000000097 " " Order of pole (three term test) = 1.14823306094552070000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 0.7081180143402361 " " y[1] (numeric) = 0.7081180143402355 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.40710165939981800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.179999999999999 " " Order of pole (three term test) = 7.09334364789368700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 0.714262181097089 " " y[1] (numeric) = 0.7142621810970884 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.32618067152777000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.189999999999994 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 0.7204011352310542 " " y[1] (numeric) = 0.7204011352310535 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.24670689978083900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.2000000000000095 " " Order of pole (three term test) = 1.07968138188947950000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 0.7265349240224019 " " y[1] (numeric) = 0.7265349240224014 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.64053445964095200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.210000000000006 " " Order of pole (three term test) = 6.65069280791924800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 0.7326635941110337 " " y[1] (numeric) = 0.732663594111033 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.09194642847427700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.220000000000009 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 0.7387871915079935 " " y[1] (numeric) = 0.7387871915079928 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.0519350175133631000000000000E-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 = 2.2300000000000058 " " Order of pole (three term test) = 1.00657467413967620000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 0.7449057616067238 " " y[1] (numeric) = 0.7449057616067231 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.04329454448214130000000000000E-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 = 2.240000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 0.7510193491940689 " " y[1] (numeric) = 0.7510193491940681 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.03480172391242450000000000000E-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 = 2.2500000000000187 " " Order of pole (three term test) = 7.58906262080238900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 0.7571279984610353 " " y[1] (numeric) = 0.7571279984610345 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.02645275147304580000000000000E-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 = 2.2600000000000104 " " Order of pole (three term test) = 9.30637404924570100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 0.7632317530133145 " " y[1] (numeric) = 0.7632317530133137 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.01824395299241730000000000000E-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 = 2.269999999999991 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 0.769330655881574 " " y[1] (numeric) = 0.7693306558815732 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.01017177893043710000000000000E-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 = 2.2799999999999967 " " Order of pole (three term test) = 6.97855120761428700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 0.7754247495315237 " " y[1] (numeric) = 0.775424749531523 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.00223279912993720000000000000E-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 = 2.2900000000000142 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 0.7815140758737626 " " y[1] (numeric) = 0.7815140758737619 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.94423697831314700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.299999999999986 " " Order of pole (three term test) = 1.04290023285311370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 0.7875986762734122 " " y[1] (numeric) = 0.7875986762734114 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.86741268935071700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.310000000000005 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 0.7936785915595413 " " y[1] (numeric) = 0.7936785915595405 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.11906561314057380000000000000E-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 = 2.3199999999999794 " " Order of pole (three term test) = 7.76568225849430700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 0.7997538620343889 " " y[1] (numeric) = 0.7997538620343881 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.71744125449677900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.329999999999978 " " Order of pole (three term test) = 9.46465262902138600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 0.8058245274823892 " " y[1] (numeric) = 0.8058245274823883 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.10219829430488000000000000000E-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 = 2.340000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 0.8118906271790036 " " y[1] (numeric) = 0.8118906271790027 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.09396313982117440000000000000E-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 = 2.349999999999983 " " Order of pole (three term test) = 2.8046842269745020000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 0.8179521998993664 " " y[1] (numeric) = 0.8179521998993655 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.08585614148283840000000000000E-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 = 2.36000000000001 " " Order of pole (three term test) = 1.70484322706218770000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 0.8240092839267467 " " y[1] (numeric) = 0.8240092839267458 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.0778742873716009000000000000E-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 = 2.3699999999999948 " " Order of pole (three term test) = 1.03544308654433050000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 0.8300619170608325 " " y[1] (numeric) = 0.8300619170608317 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.07001465968355410000000000000E-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 = 2.3799999999999977 " " Order of pole (three term test) = 1.25673103720576750000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 0.8361101366258415 " " y[1] (numeric) = 0.8361101366258407 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.06227443107484300000000000000E-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 = 2.389999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 0.8421539794784617 " " y[1] (numeric) = 0.8421539794784608 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.05465086117643940000000000000E-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 = 2.3999999999999977 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 0.8481934820156276 " " y[1] (numeric) = 0.8481934820156267 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.04714129326893470000000000000E-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 = 2.4099999999999735 " " Order of pole (three term test) = 2.23607452960411040000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 0.8542286801821355 " " y[1] (numeric) = 0.8542286801821346 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.03974315110884720000000000000E-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 = 2.4199999999999875 " " Order of pole (three term test) = 6.7631521849138310000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 0.860259609478101 " " y[1] (numeric) = 0.8602596094781001 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.03245393589844570000000000000E-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 = 2.4299999999999944 " " Order of pole (three term test) = 8.17581226411408600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 0.8662863049662644 " " y[1] (numeric) = 0.8662863049662635 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.02527122339157080000000000000E-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 = 2.44000000000002 " " Order of pole (three term test) = 9.87584662405962900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 0.8723088012791457 " " y[1] (numeric) = 0.8723088012791448 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.01819266112838550000000000000E-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 = 2.4499999999999966 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 0.8783271326260547 " " y[1] (numeric) = 0.8783271326260538 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.01121596579240000000000000E-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 = 2.4599999999999667 " " Order of pole (three term test) = 2.15649527425961380000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 0.8843413327999583 " " y[1] (numeric) = 0.8843413327999574 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.00433892068350820000000000000E-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 = 2.4700000000000113 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 0.8903514351842094 " " y[1] (numeric) = 0.8903514351842087 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.72864451638492400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.4800000000000137 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 0.8963574727591408 " " y[1] (numeric) = 0.89635747275914 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.67015828902938600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.489999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 0.9023594781085256 " " y[1] (numeric) = 0.9023594781085247 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.84284468936785800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.5000000000000115 " " Order of pole (three term test) = 7.54784081997469700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 0.9083574834259098 " " y[1] (numeric) = 0.908357483425909 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.55561969178182400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.509999999999993 " " Order of pole (three term test) = 9.0692948577867700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 0.9143515205208197 " " y[1] (numeric) = 0.9143515205208189 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.49953327353726100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.520000000000007 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 0.9203416208248439 " " y[1] (numeric) = 0.9203416208248432 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.44421353606820100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.530000000000002 " " Order of pole (three term test) = 1.3065508226369940000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 0.926327815397598 " " y[1] (numeric) = 0.9263278153975972 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.38964461953502800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.540000000000007 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 0.9323101349325704 " " y[1] (numeric) = 0.9323101349325696 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.33581110103257300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.549999999999989 " " Order of pole (three term test) = 9.38427309679936900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 0.9382886097628544 " " y[1] (numeric) = 0.9382886097628538 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.09945541109631900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.559999999999988 " " Order of pole (three term test) = 3.37063710276197800000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 0.9442632698667689 " " y[1] (numeric) = 0.9442632698667681 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.2302906619174400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.5700000000000003 " " Order of pole (three term test) = 6.72118756999626200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 0.9502341448733683 " " y[1] (numeric) = 0.9502341448733675 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.17857494840049400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.5799999999999783 " " Order of pole (three term test) = 8.03579440083760900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 0.9562012640678483 " " y[1] (numeric) = 0.9562012640678477 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.96646030294128300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.5900000000000074 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 0.9621646563968458 " " y[1] (numeric) = 0.9621646563968451 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.92328293651587300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.600000000000006 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 0.9681243504736373 " " y[1] (numeric) = 0.9681243504736365 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.02744107053396700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.609999999999997 " " Order of pole (three term test) = 6.83841863882586200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 0.9740803745832383 " " y[1] (numeric) = 0.9740803745832374 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.11812251714991800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.6199999999999846 " " Order of pole (three term test) = 8.15364403283698300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 0.9800327566874051 " " y[1] (numeric) = 0.9800327566874043 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.92989940320427700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.629999999999992 " " Order of pole (three term test) = 9.71531255848470800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 0.9859815244295429 " " y[1] (numeric) = 0.9859815244295422 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.75604763649600300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.6400000000000152 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 0.9919267051395195 " " y[1] (numeric) = 0.9919267051395187 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.83481393545401700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.649999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 0.9978683258383887 " " y[1] (numeric) = 0.9978683258383879 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.7881629982057900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.659999999999988 " " Order of pole (three term test) = 8.18498025356646400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 1.0038064132430264 " " y[1] (numeric) = 1.0038064132430256 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.84810465426955600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.6699999999999897 " " Order of pole (three term test) = 9.72703265234311600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 1.009740993770678 " " y[1] (numeric) = 1.0097409937706774 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.59707607084019500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.68000000000002 " " Order of pole (three term test) = 3.465645454054790000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 1.0156720935434238 " " y[1] (numeric) = 1.015672093543423 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.7447358783039400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.6900000000000235 " " Order of pole (three term test) = 1.37109400235189140000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 1.0215997383925577 " " y[1] (numeric) = 1.0215997383925568 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.69399615447861200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.699999999999999 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 1.027523953862889 " " y[1] (numeric) = 1.0275239538628884 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.48290302402022200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.709999999999991 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 1.0334447652169634 " " y[1] (numeric) = 1.0334447652169625 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.59434823798889100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.7199999999999926 " " Order of pole (three term test) = 1.14183129244101370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 1.039362197439204 " " y[1] (numeric) = 1.039362197439203 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.54541777532829700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.7300000000000066 " " Order of pole (three term test) = 6.75902610072167900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 1.0452762752399816 " " y[1] (numeric) = 1.0452762752399807 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.49706858118645400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.739999999999987 " " Order of pole (three term test) = 7.99702123789164600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 1.0511870230596068 " " y[1] (numeric) = 1.0511870230596059 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.44929018544173700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.7500000000000178 " " Order of pole (three term test) = 9.4559741400115200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 1.0570944650722516 " " y[1] (numeric) = 1.0570944650722505 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05025904619534040000000000000E-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 = 2.759999999999985 " " Order of pole (three term test) = 1.11742950553689950000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 1.0629986251897987 " " y[1] (numeric) = 1.0629986251897976 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04442564488446630000000000000E-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 = 2.7699999999999836 " " Order of pole (three term test) = 1.31968942503583650000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 1.0688995270656232 " " y[1] (numeric) = 1.0688995270656223 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.30927881630166600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.779999999999997 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 1.0747971940983054 " " y[1] (numeric) = 1.0747971940983045 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.26368383335106400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.7899999999999885 " " Order of pole (three term test) = 9.18683073256258200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 1.0806916494352765 " " y[1] (numeric) = 1.0806916494352756 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.21861092536663400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.8000000000000145 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 1.0865829159764004 " " y[1] (numeric) = 1.0865829159763996 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.17405102400317500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.8099999999999943 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 1.0924710163774924 " " y[1] (numeric) = 1.0924710163774916 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.12999527113517500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.8199999999999874 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 1.0983559730537735 " " y[1] (numeric) = 1.0983559730537726 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.08643501278288800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.830000000000014 " " Order of pole (three term test) = 8.84134632000514800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 1.1042378081832656 " " y[1] (numeric) = 1.1042378081832647 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.04336179324805500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.840000000000003 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 1.1101165437101268 " " y[1] (numeric) = 1.1101165437101257 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.00009591868136110000000000000E-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 = 2.8499999999999863 " " Order of pole (three term test) = 1.22237913630524610000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 1.115992201347927 " " y[1] (numeric) = 1.1159922013479262 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.95864360546030700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.859999999999997 " " Order of pole (three term test) = 7.18042080485116900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 1.1218648025828695 " " y[1] (numeric) = 1.1218648025828684 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.89622833401217400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.870000000000011 " " Order of pole (three term test) = 8.43101034947670400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 1.1277343686769505 " " y[1] (numeric) = 1.1277343686769497 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.87577681739122200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.8799999999999955 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 1.1336009206710722 " " y[1] (numeric) = 1.133600920671071 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.79377313815097800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.8899999999999966 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 1.139464479388094 " " y[1] (numeric) = 1.139464479388093 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.79470036816845500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.900000000000003 " " Order of pole (three term test) = 6.80127413953917100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 1.1453250654358373 " " y[1] (numeric) = 1.1453250654358362 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.6935189679331500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.910000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 1.1511826992100345 " " y[1] (numeric) = 1.1511826992100336 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.71535587104993600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.920000000000008 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 1.1570374008972308 " " y[1] (numeric) = 1.15703740089723 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.6763155539430490000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.9299999999999953 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 1.1628891904776344 " " y[1] (numeric) = 1.1628891904776335 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.63768746818708500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.9399999999999977 " " Order of pole (three term test) = 1.277201958861530200000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 1.168738087727919 " " y[1] (numeric) = 1.168738087727918 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.59946500440304200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.9500000000000157 " " Order of pole (three term test) = 7.46560686249001600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 1.1745841122239793 " " y[1] (numeric) = 1.1745841122239782 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.45205211845612100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.9600000000000097 " " Order of pole (three term test) = 8.7231047977338490000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 1.1804272833436391 " " y[1] (numeric) = 1.180427283343638 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.40526401152280700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.970000000000026 " " Order of pole (three term test) = 1.01870643590603880000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 1.1862676202693152 " " y[1] (numeric) = 1.1862676202693143 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.48716735181968900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.9799999999999924 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 1.1921051419906357 " " y[1] (numeric) = 1.1921051419906348 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.45050405719248400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.989999999999993 " " Order of pole (three term test) = 2.08074233425908400000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 1.1979398673070145 " " y[1] (numeric) = 1.1979398673070134 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.2677692338677500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0000000000000147 " " Order of pole (three term test) = 8.08723573899472600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 1.203771814830183 " " y[1] (numeric) = 1.2037718148301821 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.37829552709224500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.009999999999995 " " Order of pole (three term test) = 9.4249961827052800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 1.2096010029866815 " " y[1] (numeric) = 1.2096010029866806 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.34273878334329300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0199999999999942 " " Order of pole (three term test) = 1.09784685398847240000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 1.2154274500203064 " " y[1] (numeric) = 1.2154274500203055 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.30753957947293600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.030000000000015 " " Order of pole (three term test) = 1.27815433337642950000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 1.2212511739945195 " " y[1] (numeric) = 1.2212511739945187 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.27269245355182700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.040000000000012 " " Order of pole (three term test) = 7.43664818075467600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 1.2270721927948172 " " y[1] (numeric) = 1.227072192794816 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.0477400689561600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0500000000000034 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 1.2328905241310593 " " y[1] (numeric) = 1.2328905241310584 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.2040331425704900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0600000000000143 " " Order of pole (three term test) = 1.00549058443415450000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 1.2387061855397634 " " y[1] (numeric) = 1.2387061855397625 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.17021057994558700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0699999999999954 " " Order of pole (three term test) = 1.1683088377366930000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 1.2445191943863578 " " y[1] (numeric) = 1.244519194386357 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.13671933471515800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.079999999999997 " " Order of pole (three term test) = 6.7841486190051090000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 1.2503295678674005 " " y[1] (numeric) = 1.2503295678673998 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.327665856221185000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.089999999999995 " " Order of pole (three term test) = 7.87503418806686200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 1.2561373230127622 " " y[1] (numeric) = 1.2561373230127615 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.303033375183981000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1000000000000054 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 1.2619424766877727 " " y[1] (numeric) = 1.261942476687772 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.27863850437540500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.110000000000001 " " Order of pole (three term test) = 1.0595959497744270000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 1.2677450455953347 " " y[1] (numeric) = 1.267745045595334 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.25447776025247000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.120000000000003 " " Order of pole (three term test) = 1.22821308295039270000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 1.2735450462780025 " " y[1] (numeric) = 1.2735450462780018 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.230547727557047000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1299999999999875 " " Order of pole (three term test) = 7.11495120189067100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 1.2793424951200276 " " y[1] (numeric) = 1.2793424951200267 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.9424600768600010000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1399999999999757 " " Order of pole (three term test) = 1.64788236344275030000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 1.2851374083493725 " " y[1] (numeric) = 1.2851374083493716 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.91115528915230500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.150000000000018 " " Order of pole (three term test) = 9.53713374372690300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 1.2909298020396922 " " y[1] (numeric) = 1.2909298020396913 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.88014497997325300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.15999999999999 " " Order of pole (three term test) = 1.10341326111116550000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 1.2967196921122843 " " y[1] (numeric) = 1.2967196921122834 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.84942493819409900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.170000000000022 " " Order of pole (three term test) = 1.27602287713203000000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 1.3025070943380084 " " y[1] (numeric) = 1.3025070943380075 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.8189910332237900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1799999999999913 " " Order of pole (three term test) = 7.3747944858784900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 1.3082920243391754 " " y[1] (numeric) = 1.3082920243391745 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.78883921308584300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1899999999999964 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 1.3140744975914074 " " y[1] (numeric) = 1.3140744975914065 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.75896550255015700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2000000000000126 " " Order of pole (three term test) = 9.8401429081182300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 1.3198545294254682 " " y[1] (numeric) = 1.3198545294254673 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.72936600131795300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2100000000000177 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 1.3256321350290663 " " y[1] (numeric) = 1.3256321350290654 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.70003688225806800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.220000000000031 " " Order of pole (three term test) = 2.6212141074763490000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 1.3314073294486284 " " y[1] (numeric) = 1.3314073294486275 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.67097438969292600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2300000000000244 " " Order of pole (three term test) = 1.5115357740592430000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 1.3371801275910467 " " y[1] (numeric) = 1.3371801275910458 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.64217483773255200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2399999999999824 " " Order of pole (three term test) = 8.71250172009581400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 1.3429505442253986 " " y[1] (numeric) = 1.3429505442253977 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.61363460865506600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.25 " " Order of pole (three term test) = 1.00393827594962210000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 1.3487185939846411 " " y[1] (numeric) = 1.3487185939846402 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.58535015133215900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2599999999999936 " " Order of pole (three term test) = 1.1563305785146509000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 1.3544842913672777 " " y[1] (numeric) = 1.3544842913672768 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.55731797969807300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2699999999999974 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 1.3602476507390002 " " y[1] (numeric) = 1.3602476507389993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.52953467126072600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2799999999999976 " " Order of pole (three term test) = 7.6601843663629300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 1.3660086863343073 " " y[1] (numeric) = 1.3660086863343064 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.50199686565359600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2899999999999934 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 1.3717674122580958 " " y[1] (numeric) = 1.371767412258095 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.47470126322709300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2999999999999865 " " Order of pole (three term test) = 1.01317308931226840000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 1.37752384248723 " " y[1] (numeric) = 1.3775238424872291 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.44764462367814700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3100000000000507 " " Order of pole (three term test) = 2.32894976521501370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 1.3832779908720865 " " y[1] (numeric) = 1.3832779908720856 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.42082376471683600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3200000000000345 " " Order of pole (three term test) = 1.33780945823969650000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 1.3890298711380753 " " y[1] (numeric) = 1.3890298711380744 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.39423556076884800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.330000000000022 " " Order of pole (three term test) = 7.68151985255458500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 1.3947794968871394 " " y[1] (numeric) = 1.3947794968871385 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.36787694171269800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3400000000000003 " " Order of pole (three term test) = 8.81758976038690400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 1.4005268815992309 " " y[1] (numeric) = 1.40052688159923 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.3417448916505890000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3499999999999934 " " Order of pole (three term test) = 1.01175076097110540000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 1.4062720386337655 " " y[1] (numeric) = 1.4062720386337644 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.89479555963987400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3600000000000194 " " Order of pole (three term test) = 1.16043060943064440000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 1.4120149812310547 " " y[1] (numeric) = 1.4120149812310538 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.29014869888826200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.369999999999981 " " Order of pole (three term test) = 1.99562582376208550000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 1.417755722513719 " " y[1] (numeric) = 1.417755722513718 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.26467878489928400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3799999999999786 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 1.4234942754880768 " " y[1] (numeric) = 1.423494275488076 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.23942389508797700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.3899999999999895 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 1.429230653045516 " " y[1] (numeric) = 1.4292306530455152 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.21438126734495500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.399999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 1.4349648679638436 " " y[1] (numeric) = 1.4349648679638427 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.18954818706059500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.409999999999989 " " Order of pole (three term test) = 1.14467936524407860000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 1.4406969329086157 " " y[1] (numeric) = 1.4406969329086148 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.16492198610422700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.419999999999965 " " Order of pole (three term test) = 1.3097345947688308000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 1.4464268604344492 " " y[1] (numeric) = 1.4464268604344486 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.60537503137223140000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.430000000000008 " " Order of pole (three term test) = 7.49000222402325100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 1.452154662986314 " " y[1] (numeric) = 1.4521546629863131 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.11627977610602400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4400000000000035 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 1.4578803529008044 " " y[1] (numeric) = 1.4578803529008035 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.09225865437366100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4500000000000135 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 1.4636039424073954 " " y[1] (numeric) = 1.4636039424073946 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.06843418472358900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4600000000000124 " " Order of pole (three term test) = 1.11802874387733220000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 1.4693254436296792 " " y[1] (numeric) = 1.4693254436296783 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.04480391700054700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4700000000000113 " " Order of pole (three term test) = 1.27675705131062520000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 1.475044868586583 " " y[1] (numeric) = 1.475044868586582 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.02136544192852600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.480000000000005 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 1.4807622291935711 " " y[1] (numeric) = 1.4807622291935703 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.99811639025821600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.4900000000000033 " " Order of pole (three term test) = 8.31557086875027700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 1.486477537263829 " " y[1] (numeric) = 1.4864775372638284 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.48129082395184950000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.500000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 1.4921908045094305 " " y[1] (numeric) = 1.4921908045094299 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.46413295646926830000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5099999999999953 " " Order of pole (three term test) = 1.08155793133443440000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 1.4979020425424883 " " y[1] (numeric) = 1.4979020425424876 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.447111999690052700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.520000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 1.503611262876288 " " y[1] (numeric) = 1.5036112628762874 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.4302262906759104000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5300000000000034 " " Order of pole (three term test) = 1.40462009359712980000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 1.5093184769264074 " " y[1] (numeric) = 1.5093184769264067 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.41347419354208200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5399999999999765 " " Order of pole (three term test) = 1.59982501146107350000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 1.5150236960118175 " " y[1] (numeric) = 1.515023696011817 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.93123606593806500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.549999999999997 " " Order of pole (three term test) = 9.10744744693327800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 1.5207269313559713 " " y[1] (numeric) = 1.5207269313559708 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.920242948903956600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5599999999999956 " " Order of pole (three term test) = 1.03655497432275990000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 1.5264281940878732 " " y[1] (numeric) = 1.526428194087873 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.454667869638738300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5700000000000034 " " Order of pole (three term test) = 1.17931649906941730000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 1.5321274952431383 " " y[1] (numeric) = 1.5321274952431383 " " 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 = 3.5800000000000005 " " Order of pole (three term test) = 6.70627970998510300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 1.5378248457650328 " " y[1] (numeric) = 1.537824845765033 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.44388748521337100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.589999999999997 " " Order of pole (three term test) = 7.62442457147082300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 1.543520256505502 " " y[1] (numeric) = 1.5435202565055022 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.438559707844299400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.5999999999999783 " " Order of pole (three term test) = 1.733035538454540000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 1.5492137382261832 " " y[1] (numeric) = 1.5492137382261835 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.433272888344429800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6099999999999848 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 1.5549053015994057 " " y[1] (numeric) = 1.554905301599406 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.856053094637106500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.619999999999999 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 1.5605949572091753 " " y[1] (numeric) = 1.560594957209176 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.26846063866787360000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6300000000000177 " " Order of pole (three term test) = 1.2693085029745230000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 1.5662827155521477 " " y[1] (numeric) = 1.5662827155521484 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.25296026164898140000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6399999999999726 " " Order of pole (three term test) = 1.4405425326895782000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 1.5719685870385853 " " y[1] (numeric) = 1.571968587038586 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.23757713905731600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6500000000000385 " " Order of pole (three term test) = 1.63430911424197660000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 1.5776525819933038 " " y[1] (numeric) = 1.5776525819933047 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.629746560411582000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6600000000000006 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 1.5833347106566047 " " y[1] (numeric) = 1.5833347106566058 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.01192879277401700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6699999999999875 " " Order of pole (three term test) = 1.05068225528936310000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 1.5890149831851947 " " y[1] (numeric) = 1.589014983185196 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 8.38423579165783300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6800000000000055 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 1.5946934096530938 " " y[1] (numeric) = 1.5946934096530951 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 8.35438098311327800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.689999999999988 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 1.6003700000525294 " " y[1] (numeric) = 1.600370000052531 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 9.71220551762530900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.6999999999999766 " " Order of pole (three term test) = 7.63979584825509100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 1.6060447642948206 " " y[1] (numeric) = 1.6060447642948221 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 9.6778886182396300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.7100000000000213 " " Order of pole (three term test) = 8.64972477025913800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 1.6117177122112483 " " y[1] (numeric) = 1.61171771221125 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.10215134197608340000000000000E-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 = 3.7200000000000117 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 1.6173888535539154 " " y[1] (numeric) = 1.6173888535539174 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.2355726577032859000000000000E-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 = 3.7300000000000058 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 1.6230581979965943 " " y[1] (numeric) = 1.6230581979965966 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.36806311196425280000000000000E-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 = 3.7400000000000033 " " Order of pole (three term test) = 1.25284154835825720000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 1.628725755135564 " " y[1] (numeric) = 1.6287257551355663 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.3633025954486110000000000000E-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 = 3.7499999999999933 " " Order of pole (three term test) = 7.08289438855323000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 1.6343915344904347 " " y[1] (numeric) = 1.6343915344904372 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.4944342298841240000000000000E-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 = 3.7599999999999407 " " Order of pole (three term test) = 2.4017874550307210000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 1.6400555455049637 " " y[1] (numeric) = 1.6400555455049661 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.48927312911424330000000000000E-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 = 3.769999999999952 " " Order of pole (three term test) = 1.80927488980403370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 1.6457177975478579 " " y[1] (numeric) = 1.6457177975478603 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.48414914015919900000000000000E-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 = 3.7799999999999963 " " Order of pole (three term test) = 1.02186904439899940000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 1.6513782999135673 " " y[1] (numeric) = 1.65137829991357 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.61352202535290480000000000000E-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 = 3.7900000000000102 " " Order of pole (three term test) = 1.15392108546219330000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 1.6570370618230685 " " y[1] (numeric) = 1.6570370618230712 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.60801186677675150000000000000E-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 = 3.799999999999977 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 1.6626940924246356 " " y[1] (numeric) = 1.6626940924246385 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.73608595662719360000000000000E-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 = 3.8099999999999965 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 1.6683494007946043 " " y[1] (numeric) = 1.6683494007946071 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.73020103741493350000000000000E-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 = 3.819999999999995 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 1.6740029959381217 " " y[1] (numeric) = 1.6740029959381248 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.85700054091500920000000000000E-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 = 3.830000000000006 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 1.679654886789892 " " y[1] (numeric) = 1.679654886789895 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.85075189754697280000000000000E-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 = 3.83999999999999 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 1.685305082214906 " " y[1] (numeric) = 1.6853050822149094 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.9763003796903940000000000000E-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 = 3.850000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 1.6909535910091678 " " y[1] (numeric) = 1.690953591009171 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.96969869048133570000000000000E-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 = 3.860000000000008 " " Order of pole (three term test) = 6.69465921032784700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 1.6966004219004054 " " y[1] (numeric) = 1.6966004219004087 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.96314290087509360000000000000E-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 = 3.8699999999999517 " " Order of pole (three term test) = 7.54079006523742400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 1.702245583548778 " " y[1] (numeric) = 1.7022455835487815 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.0870746930615830000000000000E-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 = 3.879999999999992 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 1.7078890845475712 " " y[1] (numeric) = 1.7078890845475747 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.0801782217266370000000000000E-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 = 3.890000000000014 " " Order of pole (three term test) = 9.55859631011624300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 1.7135309334238824 " " y[1] (numeric) = 1.7135309334238862 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.20291224984367200000000000000E-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 = 3.8999999999999773 " " Order of pole (three term test) = 2.15136638375231060000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 1.7191711386393007 " " y[1] (numeric) = 1.7191711386393047 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.3248429425205308000000000000E-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 = 3.909999999999976 