(%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_g,MAX_TERMS) (%o161) array_tmp1_g (%i162) array(array_tmp1,MAX_TERMS) (%o162) array_tmp1 (%i163) array(array_tmp2,MAX_TERMS) (%o163) array_tmp2 (%i164) array(array_tmp3,MAX_TERMS) (%o164) array_tmp3 (%i165) array(array_m1,MAX_TERMS) (%o165) array_m1 (%i166) array(array_y_higher,2,MAX_TERMS) (%o166) array_y_higher (%i167) array(array_y_higher_work,2,MAX_TERMS) (%o167) array_y_higher_work (%i168) array(array_y_higher_work2,2,MAX_TERMS) (%o168) array_y_higher_work2 (%i169) array(array_y_set_initial,2,MAX_TERMS) (%o169) array_y_set_initial (%i170) array(array_given_rad_poles,2,3) (%o170) array_given_rad_poles (%i171) array(array_given_ord_poles,2,3) (%o171) array_given_ord_poles (%i172) array(array_rad_test_poles,2,3) (%o172) array_rad_test_poles (%i173) array(array_ord_test_poles,2,3) (%o173) array_ord_test_poles (%i174) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o174) array_fact_2 (%i175) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o175) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i176) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o176) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i177) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o177) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i178) 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)) (%o178) 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)) (%i179) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o179) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i180) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o180) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i181) 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) (%o181) 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) (%i182) 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) (%o182) 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) (%i183) 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) (%o183) 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 (%i184) 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) (%o184) 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) (%i185) 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) (%o185) 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 (%i186) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o186) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i187) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o187) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i188) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o188) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i189) 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) (%o189) 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) (%i190) log_revs(file,revs):=printf(file,revs) (%o190) log_revs(file, revs) := printf(file, revs) (%i191) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o191) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i192) 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) (%o192) 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) (%i193) logstart(file):=(printf(file,""),0) (%o193) logstart(file) := (printf(file, ""), 0) (%i194) logend(file):=(printf(file,"~%"),0) (%o194) logend(file) := (printf(file, "~%"), 0) (%i195) 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) (%o195) 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) (%i196) 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) (%o196) 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 (%i197) 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) (%o197) 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) (%i198) 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) (%o198) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i199) 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) (%o199) 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) (%i200) 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) (%o200) 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 ! (%i201) 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) (%o201) 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) (%i202) 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) (%o202) 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) (%i203) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o203) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i204) factorial_2(nnn):=nnn! (%o204) factorial_2(nnn) := nnn! (%i205) 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) (%o205) 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 (%i206) 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) (%o206) 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) (%i207) log10(x):=log(x)/glob_log_10 log(x) (%o207) log10(x) := ----------- glob_log_10 (%i208) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o208) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i209) 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) (%o209) 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) (%i210) exact_soln_y(x):=block(-x-cos(x)+2.0) (%o210) exact_soln_y(x) := block(- x - cos(x) + 2.0) (%i211) 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) (%o211) 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) (%i212) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o212) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i213) 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) (%o213) 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) (%i214) 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) (%o214) 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) (%i215) 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)) (%o215) 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)) (%i216) 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) (%o216) 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) (%i217) 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) (%o217) 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 (%i218) 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) (%o218) 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) (%i219) 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) (%o219) 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) (%i220) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]),array_tmp1[1]:sin(array_x[1]), array_tmp1_g[1]:cos(array_x[1]), array_tmp2[1]:array_tmp1[1]+array_const_0D0[1], array_tmp3[1]:array_tmp2[1]-array_const_1[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp3[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_y[2]:temporary, array_y_higher[1,2]:temporary), temporary:temporary*1.0/glob_h, array_y_higher[2,1]:temporary,0)),kkk:2, if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp3[1]*expt(glob_h,1) *factorial_3(0,1), if 2 <= MAX_TERMS then (array_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_tmp1_g[1]*array_x[2]/1, array_tmp1_g[2]:(-array_tmp1[1]*array_x[2])/1, array_tmp2[2]:array_tmp1[2],array_tmp3[2]:array_tmp2[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp3[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_y[3]:temporary, array_y_higher[1,3]:temporary), temporary:temporary*2.0/glob_h, array_y_higher[2,2]:temporary,0)),kkk:3, if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp3[2]*expt(glob_h,1) *factorial_3(1,2), if 3 <= MAX_TERMS then (array_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_tmp1[3]:array_tmp1_g[2]*array_x[2]/2, array_tmp1_g[3]:(-array_tmp1[2]*array_x[2])/2, array_tmp2[3]:array_tmp1[3],array_tmp3[3]:array_tmp2[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp3[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_y[4]:temporary, array_y_higher[1,4]:temporary), temporary:temporary*3.0/glob_h, array_y_higher[2,3]:temporary,0)),kkk:4, if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp3[3]*expt(glob_h,1) *factorial_3(2,3), if 