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 1.7248097085905747 " " y[1] (numeric) = 1.724809708590579 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.44597851726090940000000000000E-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 = 3.9199999999999897 " " Order of pole (three term test) = 6.80521023723341300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 1.7304466516102743 " " y[1] (numeric) = 1.7304466516102786 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.4380107237918770000000000000E-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 = 3.929999999999991 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 1.7360819759674424 " " y[1] (numeric) = 1.7360819759674466 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.4300969378042278000000000000E-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 = 3.93999999999996 " " Order of pole (three term test) = 2.5800606932377407000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 1.7417156898682393 " " y[1] (numeric) = 1.7417156898682435 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.42223660159756050000000000000E-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 = 3.950000000000001 " " Order of pole (three term test) = 9.66382067694092400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 1.7473478014565789 " " y[1] (numeric) = 1.7473478014565833 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.54150438441546940000000000000E-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 = 3.9600000000000155 " " Order of pole (three term test) = 1.0855779570746481000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 1.752978318814756 " " y[1] (numeric) = 1.7529783188147607 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.6600082005454670000000000000E-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 = 3.969999999999977 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 1.758607249964068 " " y[1] (numeric) = 1.7586072499640726 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.65149407493966150000000000000E-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 = 3.9799999999999556 " " Order of pole (three term test) = 2.05302878315913230000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 1.7642346028654243 " " y[1] (numeric) = 1.764234602865429 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.6430366436823290000000000000E-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 = 3.989999999999995 " " Order of pole (three term test) = 7.68078608056772400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 1.7698603854199537 " " y[1] (numeric) = 1.7698603854199586 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.7600941569137260000000000000E-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 = 3.9999999999999734 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 1.7754846054696003 " " y[1] (numeric) = 1.7754846054696054 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.87641238766187750000000000000E-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 = 4.009999999999978 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 1.7811072707977131 " " y[1] (numeric) = 1.7811072707977185 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.99199863229686060000000000000E-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 = 4.019999999999989 " " Order of pole (three term test) = 1.0840539842103930000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 1.7867283891296286 " " y[1] (numeric) = 1.786728389129634 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.98258568600721030000000000000E-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 = 4.029999999999957 " " Order of pole (three term test) = 2.43060611512348260000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 1.7923479681332453 " " y[1] (numeric) = 1.7923479681332508 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.09711909842336260000000000000E-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 = 4.039999999999986 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 1.7979660154195924 " " y[1] (numeric) = 1.797966015419598 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.08744162877311930000000000000E-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 = 4.049999999999983 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 1.8035825385433908 " " y[1] (numeric) = 1.8035825385433963 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.0778270494950416000000000000E-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 = 4.0599999999999845 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 1.8091975450036062 " " y[1] (numeric) = 1.809197545003612 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.19100572737031130000000000000E-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 = 4.069999999999945 " " Order of pole (three term test) = 1.91423517530679070000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 1.8148110422439978 " " y[1] (numeric) = 1.8148110422440036 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.18113544257056850000000000000E-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 = 4.0800000000000125 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 1.8204230376536576 " " y[1] (numeric) = 1.8204230376536636 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.29330282520653050000000000000E-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 = 4.089999999999988 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 1.8260335385675455 " " y[1] (numeric) = 1.8260335385675517 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.40478354125854370000000000000E-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 = 4.0999999999999455 " " Order of pole (three term test) = 2.01266336044265830000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 1.8316425522670157 " " y[1] (numeric) = 1.8316425522670219 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.39435711962785300000000000000E-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 = 4.109999999999997 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = 1.8372500859803385 " " y[1] (numeric) = 1.837250085980345 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.50485412517477950000000000000E-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 = 4.119999999999991 " " Order of pole (three term test) = 8.39197949914876700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = 1.842856146883215 " " y[1] (numeric) = 1.8428561468832214 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.49419218299624400000000000000E-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 = 4.130000000000007 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = 1.8484607420992853 " " y[1] (numeric) = 1.8484607420992918 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.483597674632160000000000000E-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 = 4.139999999999987 " " Order of pole (three term test) = 1.04859593135895800000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = 1.854063878700631 " " y[1] (numeric) = 1.8540638787006378 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.71259201570767750000000000000E-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 = 4.150000000000010 " " Order of pole (three term test) = 2.3433379242377309000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = 1.8596655637082722 " " y[1] (numeric) = 1.859665563708279 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.70140894524612200000000000000E-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 = 4.159999999999980 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = 1.8652658040926566 " " y[1] (numeric) = 1.8652658040926635 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.6902959018349324000000000000E-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 = 4.169999999999985 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = 1.8708646067741452 " " y[1] (numeric) = 1.8708646067741523 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7979377726604160000000000000E-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 = 4.179999999999932 " " Order of pole (three term test) = 1.6319296700046132000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = 1.8764619786234906 " " y[1] (numeric) = 1.8764619786234977 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.78660875549064140000000000000E-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 = 4.190000000000039 " " Order of pole (three term test) = 2.7323025801066370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = 1.8820579264623094 " " y[1] (numeric) = 1.8820579264623167 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 3.8933296682846680000000000000E-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 = 4.19999999999998 " " Order of pole (three term test) = 1.01631851934398010000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = 1.8876524570635511 " " y[1] (numeric) = 1.8876524570635587 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.9994208357586963000000000000E-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 = 4.209999999999984 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = 1.8932455771519585 " " y[1] (numeric) = 1.8932455771519663 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.1048880642663310000000000000E-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 = 4.220000000000015 " " Order of pole (three term test) = 1.2645477270295621000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = 1.898837293404525 " " y[1] (numeric) = 1.8988372934045328 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.0927999462460820000000000000E-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 = 4.229999999999953 " " Order of pole (three term test) = 1.41000086897393770000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = 1.9044276124509447 " " y[1] (numeric) = 1.9044276124509527 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.1973796877548847000000000000E-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 = 4.240000000000012 " " Order of pole (three term test) = 1.57178045600635560000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = 1.9100165408740595 " " y[1] (numeric) = 1.9100165408740675 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.1850976712710050000000000000E-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 = 4.250000000000008 " " Order of pole (three term test) = 8.75836958780259700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = 1.9156040852102978 " " y[1] (numeric) = 1.9156040852103058 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.1728903373180980000000000000E-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 = 4.259999999999998 " " Order of pole (three term test) = 9.75829727210509800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = 1.9211902519501112 " " y[1] (numeric) = 1.9211902519501194 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.2763335770035443000000000000E-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 = 4.269999999999983 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = 1.926775047538404 " " y[1] (numeric) = 1.9267750475384124 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.37918012169140450000000000000E-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 = 4.279999999999948 " " Order of pole (three term test) = 2.42089445483867070000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = 1.932358478374959 " " y[1] (numeric) = 1.9323584783749674 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.3665267503817280000000000000E-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 = 4.289999999999968 " " Order of pole (three term test) = 6.73810741895006300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = 1.9379405508148566 " " y[1] (numeric) = 1.9379405508148653 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.4685269568434450000000000000E-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 = 4.299999999999978 " " Order of pole (three term test) = 7.49983046829004500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = 1.9435212711688916 " " y[1] (numeric) = 1.9435212711689003 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.4556958138502880000000000000E-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 = 4.310000000000003 " " Order of pole (three term test) = 8.34558754279194200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = 1.9491006457039821 " " y[1] (numeric) = 1.949100645703991 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.5568627851915280000000000000E-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 = 4.319999999999982 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = 1.954678680643577 " " y[1] (numeric) = 1.9546786806435859 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.5438589395556966000000000000E-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 = 4.330000000000002 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = 1.9602553821680555 " " y[1] (numeric) = 1.9602553821680646 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 4.6442054870714790000000000000E-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 = 4.339999999999973 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = 1.9658307564151252 " " y[1] (numeric) = 1.9658307564151345 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.7439859084603553000000000000E-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 = 4.34999999999997 " " Order of pole (three term test) = 1.2764632319871560000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y[1] (analytic) = 1.9714048094802126 " " y[1] (numeric) = 1.9714048094802221 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.843205193505530400000000000E-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 = 4.359999999999971 " " Order of pole (three term test) = 7.09334364789236500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y[1] (analytic) = 1.9769775474168516 " " y[1] (numeric) = 1.9769775474168612 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8295530843290550000000000000E-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 = 4.3699999999999815 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y[1] (analytic) = 1.9825489762370654 " " y[1] (numeric) = 1.9825489762370752 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9279804604096320000000000000E-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 = 4.3800000000000034 " " Order of pole (three term test) = 8.75551259790900400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y[1] (analytic) = 1.9881191019117466 " " y[1] (numeric) = 1.9881191019117566 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0258594729149970000000000000E-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 = 4.389999999999999 " " Order of pole (three term test) = 1.9447797369871309000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y[1] (analytic) = 1.9936879303710304 " " y[1] (numeric) = 1.9936879303710404 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0118210926656270000000000000E-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 = 4.399999999999986 " " Order of pole (three term test) = 1.07968138188926380000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y[1] (analytic) = 1.999255467504665 " " y[1] (numeric) = 1.9992554675046752 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1089277946554410000000000000E-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 = 4.409999999999977 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y[1] (analytic) = 2.004821719162378 " " y[1] (numeric) = 2.004821719162388 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.0947432028115250000000000000E-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 = 4.419999999999982 " " Order of pole (three term test) = 6.65069280791789800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y[1] (analytic) = 2.0103866911542374 " " y[1] (numeric) = 2.0103866911542476 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.0806403919671660000000000000E-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 = 4.42999999999999 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y[1] (analytic) = 2.0159503892510093 " " y[1] (numeric) = 2.01595038925102 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.2869064106093130000000000000E-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 = 4.439999999999970 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y[1] (analytic) = 2.021512819184513 " " y[1] (numeric) = 2.0215128191845237 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.2723588667130210000000000000E-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 = 4.449999999999984 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y[1] (analytic) = 2.027073986647969 " " y[1] (numeric) = 2.02707398664798 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4769733711646850000000000000E-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 = 4.45999999999997 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y[1] (analytic) = 2.032633897296345 " " y[1] (numeric) = 2.032633897296356 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4619920788583260000000000000E-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 = 4.469999999999967 " " Order of pole (three term test) = 1.11580566616921450000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y[1] (analytic) = 2.038192556746699 " " y[1] (numeric) = 2.03819255674671 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4470958641771350000000000000E-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 = 4.480000000000036 " " Order of pole (three term test) = 2.4732108209212670000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y[1] (analytic) = 2.0437499705785163 " " y[1] (numeric) = 2.0437499705785274 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4322839907412460000000000000E-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 = 4.489999999999984 " " Order of pole (three term test) = 6.85084574374294500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y[1] (analytic) = 2.049306144334044 " " y[1] (numeric) = 2.049306144334055 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4175557307272990000000000000E-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 = 4.500000000000017 " " Order of pole (three term test) = 7.58906262080073700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y[1] (analytic) = 2.054861083518622 " " y[1] (numeric) = 2.054861083518633 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4029103647438630000000000000E-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 = 4.509999999999982 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y[1] (analytic) = 2.06041479360101 " " y[1] (numeric) = 2.0604147936010215 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.6038810689773770000000000000E-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 = 4.519999999999965 " " Order of pole (three term test) = 9.30637404924356800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y[1] (analytic) = 2.0659672800137105 " " y[1] (numeric) = 2.065967280013722 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.5888200978792860000000000000E-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 = 4.52999999999997 " " Order of pole (three term test) = 1.03021956968490480000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y[1] (analytic) = 2.071518548153289 " " y[1] (numeric) = 2.0715185481533007 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.5738431434248580000000000000E-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 = 4.539999999999962 " " Order of pole (three term test) = 1.140201831210050100000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y[1] (analytic) = 2.0770686033806895 " " y[1] (numeric) = 2.0770686033807015 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.7727552409370570000000000000E-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 = 4.549999999999967 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y[1] (analytic) = 2.082617451021548 " " y[1] (numeric) = 2.0826174510215605 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9706106225617610000000000000E-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 = 4.56 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y[1] (analytic) = 2.088165096366503 " " y[1] (numeric) = 2.0881650963665153 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9547484523318170000000000000E-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 = 4.569999999999983 " " Order of pole (three term test) = 7.71840761537685300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y[1] (analytic) = 2.0937115446714976 " " y[1] (numeric) = 2.0937115446715104 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.1510799414694250000000000000E-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 = 4.579999999999943 " " Order of pole (three term test) = 1.70696450705101480000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y[1] (analytic) = 2.099256801158088 " " y[1] (numeric) = 2.0992568011581003 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9232857404306460000000000000E-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 = 4.589999999999999 " " Order of pole (three term test) = 1.88710487889022750000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y[1] (analytic) = 2.1048008710137367 " " y[1] (numeric) = 2.104800871013749 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9076837372330230000000000000E-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 = 4.599999999999971 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y[1] (analytic) = 2.110343759392113 " " y[1] (numeric) = 2.110343759392126 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.1026015445756130000000000000E-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 = 4.609999999999970 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y[1] (analytic) = 2.1158854714133857 " " y[1] (numeric) = 2.1158854714133986 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.0866182313020360000000000000E-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 = 4.619999999999996 " " Order of pole (three term test) = 1.27324911403774470000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999999772 " " y[1] (analytic) = 2.1214260121645094 " " y[1] (numeric) = 2.1214260121645223 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.0707217747894400000000000000E-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 = 4.62999999999996 " " Order of pole (three term test) = 7.03198763222018800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999977 " " y[1] (analytic) = 2.1269653866995144 " " y[1] (numeric) = 2.1269653866995277 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2637015058224030000000000000E-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 = 4.639999999999969 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999977 " " y[1] (analytic) = 2.1325036000397897 " " y[1] (numeric) = 2.132503600039803 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2474343749071730000000000000E-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 = 4.649999999999978 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1599999999999766 " " y[1] (analytic) = 2.138040657174362 " " y[1] (numeric) = 2.1380406571743755 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2312548878790490000000000000E-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 = 4.659999999999975 " " Order of pole (three term test) = 9.46465262901914400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1699999999999764 " " y[1] (analytic) = 2.143576563060175 " " y[1] (numeric) = 2.143576563060188 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2151623250080680000000000000E-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 = 4.669999999999941 " " Order of pole (three term test) = 1.04454948058858550000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999976 " " y[1] (analytic) = 2.149111322622362 " " y[1] (numeric) = 2.1491113226223755 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.1991559745008680000000000000E-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 = 4.680000000000000 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999976 " " y[1] (analytic) = 2.15464494075452 " " y[1] (numeric) = 2.1546449407545336 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.389342970137369000000000000E-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 = 4.69 " " Order of pole (three term test) = 1.27146168174275180000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999758 " " y[1] (analytic) = 2.1601774223189762 " " y[1] (numeric) = 2.16017742231899 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.3729790725120870000000000000E-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 = 4.699999999999983 " " Order of pole (three term test) = 7.01171056743468400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999999755 " " y[1] (analytic) = 2.1657087721470543 " " y[1] (numeric) = 2.1657087721470685 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.5617570090523090000000000000E-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 = 4.709999999999948 " " Order of pole (three term test) = 1.54637293279077880000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999999753 " " y[1] (analytic) = 2.1712389950393387 " " y[1] (numeric) = 2.171238995039353 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.5450439807270180000000000000E-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 = 4.71999999999997 " " Order of pole (three term test) = 8.52421613530861100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.229999999999975 " " y[1] (analytic) = 2.176768095765933 " " y[1] (numeric) = 2.176768095765947 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.5284192389826770000000000000E-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 = 4.729999999999964 " " Order of pole (three term test) = 9.395826522326299000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999975 " " y[1] (analytic) = 2.1822960790667185 " " y[1] (numeric) = 2.182296079066733 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.7153783877572670000000000000E-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 = 4.739999999999966 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999747 " " y[1] (analytic) = 2.18782294965161 " " y[1] (numeric) = 2.187822949651624 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.4954317795527960000000000000E-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 = 4.7499999999999485 " " Order of pole (three term test) = 1.1408500308703541000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2599999999999745 " " y[1] (analytic) = 2.1933487122008044 " " y[1] (numeric) = 2.193348712200819 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.6815385276093680000000000000E-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 = 4.759999999999965 " " Order of pole (three term test) = 1.25673103720543660000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2699999999999743 " " y[1] (analytic) = 2.1988733713650346 " " y[1] (numeric) = 2.1988733713650492 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.6647511929959160000000000000E-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 = 4.769999999999931 " " Order of pole (three term test) = 1.38410153914523220000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999974 " " y[1] (analytic) = 2.204396931765813 " " y[1] (numeric) = 2.204396931765828 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 6.8495074173448330000000000000E-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 = 4.779999999999979 " " Order of pole (three term test) = 7.62036483465528900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999974 " " y[1] (analytic) = 2.209919397995678 " " y[1] (numeric) = 2.209919397995693 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 6.832390877511840000000000000E-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 = 4.789999999999963 " " Order of pole (three term test) = 8.38930796204282300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999999736 " " y[1] (analytic) = 2.215440774618433 " " y[1] (numeric) = 2.2154407746184486 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 7.0158148765810250000000000000E-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 = 4.799999999999990 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999999734 " " y[1] (analytic) = 2.220961066169389 " " y[1] (numeric) = 2.2209610661694046 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.9983767754921760000000000000E-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 = 4.809999999999977 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.319999999999973 " " y[1] (analytic) = 2.226480277155599 " " y[1] (numeric) = 2.2264802771556145 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.9810285337937230000000000000E-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 = 4.819999999999963 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.329999999999973 " " y[1] (analytic) = 2.231998412056092 " " y[1] (numeric) = 2.2319984120561074 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.9637694457112290000000000000E-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 = 4.82999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999728 " " y[1] (analytic) = 2.2375154753221063 " " y[1] (numeric) = 2.2375154753221222 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.1450730647128960000000000000E-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 = 4.839999999999964 " " Order of pole (three term test) = 6.76315218491206100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3499999999999726 " " y[1] (analytic) = 2.243031471377319 " " y[1] (numeric) = 2.243031471377335 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.1275021142638750000000000000E-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 = 4.849999999999937 " " Order of pole (three term test) = 1.48734766430087540000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3599999999999723 " " y[1] (analytic) = 2.2485464046180716 " " y[1] (numeric) = 2.2485464046180876 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.1100207324019060000000000000E-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 = 4.85999999999999 " " Order of pole (three term test) = 8.17581226411187100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999972 " " y[1] (analytic) = 2.2540602794135953 " " y[1] (numeric) = 2.2540602794136118 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 7.2896456738623680000000000000E-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 = 4.869999999999948 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999972 " " y[1] (analytic) = 2.259573100106235 " " y[1] (numeric) = 2.259573100106251 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.0753238980631370000000000000E-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 = 4.879999999999997 " " Order of pole (three term test) = 9.87584662405687700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999717 " " y[1] (analytic) = 2.265084871011666 " " y[1] (numeric) = 2.265084871011682 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 7.2541656053327160000000000000E-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 = 4.8899999999999375 " " Order of pole (three term test) = 1.08510070114323440000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999999715 " " y[1] (analytic) = 2.270595596419116 " " y[1] (numeric) = 2.2705955964191324 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 7.2365597776925130000000000000E-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 = 4.899999999999958 " " Order of pole (three term test) = 1.19201633185513220000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999999713 " " y[1] (analytic) = 2.276105280591578 " " y[1] (numeric) = 2.2761052805915947 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 7.4141517609925020000000000000E-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 = 4.909999999999974 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.419999999999971 " " y[1] (analytic) = 2.2816139277660246 " " y[1] (numeric) = 2.2816139277660414 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 7.3962512977931470000000000000E-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 = 4.919999999999975 " " Order of pole (three term test) = 7.18831758086336800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.429999999999971 " " y[1] (analytic) = 2.2871215421536197 " " y[1] (numeric) = 2.287121542153637 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.572609878810340000000000000E-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 = 4.929999999999971 " " Order of pole (three term test) = 7.89206794404033200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999999706 " " y[1] (analytic) = 2.292628127939928 " " y[1] (numeric) = 2.292628127939945 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 7.360718368864291000000000000E-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 = 4.9399999999999755 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4499999999999704 " " y[1] (analytic) = 2.2981336892851196 " " y[1] (numeric) = 2.298133689285137 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5363236111559770000000000000E-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 = 4.949999999999993 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999997 " " y[1] (analytic) = 2.303638230324179 " " y[1] (numeric) = 2.3036382303241965 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5183155741060780000000000000E-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 = 4.959999999999943 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.46999999999997 " " y[1] (analytic) = 2.3091417551671043 " " y[1] (numeric) = 2.3091417551671216 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5003966930125050000000000000E-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 = 4.969999999999952 " " Order of pole (three term test) = 1.14452797012442850000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.47999999999997 " " y[1] (analytic) = 2.3146442678991104 " " y[1] (numeric) = 2.3146442678991277 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.4825662951104310000000000000E-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 = 4.979999999999941 " " Order of pole (three term test) = 1.25540049541595780000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999999696 " " y[1] (analytic) = 2.3201457725808265 " " y[1] (numeric) = 2.3201457725808443 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 7.6562294507224460000000000000E-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 = 4.989999999999987 " " Order of pole (three term test) = 6.88379029624510300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999999694 " " y[1] (analytic) = 2.325646273248495 " " y[1] (numeric) = 2.3256462732485126 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 7.6381213249554520000000000000E-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 = 4.999999999999984 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.509999999999969 " " y[1] (analytic) = 2.3311457739141628 " " y[1] (numeric) = 2.331145773914181 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 7.8106044708137610000000000000E-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 = 5.00999999999999 " " Order of pole (three term test) = 8.2744268889607100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.519999999999969 " " y[1] (analytic) = 2.3366442785658785 " " y[1] (numeric) = 2.336644278565897 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.9822791106013740000000000000E-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 = 5.020000000000017 " " Order of pole (three term test) = 1.81385897155685000000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999687 " " y[1] (analytic) = 2.3421417911678812 " " y[1] (numeric) = 2.3421417911679 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.9635429776444730000000000000E-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 = 5.029999999999952 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999999685 " " y[1] (analytic) = 2.3476383156607885 " " y[1] (numeric) = 2.347638315660807 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.9448979381871830000000000000E-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 = 5.039999999999937 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5499999999999683 " " y[1] (analytic) = 2.353133855961786 " " y[1] (numeric) = 2.353133855961805 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.1150657771432790000000000000E-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 = 5.049999999999966 " " Order of pole (three term test) = 1.19290518578137660000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999968 " " y[1] (analytic) = 2.3586284159648123 " " y[1] (numeric) = 2.3586284159648314 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0961612665644990000000000000E-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 = 5.059999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999968 " " y[1] (analytic) = 2.3641219995407416 " " y[1] (numeric) = 2.3641219995407607 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0773479656558690000000000000E-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 = 5.069999999999967 " " Order of pole (three term test) = 7.15383084300071900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999999677 " " y[1] (analytic) = 2.369614610537566 " " y[1] (numeric) = 2.3696146105375853 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0586252037079760000000000000E-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 = 5.0799999999999965 " " Order of pole (three term test) = 7.8325522823882110000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999999674 " " y[1] (analytic) = 2.375106252780576 " " y[1] (numeric) = 2.3751062527805953 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0399923166371520000000000000E-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 = 5.08999999999998 " " Order of pole (three term test) = 8.574139100710501000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999999672 " " y[1] (analytic) = 2.3805969300725383 " " y[1] (numeric) = 2.3805969300725573 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0214486469033760000000000000E-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 = 5.099999999999962 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.609999999999967 " " y[1] (analytic) = 2.3860866461938715 " " y[1] (numeric) = 2.3860866461938905 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0029935434294120000000000000E-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 = 5.109999999999944 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.619999999999967 " " y[1] (analytic) = 2.3915754049028224 " " y[1] (numeric) = 2.3915754049028415 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 7.984626361521150000000000000E-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 = 5.119999999999963 " " Order of pole (three term test) = 1.12354570092031920000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999999666 " " y[1] (analytic) = 2.3970632099356375 " " y[1] (numeric) = 2.397063209935657 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.1516103340167710000000000000E-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 = 5.1299999999999235 " " Order of pole (three term test) = 1.2290550414404419000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999999664 " " y[1] (analytic) = 2.402550065006736 " " y[1] (numeric) = 2.4025500650067557 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.1329939875146660000000000000E-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 = 5.139999999999944 " " Order of pole (three term test) = 1.34423751399883160000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999966 " " y[1] (analytic) = 2.408035973808879 " " y[1] (numeric) = 2.4080359738088983 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.1144656665970560000000000000E-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 = 5.149999999999908 " " Order of pole (three term test) = 2.20493774715008580000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999966 " " y[1] (analytic) = 2.4135209400133357 " " y[1] (numeric) = 2.413520940013355 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 7.9120241747093280000000000000E-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 = 5.159999999999974 " " Order of pole (three term test) = 8.03579440083518600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999657 " " y[1] (analytic) = 2.4190049672700518 " " y[1] (numeric) = 2.4190049672700713 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.0776705702487150000000000000E-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 = 5.170000000000005 " " Order of pole (three term test) = 1.75686147560077830000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999999655 " " y[1] (analytic) = 2.4244880592078153 " " y[1] (numeric) = 2.424488059207835 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.059402544464290000000000000E-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 = 5.180000000000004 " " Order of pole (three term test) = 1.92017798297877270000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999999653 " " y[1] (analytic) = 2.4299702194344164 " " y[1] (numeric) = 2.4299702194344364 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.2239750443954670000000000000E-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 = 5.189999999999977 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.699999999999965 " " y[1] (analytic) = 2.435451451536813 " " y[1] (numeric) = 2.4354514515368324 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.0231224568540340000000000000E-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 = 5.199999999999983 " " Order of pole (three term test) = 1.1462948703742660000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.709999999999965 " " y[1] (analytic) = 2.440931759081286 " " y[1] (numeric) = 2.4409317590813058 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1870434799760130000000000000E-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 = 5.209999999999978 " " Order of pole (three term test) = 1.25221186219824340000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999647 " " y[1] (analytic) = 2.4464111456136037 " " y[1] (numeric) = 2.4464111456136237 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1687064249539580000000000000E-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 = 5.219999999999955 " " Order of pole (three term test) = 6.83841863882363700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999999645 " " y[1] (analytic) = 2.4518896146591747 " " y[1] (numeric) = 2.4518896146591946 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1504543776252750000000000000E-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 = 5.229999999999957 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999999642 " " y[1] (analytic) = 2.4573671697232045 " " y[1] (numeric) = 2.4573671697232244 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1322867373961860000000000000E-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 = 5.239999999999934 " " Order of pole (three term test) = 8.15364403283435300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999964 " " y[1] (analytic) = 2.4628438142908498 " " y[1] (numeric) = 2.4628438142908697 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.11420290937410000000000000E-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 = 5.249999999999964 " " Order of pole (three term test) = 8.90103487763361600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999964 " " y[1] (analytic) = 2.468319551827371 " " y[1] (numeric) = 2.4683195518273915 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2761179110619380000000000000E-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 = 5.259999999999959 " " Order of pole (three term test) = 9.7153125584815400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7699999999999636 " " y[1] (analytic) = 2.4737943857782843 " " y[1] (numeric) = 2.4737943857783047 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2578017682241470000000000000E-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 = 5.269999999999912 " " Order of pole (three term test) = 2.1204636966837193000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999999634 " " y[1] (analytic) = 2.479268319569509 " " y[1] (numeric) = 2.4792683195695293 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2395695100278390000000000000E-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 = 5.27999999999994 " " Order of pole (three term test) = 1.15683916322577340000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.789999999999963 " " y[1] (analytic) = 2.4847413566075183 " " y[1] (numeric) = 2.4847413566075387 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.221420550988010000000000000E-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 = 5.289999999999927 " " Order of pole (three term test) = 1.2620409872933988000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.799999999999963 " " y[1] (analytic) = 2.490213500279485 " " y[1] (numeric) = 2.4902135002795056 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2033543111103390000000000000E-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 = 5.29999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999627 " " y[1] (analytic) = 2.495684753953428 " " y[1] (numeric) = 2.4956847539534484 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.1853702158265830000000000000E-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 = 5.309999999999933 " " Order of pole (three term test) = 2.25191386515878560000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999999625 " " y[1] (analytic) = 2.5011551209783542 " " y[1] (numeric) = 2.5011551209783747 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.1674676959309120000000000000E-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 = 5.319999999999995 " " Order of pole (three term test) = 8.18498025356378200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999999623 " " y[1] (analytic) = 2.5066246046844043 " " y[1] (numeric) = 2.5066246046844247 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.1496461875171270000000000000E-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 = 5.329999999999944 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999962 " " y[1] (analytic) = 2.5120932083829914 " " y[1] (numeric) = 2.5120932083830123 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 8.3086856782627740000000000000E-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 = 5.339999999999956 " " Order of pole (three term test) = 9.72703265233981100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999962 " " y[1] (analytic) = 2.5175609353669444 " " y[1] (numeric) = 2.5175609353669652 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 8.2906405838040780000000000000E-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 = 5.349999999999950 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999617 " " y[1] (analytic) = 2.523027788910643 " " y[1] (numeric) = 2.5230277889106643 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.4486909603190090000000000000E-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 = 5.3600000000000145 " " Order of pole (three term test) = 2.31043030270242140000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8699999999999615 " " y[1] (analytic) = 2.5284937722701586 " " y[1] (numeric) = 2.52849377227018 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.4304269627148810000000000000E-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 = 5.369999999999939 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999999613 " " y[1] (analytic) = 2.5339588886833884 " " y[1] (numeric) = 2.5339588886834097 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.4122446374331930000000000000E-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 = 5.379999999999982 " " Order of pole (three term test) = 1.37109400235142370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.889999999999961 " " y[1] (analytic) = 2.5394231413701913 " " y[1] (numeric) = 2.539423141370213 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 8.5690214159865730000000000000E-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 = 5.389999999999948 " " Order of pole (three term test) = 1.49336424513128230000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.899999999999961 " " y[1] (analytic) = 2.544886533532522 " " y[1] (numeric) = 2.544886533532544 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 8.5506253406307250000000000000E-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 = 5.3999999999999435 " " Order of pole (three term test) = 2.4394210178615958000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999999606 " " y[1] (analytic) = 2.550349068354562 " " y[1] (numeric) = 2.5503490683545844 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 8.7064397450616580000000000000E-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 = 5.409999999999922 " " Order of pole (three term test) = 1.77074794040984720000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999999604 " " y[1] (analytic) = 2.5558107490028537 " " y[1] (numeric) = 2.5558107490028754 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 8.514077691841170000000000000E-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 = 5.41999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.92999999999996 " " y[1] (analytic) = 2.5612715786264255 " " y[1] (numeric) = 2.5612715786264477 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 8.6693112428206750000000000000E-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 = 5.429999999999967 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.93999999999996 " " y[1] (analytic) = 2.5667315603569274 " " y[1] (numeric) = 2.5667315603569496 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 8.6508697814178110000000000000E-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 = 5.439999999999976 " " Order of pole (three term test) = 1.14183129244061960000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999598 " " y[1] (analytic) = 2.5721906973087525 " " y[1] (numeric) = 2.572190697308775 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.80515963534510000000000000E-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 = 5.449999999999982 " " Order of pole (three term test) = 1.24248644508978530000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9599999999999596 " " y[1] (analytic) = 2.5776489925791677 " " y[1] (numeric) = 2.5776489925791903 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.7865142878477410000000000000E-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 = 5.459999999999944 " " Order of pole (three term test) = 6.75902610071922800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9699999999999593 " " y[1] (analytic) = 2.5831064492484366 " " y[1] (numeric) = 2.5831064492484592 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.7679505848250520000000000000E-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 = 5.4699999999999696 " " Order of pole (three term test) = 7.35257681516448800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999959 " " y[1] (analytic) = 2.588563070379945 " " y[1] (numeric) = 2.588563070379968 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.7494679814886170000000000000E-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 = 5.479999999999945 