4 <= MAX_TERMS then (array_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_tmp1[4]:array_tmp1_g[3]*array_x[2]/3, array_tmp1_g[4]:(-array_tmp1[3]*array_x[2])/3, array_tmp2[4]:array_tmp1[4],array_tmp3[4]:array_tmp2[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp3[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_y[5]:temporary, array_y_higher[1,5]:temporary), temporary:temporary*4.0/glob_h, array_y_higher[2,4]:temporary,0)),kkk:5, if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp3[4]*expt(glob_h,1) *factorial_3(3,4), if 5 <= MAX_TERMS then (array_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_tmp1[5]:array_tmp1_g[4]*array_x[2]/4, array_tmp1_g[5]:(-array_tmp1[4]*array_x[2])/4, array_tmp2[5]:array_tmp1[5],array_tmp3[5]:array_tmp2[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp3[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_y[6]:temporary, array_y_higher[1,6]:temporary), temporary:temporary*5.0/glob_h, array_y_higher[2,5]:temporary,0)),kkk:6, if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp3[5]*expt(glob_h,1) *factorial_3(4,5), if 6 <= MAX_TERMS then (array_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_tmp1[kkk] :array_tmp1_g[kkk-1]*array_x[2]/(kkk-1), array_tmp1_g[kkk] :(-array_tmp1[kkk-1]*array_x[2])/(kkk-1), array_tmp2[kkk]:array_tmp1[kkk], array_tmp3[kkk]:array_tmp2[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp3[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_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))),order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp3[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_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) (%o220) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : array_tmp2 - array_const_1 , 1 1 1 if not array_y_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary), 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 if not array_y_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp3 expt(glob_h, 1) factorial_3(0, 1), 1 if 2 <= MAX_TERMS then (array_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_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 , 2 2 2 2 if not array_y_set_initial then (if 2 <= MAX_TERMS 1, 3 then (temporary : array_tmp3 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 if not array_y_set_initial then (if 2 <= MAX_TERMS 1, 3 then (temporary : array_tmp3 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_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 , 3 3 3 3 if not array_y_set_initial then (if 3 <= MAX_TERMS 1, 4 then (temporary : array_tmp3 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 if not array_y_set_initial then (if 3 <= MAX_TERMS 1, 4 then (temporary : array_tmp3 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_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 , 4 4 4 4 if not array_y_set_initial then (if 4 <= MAX_TERMS 1, 5 then (temporary : array_tmp3 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 if not array_y_set_initial then (if 4 <= MAX_TERMS 1, 5 then (temporary : array_tmp3 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_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2 : array_tmp1 , array_tmp3 : array_tmp2 , 5 5 5 5 if not array_y_set_initial then (if 5 <= MAX_TERMS 1, 6 then (temporary : array_tmp3 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 if not array_y_set_initial then (if 5 <= MAX_TERMS 1, 6 then (temporary : array_tmp3 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_tmp1_g array_x kkk - 1 2 while kkk <= MAX_TERMS do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 , kkk kkk - 1 kkk kkk array_tmp3 : array_tmp2 , 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_tmp3 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))), order_d : 1, if order_d + kkk <= MAX_TERMS then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp3 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_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) (%i221) exact_soln_y(x):=block(-x-cos(x)+2.0) (%o221) exact_soln_y(x) := block(- x - cos(x) + 2.0) (%i222) 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_g[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_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_g), zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3),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_0),array_const_0[1]:0, zero_ats_ar(array_m1),array_m1[1]:-1.0,iiif:0, while iiif <= MAX_TERMS do (jjjf:0, while jjjf <= MAX_TERMS do (array_fact_1[iiif]:0, array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf), iiif:1+iiif),array_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/sub_sin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; "), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:0.1,"), omniout_str(ALWAYS,"x_end: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,"/* 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," (2.0 - cos(x) - x) "), 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_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 ) = sin ( x ) - 1 , 0 ; "), omniout_int(INFO, "Iterations ",32, glob_iter,4," "), prog_report(x_start,x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-09T00:55:17-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "sub_sin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_str(html_log_file,"16"), logitem_good_digits(html_log_file, array_last_rel_error[ 1]), logitem_integer(html_log_file, MAX_TERMS), if glob_least_given_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_given_sing), 0) else ( logitem_str(html_log_file, "NOT GIVEN"),0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "sub_sin_c diffeq.max"), logitem_str(html_log_file, "sub_sin_c 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))) (%o222) 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_g : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term 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_g), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3), zero_ats_ar(array_m1), zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0), 1 array_const_0D0 : 0.0, zero_ats_ar(array_const_0), array_const_0 : 0, 1 1 zero_ats_ar(array_m1), array_m1 : - 1.0, iiif : 0, 1 while iiif <= MAX_TERMS do (jjjf : 0, while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0, iiif iiif, jjjf jjjf : 1 + jjjf), iiif : 1 + iiif), array_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/sub_sin_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; "), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end: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, "/* 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, " (2.0 - cos(x) - x) "), 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_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 ) = sin ( x ) - 1 , 0 ; "), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2014-01-09T00:55:17-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sub_sin_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; "), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, MAX_TERMS), 1 if glob_least_given_sing < glob_large_float then (logitem_float(html_log_file, glob_least_given_sing), 0) else (logitem_str(html_log_file, "NOT GIVEN"), 0), if glob_least_ratio_sing < glob_large_float then (logitem_float(html_log_file, glob_least_ratio_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_3_sing < glob_large_float then (logitem_float(html_log_file, glob_least_3_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_6_sing < glob_large_float then (logitem_float(html_log_file, glob_least_6_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then (logitem_time(html_log_file, glob_total_exp_sec), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "sub_sin_c diffeq.max"), logitem_str(html_log_file, "sub_sin_c 