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.989999999999959 " " y[1] (analytic) = 2.5940188590203235 " " y[1] (numeric) = 2.5940188590203466 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.9022633092669930000000000000E-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 = 5.489999999999989 " " Order of pole (three term test) = 8.6966181952987500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999587 " " y[1] (analytic) = 2.59947381819957 " " y[1] (numeric) = 2.599473818199593 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8835820351510690000000000000E-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 = 5.500000000000010 " " Order of pole (three term test) = 2.83679224200245900000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999959 " " y[1] (analytic) = 2.60492795093117 " " y[1] (numeric) = 2.6049279509311924 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.6945013946574360000000000000E-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 = 5.509999999999915 " " Order of pole (three term test) = 2.05601416275659370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999959 " " y[1] (analytic) = 2.6103812602122147 " " y[1] (numeric) = 2.610381260212238 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8464621104144410000000000000E-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 = 5.519999999999948 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999999585 " " y[1] (analytic) = 2.6158337490235244 " " y[1] (numeric) = 2.6158337490235475 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8280223927929690000000000000E-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 = 5.529999999999932 " " Order of pole (three term test) = 2.42889418302388050000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999958 " " y[1] (analytic) = 2.6212854203297615 " " y[1] (numeric) = 2.6212854203297846 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8096621348842540000000000000E-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 = 5.539999999999963 " " Order of pole (three term test) = 1.3196894250353630000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999958 " " y[1] (analytic) = 2.6267362770795493 " " y[1] (numeric) = 2.6267362770795724 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7913808149320760000000000000E-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 = 5.549999999999953 " " Order of pole (three term test) = 7.16918499394993400000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999958 " " y[1] (analytic) = 2.632186322205586 " " y[1] (numeric) = 2.632186322205609 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7731779157841890000000000000E-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 = 5.55999999999998 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999958 " " y[1] (analytic) = 2.6376355586247615 " " y[1] (numeric) = 2.6376355586247846 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7550529248413460000000000000E-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 = 5.5700000000000065 " " Order of pole (three term test) = 2.53777313818400460000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999957 " " y[1] (analytic) = 2.643083989238268 " " y[1] (numeric) = 2.643083989238291 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7370053340070030000000000000E-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 = 5.579999999999953 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999957 " " y[1] (analytic) = 2.648531616931715 " " y[1] (numeric) = 2.6485316169317383 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 8.886708382707650000000000000E-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 = 5.589999999999957 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999957 " " y[1] (analytic) = 2.653978444575239 " " y[1] (numeric) = 2.6539784445752623 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 8.8684699644651030000000000000E-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 = 5.599999999999948 " " Order of pole (three term test) = 1.08303328915873150000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999957 " " y[1] (analytic) = 2.659424475023614 " " y[1] (numeric) = 2.6594244750236378 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 9.0172958687576370000000000000E-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 = 5.609999999999914 " " Order of pole (three term test) = 1.1756666024443970000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999957 " " y[1] (analytic) = 2.6648697111163626 " " y[1] (numeric) = 2.6648697111163866 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 8.9988704632983260000000000000E-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 = 5.619999999999997 " " Order of pole (three term test) = 1.27603644831562970000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999956 " " y[1] (analytic) = 2.6703141556778625 " " y[1] (numeric) = 2.6703141556778864 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 8.9805228650393840000000000000E-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 = 5.630000000000014 " " Order of pole (three term test) = 3.46193361145998750000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999956 " " y[1] (analytic) = 2.6757578115174545 " " y[1] (numeric) = 2.6757578115174785 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 8.9622525733386790000000000000E-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 = 5.639999999999919 " " Order of pole (three term test) = 7.51279175660009600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999956 " " y[1] (analytic) = 2.6812006814295497 " " y[1] (numeric) = 2.681200681429574 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 9.1096898158069580000000000000E-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 = 5.649999999999954 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999956 " " y[1] (analytic) = 2.6866427681937353 " " y[1] (numeric) = 2.6866427681937597 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 9.091237149542820000000000000E-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 = 5.6599999999999655 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.1699999999999555 " " y[1] (analytic) = 2.6920840745748773 " " y[1] (numeric) = 2.692084074574902 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.2378228401097440000000000000E-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 = 5.66999999999997 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999955 " " y[1] (analytic) = 2.697524603323227 " " y[1] (numeric) = 2.697524603323252 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.2191914472127680000000000000E-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 = 5.679999999999896 " " Order of pole (three term test) = 2.07977333681143430000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999955 " " y[1] (analytic) = 2.7029643571745217 " " y[1] (numeric) = 2.7029643571745465 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.2006376945346440000000000000E-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 = 5.689999999999967 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999955 " " y[1] (analytic) = 2.708403338850088 " " y[1] (numeric) = 2.708403338850113 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.1821610891094920000000000000E-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 = 5.699999999999994 " " Order of pole (three term test) = 1.2223791363047930000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999955 " " y[1] (analytic) = 2.7138415510569414 " " y[1] (numeric) = 2.7138415510569667 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.3273997340025440000000000000E-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 = 5.709999999999925 " " Order of pole (three term test) = 1.32502339718091670000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.2199999999999545 " " y[1] (analytic) = 2.7192789964878883 " " y[1] (numeric) = 2.7192789964879136 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.3087487507339030000000000000E-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 = 5.719999999999976 " " Order of pole (three term test) = 1.43608416096970400000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999954 " " y[1] (analytic) = 2.7247156778216235 " " y[1] (numeric) = 2.724715677821649 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.2901748125481720000000000000E-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 = 5.729999999999997 " " Order of pole (three term test) = 7.78117499691378900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999954 " " y[1] (analytic) = 2.73015159772283 " " y[1] (numeric) = 2.7301515977228554 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.2716774345302850000000000000E-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 = 5.739999999999975 " " Order of pole (three term test) = 8.43101034947349300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999954 " " y[1] (analytic) = 2.7355867588422758 " " y[1] (numeric) = 2.7355867588423015 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.4155939628119470000000000000E-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 = 5.74999999999994 " " Order of pole (three term test) = 9.13384059212823100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999954 " " y[1] (analytic) = 2.741021163816911 " " y[1] (numeric) = 2.741021163816937 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.3969264124310530000000000000E-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 = 5.759999999999987 " " Order of pole (three term test) = 1.97877677890864360000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999953 " " y[1] (analytic) = 2.746454815269963 " " y[1] (numeric) = 2.746454815269989 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.3783353099773560000000000000E-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 = 5.769999999999972 " " Order of pole (three term test) = 1.07156859559322430000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999953 " " y[1] (analytic) = 2.7518877158110326 " " y[1] (numeric) = 2.7518877158110584 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.3598201784597560000000000000E-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 = 5.779999999999939 " " Order of pole (three term test) = 1.16041448009515670000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999953 " " y[1] (analytic) = 2.757319868036187 " " y[1] (numeric) = 2.757319868036213 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 9.5024388301436740000000000000E-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 = 5.78999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999953 " " y[1] (analytic) = 2.7627512745280542 " " y[1] (numeric) = 2.7627512745280804 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 9.4837575943674180000000000000E-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 = 5.799999999999919 " " Order of pole (three term test) = 6.80127413953652200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3099999999999525 " " y[1] (analytic) = 2.7681819378559154 " " y[1] (numeric) = 2.768181937855942 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 9.6255785165774950000000000000E-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 = 5.8099999999999765 " " Order of pole (three term test) = 7.3621500792920900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999952 " " y[1] (analytic) = 2.773611860575797 " " y[1] (numeric) = 2.7736118605758238 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 9.6067344424580830000000000000E-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 = 5.819999999999915 " " Order of pole (three term test) = 1.59363869402363660000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999952 " " y[1] (analytic) = 2.7790410452305605 " " y[1] (numeric) = 2.7790410452305876 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 9.7477659955203610000000000000E-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 = 5.829999999999938 " " Order of pole (three term test) = 8.62295451709030800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999952 " " y[1] (analytic) = 2.7844694943499944 " " y[1] (numeric) = 2.7844694943500214 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 9.7287622851754640000000000000E-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 = 5.839999999999877 " " Order of pole (three term test) = 2.7990766949631163000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999952 " " y[1] (analytic) = 2.7898972104509014 " " y[1] (numeric) = 2.789897210450929 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 9.8690127032507860000000000000E-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 = 5.849999999999964 " " Order of pole (three term test) = 1.00942118750517900000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3599999999999515 " " y[1] (analytic) = 2.7953241960371904 " " y[1] (numeric) = 2.795324196037218 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 9.84985249644279900000000000E-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 = 5.859999999999973 " " Order of pole (three term test) = 1.09192526111519440000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999951 " " y[1] (analytic) = 2.800750453599961 " " y[1] (numeric) = 2.800750453599989 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9893298899917150000000000000E-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 = 5.869999999999927 " " Order of pole (three term test) = 1.18101451116945130000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999951 " " y[1] (analytic) = 2.8061759856175934 " " y[1] (numeric) = 2.8061759856176214 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9700162655324440000000000000E-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 = 5.879999999999955 " " Order of pole (three term test) = 1.27720195886101560000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999950 " " y[1] (analytic) = 2.8116007945558334 " " y[1] (numeric) = 2.8116007945558614 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9507797389756210000000000000E-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 = 5.889999999999967 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999950 " " y[1] (analytic) = 2.817024882867878 " " y[1] (numeric) = 2.817024882867906 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9316198414517630000000000000E-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 = 5.899999999999942 " " Order of pole (three term test) = 7.46560686248702200000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.40999999999995 " " y[1] (analytic) = 2.822448252994461 " " y[1] (numeric) = 2.822448252994489 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9125361079237640000000000000E-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 = 5.909999999999932 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999995 " " y[1] (analytic) = 2.8278709073639376 " " y[1] (numeric) = 2.827870907363966 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.005056820535628000000000000E-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 = 5.91999999999997 " " Order of pole (three term test) = 8.72310479773039100000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.42999999999995 " " y[1] (analytic) = 2.8332928483923676 " " y[1] (numeric) = 2.833292848392396 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.0031334899437135000000000000E-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 = 5.92999999999997 " " Order of pole (three term test) = 1.88546498360115670000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.43999999999995 " " y[1] (analytic) = 2.8387140784835974 " " y[1] (numeric) = 2.838714078483626 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.0012177572172574000000000000E-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 = 5.939999999999921 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4499999999999496 " " y[1] (analytic) = 2.8441346000293435 " " y[1] (numeric) = 2.844134600029372 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 9.9930957663223020000000000000E-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 = 5.949999999999940 " " Order of pole (three term test) = 1.10065954531566330000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999950 " " y[1] (analytic) = 2.8495544154092736 " " y[1] (numeric) = 2.849554415409302 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 9.974089028344411000000000000E-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 = 5.9599999999999245 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999950 " " y[1] (analytic) = 2.8549735269910865 " " y[1] (numeric) = 2.854973526991115 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 9.955156908357821000000000000E-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 = 5.96999999999996 " " Order of pole (three term test) = 1.2843749088516870000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999949 " " y[1] (analytic) = 2.8603919371305935 " " y[1] (numeric) = 2.8603919371306223 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.0091553631356841000000000000E-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 = 5.979999999999894 " " Order of pole (three term test) = 