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))) (%i223) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o223) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i224) 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_tmp1 in translation. warning: encountered undefined variable array_tmp1_g in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_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_0 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/sub_sin_cpostode.ode#################" "diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; " "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "/* 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(" " (2.0 - cos(x) - x) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900000. "" step_error = 2.040816326530612300000000000000000E-17 "" est_needed_step_err = 2.040816326530612300000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.4672086055323014000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" estimated_step_error = 2.4672086055323014000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.65571566460656540000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" estimated_step_error = 1.65571566460656540000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.111131969458435300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" estimated_step_error = 1.111131969458435300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.4566803670241850000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" estimated_step_error = 7.4566803670241850000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.004093412037816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" estimated_step_error = 5.004093412037816000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" best_h = 3.200000E-5 "" opt_iter = 6 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.3581901424816235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" estimated_step_error = 3.3581901424816235000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.25364312158091970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" estimated_step_error = 2.25364312158091970000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.512394117654306500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" estimated_step_error = 1.512394117654306500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.0149502701580553000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" estimated_step_error = 1.0149502701580553000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.81121272440810700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" estimated_step_error = 6.81121272440810700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.570923134360027000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" estimated_step_error = 4.570923134360027000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 2.048000E-3 "" opt_iter = 12 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.0674887502340364000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 3.0674887502340364000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.05854901161817100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" estimated_step_error = 2.05854901161817100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.3814583197406785000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" estimated_step_error = 1.3814583197406785000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 9.27066811845142800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" estimated_step_error = 9.27066811845142800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.22124900214134000000000000000000000000000000000000000000000000000000000000000000E-66 "" estimated_step_error = 6.22124900214134000000000000000000000000000000000000000000000000000000000000000000E-66 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.1747508757515434000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 4.1747508757515434000000000000000000000000000000000000000000000000000000000E-58 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.80127475800900200000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 2.80127475800900200000000000000000000000000000000000000000000000000E-50 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 0.9049958347219743 " " y[1] (numeric) = 0.9049958347219743 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.9334665397530600E-2 " " Order of pole (three term test) = 22.00996671107938 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 0.8960439020433032 " " y[1] (numeric) = 0.8960439020433032 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10911481154043474 " " Order of pole (three term test) = 22.0120512753347 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 0.8871913641461339 " " y[1] (numeric) = 0.8871913641461338 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.251390702719110400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11885131321356734 " " Order of pole (three term test) = 22.014331012573983 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 0.8784381062852119 " " y[1] (numeric) = 0.878438106285212 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.263860272774515500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1285402759460775 " " Order of pole (three term test) = 22.016805010932735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 0.8697840037873629 " " y[1] (numeric) = 0.8697840037873629 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13817782428205685 " " Order of pole (three term test) = 22.019472280844614 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 0.8612289220639576 " " y[1] (numeric) = 0.8612289220639577 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.289114887090041200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14776010333066988 " " Order of pole (three term test) = 22.0223317554372 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 0.8527727166243732 " " y[1] (numeric) = 0.852772716624373 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.301897918380735800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15728328030805885 " " Order of pole (three term test) = 22.025382290958774 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 0.8444152330904394 " " y[1] (numeric) = 0.8444152330904393 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.314783273818851700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16674354607040723 " " Order of pole (three term test) = 22.028622667235826 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 0.8361563072118786 " " y[1] (numeric) = 0.8361563072118786 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17613711663754492 " " Order of pole (three term test) = 22.032051588161032 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 0.8279957648827295 " " y[1] (numeric) = 0.8279957648827297 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.681711843737266700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18546023470649134 " " Order of pole (three term test) = 22.035667682211745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 0.8199334221587583 " " y[1] (numeric) = 0.8199334221587584 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.35404045575079800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19470917115432534 " " Order of pole (three term test) = 22.039469502998557 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 0.8119690852758515 " " y[1] (numeric) = 0.8119690852758518 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.73464358374673500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20388022652978527 " " Order of pole (three term test) = 22.04345552984385 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 0.8041025506693945 " " y[1] (numeric) = 0.8041025506693945 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21296973253299992 " " Order of pole (three term test) = 22.04762416839002 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 0.7963336049946251 " " y[1] (numeric) = 0.7963336049946251 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22197405348275998 " " Order of pole (three term test) = 22.051973751237238 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 0.7886620251479705 " " y[1] (numeric) = 0.7886620251479703 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.40772978693484600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23088958777074148 " " Order of pole (three term test) = 22.056502538610356 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 0.7810875782893553 " " y[1] (numeric) = 0.7810875782893552 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.42138097632615600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2397127693021017 " " Order of pole (three term test) = 22.061208719054815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 0.7736100218654866 " " y[1] (numeric) = 0.7736100218654867 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.4351197544571100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2484400689218684 " " Order of pole (three term test) = 22.066090410161177 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 0.7662291036341092 " " y[1] (numeric) = 0.7662291036341093 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.44894395078382700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2570679958265566 " " Order of pole (three term test) = 22.071145659318088 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 0.7589445616892291 " " y[1] (numeric) = 0.7589445616892289 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.92570256292255600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26559309896044203 " " Order of pole (three term test) = 22.076372444493295 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 0.7517561244873029 " " y[1] (numeric) = 0.7517561244873027 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.95367869568692300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.274011968395937 " " Order of pole (three term test) = 22.08176867504241 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 0.7446635108743939 " " y[1] (numeric) = 0.7446635108743939 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28232123669751796 " " Order of pole (three term test) = 22.087332192545162 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 0.7376664301142865 " " y[1] (numeric) = 0.7376664301142865 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29051758026865254 " " Order of pole (three term test) = 22.093060771668732 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 0.7307645819175589 " " y[1] (numeric) = 0.730764581917559 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.519262224931429700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2985977206811961 " " Order of pole (three term test) = 22.098952121057852 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 0.7239576564716129 " " y[1] (numeric) = 0.7239576564716129 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3065584259867172 " " Order of pole (three term test) = 22.105003884251314 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 0.7172453344716537 " " y[1] (numeric) = 0.7172453344716536 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.547898565897236600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31439651200923424 " " Order of pole (three term test) = 22.111213640624534 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 0.7106272871526208 " " y[1] (numeric) = 0.7106272871526209 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.562314091643816600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3221088436188457 " " Order of pole (three term test) = 22.117578906357753 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 0.704103176322065 " " y[1] (numeric) = 0.704103176322065 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3296923359857368 " " Order of pole (three term test) = 22.12409713542955 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 0.6976726543939654 " " y[1] (numeric) = 0.6976726543939654 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3371439558140727 " " Order of pole (three term test) = 22.130765720635207 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 0.6913353644234898 " " y[1] (numeric) = 0.6913353644234896 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.605910939549549400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3444607225552759 " " Order of pole (three term test) = 22.137581994629546 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 0.6850909401426869 " " y[1] (numeric) = 0.6850909401426869 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35163970960020535 " " Order of pole (three term test) = 22.14454323099386 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 0.6789390059971147 " " y[1] (numeric) = 0.6789390059971149 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.2704646951154100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3586780454497616 " " Order of pole (three term test) = 22.151646645326416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 0.6728791771833947 " " y[1] (numeric) = 0.6728791771833948 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.649958955889287100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3655729148634481 " " Order of pole (three term test) = 22.158889396356194 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 0.6669110596876916 " " y[1] (numeric) = 0.6669110596876917 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.664724266448758500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37232155998543004 " " Order of pole (three term test) = 22.166268587079344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 0.6610342503251146 " " y[1] (numeric) = 0.6610342503251149 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.35904841263253300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3789212814476387 " " Order of pole (three term test) = 22.173781265917974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 0.6552483367800365 " " y[1] (numeric) = 0.6552483367800366 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.69435458635563500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3853694394494849 " " Order of pole (three term test) = 22.18142442790071 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 0.6495528976473229 " " y[1] (numeric) = 0.649552897647323 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.70921110297002520000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3916634548137418 " " Order of pole (three term test) = 22.189195015864662 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 0.6439475024744746 " " y[1] (numeric) = 0.6439475024744747 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.724089340138662300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39780081001818307 " " Order of pole (three term test) = 22.19708992167827 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 0.6384317118046708 " " y[1] (numeric) = 0.6384317118046711 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.477969543482924400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40377905020255717 " " Order of pole (three term test) = 22.205105987484455 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 0.6330050772207155 " " y[1] (numeric) = 0.6330050772207159 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.26167829253308700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40959578415049913 " " Order of pole (three term test) = 22.213240006963773 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 0.6276671413898783 " " y[1] (numeric) = 0.6276671413898786 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.53761715856824300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41524868524598557 " " Order of pole (three term test) = 22.221488726616897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 0.6224174381096271 " " y[1] (numeric) = 0.6224174381096274 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.567454755114401500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42073549240394825 " " Order of pole (three term test) = 22.229848847065927 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 0.6172554923542485 " " y[1] (numeric) = 0.6172554923542488 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.39593266504944900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42605401097468165 " " Order of pole (three term test) = 22.238317024374176 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 0.6121808203223499 " " y[1] (numeric) = 0.6121808203223502 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.440662241135997000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4312021136216694 " " Order of pole (three term test) = 22.246889871383612 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 0.6071929294852388 " " y[1] (numeric) = 0.6071929294852391 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.65690366508836800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43617774117249336 " " Order of pole (three term test) = 22.25556395906974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 0.6022913186361757 " " y[1] (numeric) = 0.6022913186361759 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.68666454346092200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4409789034424741 " " Order of pole (three term test) = 22.264335817913135 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 0.5974754779404939 " " y[1] (numeric) = 0.5974754779404943 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.574570332754627000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44560368003071776 " " Order of pole (three term test) = 22.273201939287212 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 0.5927448889865837 " " y[1] (numeric) = 0.5927448889865838 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.8730199876093498000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45005022108825277 " " Order of pole (three term test) = 22.282158776861642 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 0.588099024837731 " " y[1] (numeric) = 0.5880990248377312 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.77563293845450800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4543167480579418 " " Order of pole (three term test) = 22.29120274802082 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 0.583537350084813 " " y[1] (numeric) = 0.583537350084813 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4584015543858837 " " Order of pole (three term test) = 22.300330235296865 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 0.5790593208998364 " " y[1] (numeric) = 0.5790593208998365 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.917287201076241500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4623030062040104 " " Order of pole (three term test) = 22.309537587816557 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 0.5746643850903214 " " y[1] (numeric) = 0.5746643850903217 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.79585086580923300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4660195429836133 " " Order of pole (three term test) = 22.318821122761666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 0.5703519821545203 " " y[1] (numeric) = 0.5703519821545204 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.946557668531734800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4695496781595341 " " Order of pole (three term test) = 22.32817712684198 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 0.5661215433374659 " " y[1] (numeric) = 0.566121543337466 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.96110364936836700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4728919997247698 " " Order of pole (three term test) = 22.337601857780612 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 0.561972491687848 " " y[1] (numeric) = 0.561972491687848 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47604517079525815 " " Order of pole (three term test) = 22.347091545810855 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 0.5579042421157073 " " y[1] (numeric) = 0.5579042421157073 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4790079301446125 " " Order of pole (three term test) = 22.35664239518402 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 0.5539162014509439 " " y[1] (numeric) = 0.5539162014509441 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.00863170897333100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48177909270859653 " " Order of pole (three term test) = 22.366250585687705 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 0.5500077685026349 " " y[1] (numeric) = 0.5500077685026349 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48435755005913284 " " Order of pole (three term test) = 22.37591227417382 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 0.5461783341191505 " " y[1] (numeric) = 0.5461783341191507 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.065423160424953600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48674227084765975 " " Order of pole (three term test) = 22.385623596095773 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 0.5424272812490719 " " y[1] (numeric) = 0.5424272812490721 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.093536822368504000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48893230121765835 " " Order of pole (three term test) = 22.395380667054294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 0.5387539850028932 " " y[1] (numeric) = 0.5387539850028935 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.1821706504084310000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49092676518617984 " " Order of pole (three term test) = 22.405179584351078 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 0.5351578127155113 " " y[1] (numeric) = 0.5351578127155117 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.2237138181257290000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49272486499423024 " " Order of pole (three term test) = 22.41501642854988 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 0.5316381240094915 " " y[1] (numeric) = 0.531638124009492 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.35322355178076200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49432588142586004 " " Order of pole (three term test) = 22.42488726504416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 0.5281942708591049 " " y[1] (numeric) = 0.5281942708591052 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.30576524137256500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49572917409584344 " " Order of pole (three term test) = 22.434788145630925 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 0.5248255976551296 " " y[1] (numeric) = 0.5248255976551298 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.230826505359214000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4969341817058226 " " Order of pole (three term test) = 22.444715110089966 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 0.5215314412704118 " " y[1] (numeric) = 0.5215314412704123 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.51509946875483200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4979404222688202 " " Order of pole (three term test) = 22.45466418776785 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 0.5183111311261789 " " y[1] (numeric) = 0.5183111311261793 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.5680044896036100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49874749330202733 " " Order of