6.93580778086070300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999949 " " y[1] (analytic) = 2.865809648171798 " " y[1] (numeric) = 2.865809648171827 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.0072475908743132000000000000E-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 = 5.98999999999999 " " Order of pole (three term test) = 7.48990682416573800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999999485 " " y[1] (analytic) = 2.871226662446972 " " y[1] (numeric) = 2.8712266624470013 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0208141430786623000000000000E-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 = 5.999999999999944 " " Order of pole (three term test) = 1.61744714779826710000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999948 " " y[1] (analytic) = 2.876642982276737 " " y[1] (numeric) = 2.8766429822767665 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0188920916041738000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.00999999999996 " " Order of pole (three term test) = 8.73108662854452800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999948 " " y[1] (analytic) = 2.882058609970141 " " y[1] (numeric) = 2.8820586099701697 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.001568758539338900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.019999999999919 " " Order of pole (three term test) = 9.42499618270131300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999948 " " y[1] (analytic) = 2.8874735478247318 " " y[1] (numeric) = 2.8874735478247606 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.9969049628177610000000000000E-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 = 6.029999999999945 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999948 " " y[1] (analytic) = 2.892887798126639 " " y[1] (numeric) = 2.892887798126668 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.9781950267642020000000000000E-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 = 6.039999999999945 " " Order of pole (three term test) = 1.09784685398800420000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999947 " " y[1] (analytic) = 2.8983013631506456 " " y[1] (numeric) = 2.8983013631506744 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.9595573487482450000000000000E-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 = 6.049999999999966 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999947 " " y[1] (analytic) = 2.9037142451602636 " " y[1] (numeric) = 2.903714245160293 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0093929834506303000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.059999999999923 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999947 " " y[1] (analytic) = 2.9091264464078095 " " y[1] (numeric) = 2.909126446407839 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0075150870906968000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.069999999999991 " " Order of pole (three term test) = 1.37886698951137340000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999947 " " y[1] (analytic) = 2.9145379691344764 " " y[1] (numeric) = 2.914537969134506 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0208814355844595000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.079999999999951 " " Order of pole (three term test) = 7.43664818075149000000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999947 " " y[1] (analytic) = 2.9199488155704088 " " y[1] (numeric) = 2.9199488155704385 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0189896789044156000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.08999999999998 " " Order of pole (three term test) = 1.60412440517214070000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999946 " " y[1] (analytic) = 2.9253589879347737 " " y[1] (numeric) = 2.9253589879348034 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0171051547064902000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.099999999999988 " " Order of pole (three term test) = 1.72987608852456370000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999946 " " y[1] (analytic) = 2.930768488435833 " " y[1] (numeric) = 2.930768488435863 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0152278208721308000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.109999999999973 " " Order of pole (three term test) = 9.32627593297653800000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999946 " " y[1] (analytic) = 2.9361773192710157 " " y[1] (numeric) = 2.9361773192710454 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.013357635612464000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.11999999999995 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999946 " " y[1] (analytic) = 2.941585482626987 " " y[1] (numeric) = 2.941585482627017 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0114945574650566000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.129999999999899 " " Order of pole (three term test) = 2.16782596125554230000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.6399999999999455 " " y[1] (analytic) = 2.9469929806797195 " " y[1] (numeric) = 2.9469929806797497 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0247077773099791000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.139999999999960 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999945 " " y[1] (analytic) = 2.952399815594563 " " y[1] (numeric) = 2.9523998155945934 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0228311934683847000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.149999999999968 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999945 " " y[1] (analytic) = 2.957805989526314 " " y[1] (numeric) = 2.957805989526344 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0209616985271036000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.159999999999923 " " Order of pole (three term test) = 1.3568297238004330000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999945 " " y[1] (analytic) = 2.963211504619281 " " y[1] (numeric) = 2.963211504619311 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.019099251698004100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.169999999999943 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999945 " " y[1] (analytic) = 2.9686163630073565 " " y[1] (numeric) = 2.9686163630073867 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0172438125084006000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.179999999999966 " " Order of pole (three term test) = 7.87503418806346900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999944 " " y[1] (analytic) = 2.9740205668140822 " " y[1] (numeric) = 2.974020566814113 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0303276252214931000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.189999999999876 " " Order of pole (three term test) = 2.54491747246716600000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999944 " " y[1] (analytic) = 2.9794241181527177 " " y[1] (numeric) = 2.9794241181527483 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0284589996087184000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.199999999999911 " " Order of pole (three term test) = 1.82738605475029510000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999944 " " y[1] (analytic) = 2.984827019126303 " " y[1] (numeric) = 2.9848270191263335 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0265973633749695000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.20999999999996 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999944 " " y[1] (analytic) = 2.990229271827728 " " y[1] (numeric) = 2.9902292718277588 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0247426767020046000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.21999999999994 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999944 " " y[1] (analytic) = 2.9956308783397962 " " y[1] (numeric) = 2.9956308783398273 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.037719463845714000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.229999999999940 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999943 " " y[1] (analytic) = 3.0010318407352896 " " y[1] (numeric) = 3.001031840735321 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.0506497622374152000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.239999999999957 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999943 " " y[1] (analytic) = 3.0064321610770333 " " y[1] (numeric) = 3.006432161077065 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.048762526810481000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.249999999999917 " " Order of pole (three term test) = 1.3220972187492680000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999943 " " y[1] (analytic) = 3.0118318414179575 " " y[1] (numeric) = 3.011831841417989 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.0468822815987662000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.2599999999999865 " " Order of pole (three term test) = 2.13448536056627300000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999943 " " y[1] (analytic) = 3.0172308838011626 " " y[1] (numeric) = 3.0172308838011945 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0597274236077865000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.26999999999989 " " Order of pole (three term test) = 1.5314029240783142000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.7799999999999425 " " y[1] (analytic) = 3.022629290259982 " " y[1] (numeric) = 3.022629290260014 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0578347537436299000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.279999999999977 " " Order of pole (three term test) = 8.23941181721019900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999942 " " y[1] (analytic) = 3.0280270628180426 " " y[1] (numeric) = 3.0280270628180745 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0559490534885581000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.28999999999987 " " Order of pole (three term test) = 2.65952173119309470000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999942 " " y[1] (analytic) = 3.033424203489327 " " y[1] (numeric) = 3.033424203489359 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0540702837547268000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.299999999999964 " " Order of pole (three term test) = 9.53713374372268600000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999942 " " y[1] (analytic) = 3.0388207142782355 " " y[1] (numeric) = 3.0388207142782675 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0521984057489520000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.309999999999924 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999942 " " y[1] (analytic) = 3.044216597179646 " " y[1] (numeric) = 3.0442165971796786 " " absolute error = 3.24185123190545700000000000000E-14 " " relative error = 1.064921344594505000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.319999999999944 " " Order of pole (three term test) = 1.10341326111068190000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.8299999999999415 " " y[1] (analytic) = 3.049611854178976 " " y[1] (numeric) = 3.0496118541790085 " " absolute error = 3.24185123190545700000000000000E-14 " " relative error = 1.0630373263610741000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.329999999999921 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999941 " " y[1] (analytic) = 3.0550064872522382 " " y[1] (numeric) = 3.055006487252271 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 1.075696620155534000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.339999999999965 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999941 " " y[1] (analytic) = 3.0604004983661044 " " y[1] (numeric) = 3.0604004983661377 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 1.0883115055214693000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.349999999999903 " " Order of pole (three term test) = 2.05795190344740450000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999940 " " y[1] (analytic) = 3.065793889477962 " " y[1] (numeric) = 3.0657938894779955 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 1.0863969314136149000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.360000000000000 " " Order of pole (three term test) = 2.21243834576257570000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999940 " " y[1] (analytic) = 3.0711866625359723 " " y[1] (numeric) = 3.0711866625360056 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 1.0844893000170933000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.369999999999888 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.87999999999994 " " y[1] (analytic) = 3.0765788194791286 " " y[1] (numeric) = 3.0765788194791623 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0970230872979499000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.379999999999901 " " Order of pole (three term test) = 1.7041343058635860000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.88999999999994 " " y[1] (analytic) = 3.081970362237315 " " y[1] (numeric) = 3.0819703622373487 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0951039751110336000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.38999999999992 " " Order of pole (three term test) = 9.15718688813638500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999994 " " y[1] (analytic) = 3.0873612927313605 " " y[1] (numeric) = 3.0873612927313943 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0931917825123004000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.39999999999995 " " Order of pole (three term test) = 9.84014290811369500000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90999999999994 " " y[1] (analytic) = 3.0927516128730987 " " y[1] (numeric) = 3.0927516128731325 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0912864715071968000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.409999999999926 " " Order of pole (three term test) = 1.05728473108101520000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9199999999999395 " " y[1] (analytic) = 3.0981413245654212 " " y[1] (numeric) = 3.0981413245654554 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.1037220570708266000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.4199999999999235 " " Order of pole (three term test) = 1.13588376851264980000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999940 " " y[1] (analytic) = 3.1035304297023356 " " y[1] (numeric) = 3.10353042970237 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.1018055061162878000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.429999999999937 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999939 " " y[1] (analytic) = 3.108918930169019 " " y[1] (numeric) = 3.1089189301690534 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.0998958135134063000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.439999999999931 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999939 " " y[1] (analytic) = 3.1143068278418737 " " y[1] (numeric) = 3.114306827841908 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.097992941888481100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.449999999999928 " " Order of pole (three term test) = 7.03784147094921900000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999939 " " y[1] (analytic) = 3.1196941245885808 " " y[1] (numeric) = 3.1196941245886154 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1103318782213305000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.459999999999921 " " Order of pole (three term test) = 7.55767887029269700000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999385 " " y[1] (analytic) = 3.1250808222681554 " " y[1] (numeric) = 3.12508082226819 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1084180006315564000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.46999999999994 " " Order of pole (three term test) = 8.11501856214976300000000000000E-14 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999938 " " y[1] (analytic) = 3.130466922730999 " " y[1] (numeric) = 3.1304669227310336 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.106510920680359000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.479999999999941 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999938 " " y[1] (analytic) = 3.1358524278189526 " " y[1] (numeric) = 3.135852427818987 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1046106016027343000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.489999999999935 " " Order of pole (three term test) = 0.0 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999938 " " y[1] (analytic) = 3.1412373393653508 " " y[1] (numeric) = 3.1412373393653854 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1027170069009579000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.499999999999920 " " Order of pole (three term test) = 1.00393827594915620000000000000E-13 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; " Iterations = 491 "Total Elapsed Time "= 12 Seconds "Elapsed Time(since restart) "= 12 Seconds "Time to Timeout "= 9 Minutes 47 Seconds Percent Done = 100.40816326530484 "%" (%o226) true (%o226) diffeq.max