pole (three term test) = 22.464631399166155 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 0.5151639892590946 " " y[1] (numeric) = 0.515163989259095 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.62034651313164900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4993550719877917 " " Order of pole (three term test) = 22.474612757533215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 0.5120893303890565 " " y[1] (numeric) = 0.5120893303890568 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.50407824616266900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49976291530273964 " " Order of pole (three term test) = 22.484604270458767 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 0.5090864619877223 " " y[1] (numeric) = 0.5090864619877228 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.72325710874575900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999708601149831 " " Order of pole (three term test) = 22.494601941470865 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 0.5061546843477637 " " y[1] (numeric) = 0.506154684347764 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.58033833701925600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999788232493701 " " Order of pole (three term test) = 22.504601771634402 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 0.5032932906528346 " " y[1] (numeric) = 0.5032932906528347 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.20591660020950800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4997868015207525 " " Order of pole (three term test) = 22.51459976115064 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 0.5005015670482528 " " y[1] (numeric) = 0.5005015670482531 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.65466262876728200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49939487173526215 " " Order of pole (three term test) = 22.52459191095709 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 0.49777879271238634 " " y[1] (numeric) = 0.49777879271238656 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.460708414577383400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4988031906595868 " " Order of pole (three term test) = 22.53457422432703 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 0.4951242399287329 " " y[1] (numeric) = 0.495124239928733 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.242311999883018500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4980119949582683 " " Order of pole (three term test) = 22.544542708468235 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 0.4925371741586916 " " y[1] (numeric) = 0.49253717415869197 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 7.88931433008157200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4970216010990379 " " Order of pole (three term test) = 22.554493376119932 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 0.4900168541150177 " " y[1] (numeric) = 0.49001685411501794 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.53136668790809770000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49583240522623423 " " Order of pole (three term test) = 22.564422247147764 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 0.4875625318359479 " " y[1] (numeric) = 0.4875625318359483 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 7.96980968073139800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4944448830023508 " " Order of pole (three term test) = 22.574325350135688 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 0.4851734527599988 " " y[1] (numeric) = 0.48517345275999896 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.43245189419200900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49285958941777663 " " Order of pole (three term test) = 22.584198723974538 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 0.4828488558014198 " " y[1] (numeric) = 0.48284885580141995 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.448976873257070000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49107715856880907 " " Order of pole (three term test) = 22.594038419446434 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 0.4805879734263029 " " y[1] (numeric) = 0.48058797342630327 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.08547196569396600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4890983034040223 " " Order of pole (three term test) = 22.603840500804395 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 0.47839003172933536 " " y[1] (numeric) = 0.4783900317293357 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.96224597706480500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48692381543909746 " " Order of pole (three term test) = 22.613601047346545 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 0.4762542505111883 " " y[1] (numeric) = 0.47625425051118864 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.99346844736921500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48455456444022804 " " Order of pole (three term test) = 22.623316154984416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 0.47417984335653707 " " y[1] (numeric) = 0.47417984335653734 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 5.85338579960671600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48199149807622393 " " Order of pole (three term test) = 22.632981937804487 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 0.4721660177127015 " " y[1] (numeric) = 0.47216601771270195 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.40536152943300600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4792356415394569 " " Order of pole (three term test) = 22.64259452962251 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 0.47021197496890166 " " y[1] (numeric) = 0.47021197496890194 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 5.90277940443022100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47628809713579756 " " Order of pole (three term test) = 22.652150085529918 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 0.46831691053611635 " " y[1] (numeric) = 0.4683169105361167 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.11199830487139800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4731500438437071 " " Order of pole (three term test) = 22.661644783431754 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 0.46648001392754324 " " y[1] (numeric) = 0.4664800139275435 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 5.95000316989788400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4698227368426621 " " Order of pole (three term test) = 22.67107482557545 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 0.46470046883964555 " " y[1] (numeric) = 0.4647004688396459 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.16734605883254500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4663075070111001 " " Order of pole (three term test) = 22.68043644006989 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 0.4629774532337826 " " y[1] (numeric) = 0.4629774532337829 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.19402003404609200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4626057603940838 " " Order of pole (three term test) = 22.689725882394082 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 0.46131013941841237 " " y[1] (numeric) = 0.46131013941841265 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.01668449139687400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4587189776409047 " " Order of pole (three term test) = 22.698939436894964 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 0.45969769413186 " " y[1] (numeric) = 0.4596976941318605 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.08680197325073970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45464871341284047 " " Order of pole (three term test) = 22.70807341827357 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 0.4581392786256444 " " y[1] (numeric) = 0.45813927862564474 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.26999240027404800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4503965957613134 " " Order of pole (three term test) = 22.71712417305915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 0.45663404874835023 " " y[1] (numeric) = 0.4566340487483506 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.50961639159214500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4459643254766893 " " Order of pole (three term test) = 22.72608808107045 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 0.4551811550300444 " " y[1] (numeric) = 0.45518115503004486 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.75631800531703300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44135367540798665 " " Order of pole (three term test) = 22.7349615568638 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 0.45377974276722166 " " y[1] (numeric) = 0.4537797427672218 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.6699182003635900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43656648975375795 " " Order of pole (three term test) = 22.743741051167184 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 0.45242895210827294 " " y[1] (numeric) = 0.4524289521082732 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.13479210079079800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4316046833244364 " " Order of pole (three term test) = 22.75242305229993 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 0.4511279181394723 " " y[1] (numeric) = 0.4511279181394727 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.61347841697242700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4264702407764377 " " Order of pole (three term test) = 22.76100408757736 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 0.4498757709714658 " " y[1] (numeric) = 0.44987577097146614 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.40353068288872800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.42116521581832234 " " Order of pole (three term test) = 22.76948072469976 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 0.4486716358262599 " " y[1] (numeric) = 0.44867163582626024 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.42340011697376800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4156917303893413 " " Order of pole (three term test) = 22.77784957312531 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 0.4475146331246991 " " y[1] (numeric) = 0.4475146331246994 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.44259254858239500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4100519738106868 " " Order of pole (three term test) = 22.786107285426215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 0.44640387857442243 " " y[1] (numeric) = 0.44640387857442293 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.11916671216383560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40424820190979466 " " Order of pole (three term test) = 22.79425055862767 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 0.44533848325829295 " " y[1] (numeric) = 0.44533848325829345 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.12184412500357850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39828273611804277 " " Order of pole (three term test) = 22.802276135528963 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 0.44431755372328774 " " y[1] (numeric) = 0.44431755372328813 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.74550319613984100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39215796254220964 " " Order of pole (three term test) = 22.810180806006343 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 0.44334019206984254 " " y[1] (numeric) = 0.443340192069843 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.00168948765218660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3858763310100625 " " Order of pole (three term test) = 22.817961408297002 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 0.4424054960416417 " " y[1] (numeric) = 0.4424054960416422 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.12928154272815650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3794403540904604 " " Order of pole (three term test) = 22.82561483026377 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 0.44151255911584264 " " y[1] (numeric) = 0.441512559115843 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.54376971868104700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3728526060883595 " " Order of pole (three term test) = 22.833138010639914 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 0.4406604705937267 " " y[1] (numeric) = 0.4406604705937271 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.81808295841130600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3661157220151252 " " Order of pole (three term test) = 22.84052794025358 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 0.43984831569176963 " " y[1] (numeric) = 0.43984831569177 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.83436504713381200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35923239653456274 " " Order of pole (three term test) = 22.847781663231448 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 0.43907517563311815 " " y[1] (numeric) = 0.4390751756331185 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.58564651047023900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35220538288508735 " " Order of pole (three term test) = 22.85489627818106 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 0.43834012773946696 " " y[1] (numeric) = 0.43834012773946734 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.86476126707160900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34503749177846765 " " Order of pole (three term test) = 22.86186893935128 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 0.4376422455233264 " " y[1] (numeric) = 0.4376422455233267 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.34206955556568600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3377315902755749 " " Order of pole (three term test) = 22.868696857770626 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 0.43698059878066964 " " y[1] (numeric) = 0.4369805987806699 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.35167229233443800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.33029060063959975 " " Order of pole (three term test) = 22.875377302362747 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 0.43635425368395286 " " y[1] (numeric) = 0.43635425368395325 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.9051053206931300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3227174991671846 " " Order of pole (three term test) = 22.881907601038883 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 0.4357622728754973 " " y[1] (numeric) = 0.4357622728754977 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.91720286051074300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3150153149979452 " " Order of pole (three term test) = 22.88828514176664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 0.43520371556122384 " " y[1] (numeric) = 0.43520371556122406 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.10208431099192600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30718712890285527 " " Order of pole (three term test) = 22.89450737361477 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 0.4346776376047312 " " y[1] (numeric) = 0.43467763760473166 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.02165184364485240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2992360720519778 " " Order of pole (three term test) = 22.90057180777347 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 0.43418309162171065 " " y[1] (numeric) = 0.434183091621711 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.67111649013124500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29116532476204 " " Order of pole (three term test) = 22.906476018549945 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 0.4337191270746812 " " y[1] (numeric) = 0.4337191270746816 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.95920964426123500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28297811522435073 " " Order of pole (three term test) = 22.91221764433861 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 0.43328479036804457 " " y[1] (numeric) = 0.4332847903680448 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.12468034560872200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2746777182135627 " " Order of pole (three term test) = 22.917794388565703 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 0.4328791249434423 " " y[1] (numeric) = 0.43287912494344266 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.97659499449354200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2662674537778101 " " Order of pole (three term test) = 22.923204020607894 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 0.43250117137541255 " " y[1] (numeric) = 0.4325011713754129 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.70094809982476800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2577506859107314 " " Order of pole (three term test) = 22.928444376684478 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 0.43214996746733036 " " y[1] (numeric) = 0.43214996746733064 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.42267215205267200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24913082120591865 " " Order of pole (three term test) = 22.933513360722902 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 0.43182454834762707 " " y[1] (numeric) = 0.43182454834762735 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.42751222037639700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24041130749432332 " " Order of pole (three term test) = 22.93840894519714 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 0.4315239465662768 " " y[1] (numeric) = 0.4315239465662771 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.43198965816048700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23159563246517184 " " Order of pole (three term test) = 22.94312917193868 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 0.4312471921915406 " " y[1] (numeric) = 0.43124719219154084 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.148893927787223000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22268732227093482 " " Order of pole (three term test) = 22.947672152919743 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 0.4309933129069583 " " y[1] (numeric) = 0.43099331290695875 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03038538313918450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21368994011691422 " " Order of pole (three term test) = 22.952036071008536 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 0.43076133410858053 " " y[1] (numeric) = 0.430761334108581 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.0309402787254870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20460708483600784 " " Order of pole (three term test) = 22.956219180695985 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 0.4305502790024269 " " y[1] (numeric) = 0.43055027900242737 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03144564411618790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19544238944922526 " " Order of pole (three term test) = 22.96021980879399 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 0.4303591687021655 " " y[1] (numeric) = 0.43035916870216595 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03190367987117090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1861995197125269 " " Order of pole (three term test) = 22.964036355104668 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 0.43018702232700057 " " y[1] (numeric) = 0.43018702232700085 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.4519788313211600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1768821726505705 " " Order of pole (three term test) = 22.967667293060373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 0.43003285709975914 " " y[1] (numeric) = 0.43003285709975936 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.16343347395711500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16749407507795155 " " Order of pole (three term test) = 22.97111117033433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 0.4298956884451688 " " y[1] (numeric) = 0.4298956884451691 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.74762148911451900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1580389821085259 " " Order of pole (three term test) = 22.97436660942156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 0.42977453008831423 " " y[1] (numeric) = 0.42977453008831457 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.74980563224873200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14852067565341515 " " Order of pole (three term test) = 22.97743230818981 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 0.4296683941532633 " " y[1] (numeric) = 0.4296683941532637 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.0436733049580200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13894296290829242 " " Order of pole (three term test) = 22.980307040400476 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 0.4295762912618546 " " y[1] (numeric) = 0.42957629126185487 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.46115164645110500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12930967483055433 " " Order of pole (three term test) = 22.982989656198992 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 0.42949723063263345 " " y[1] (numeric) = 0.4294972306326338 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.75480919625376400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11962466460699014 " " Order of pole (three term test) = 22.985479082574802 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 0.4294302201799305 " " y[1] (numeric) = 0.4294302201799308 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.7560192957075190000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10989180611255746 " " Order of pole (three term test) = 22.987774323790543 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 0.4293742666130682 " " y[1] (numeric) = 0.42937426661306866 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.0342706686943930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10011499236088425 " " Order of pole (three term test) = 22.989874461780346 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 0.42932837553569025 " " y[1] (numeric) = 0.4293283755356907 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03438122228924350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.02981339471153400E-2 " " Order of pole (three term test) = 22.991778656517 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 0.4292915515451994 " " y[1] (numeric) = 0.42929155154519977 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.05161206224884300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.04451574837267700E-2 " " Order of pole (three term test) = 22.99348614634802 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 0.4292627983322972 " " y[1] (numeric) = 0.42926279833229747 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.4658702602369500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.0560004029932500E-2 " " Order of pole (three term test) = 22.99499624830023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 0.429241118780614 " " y[1] (numeric) = 0.4292411187806145 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.16391542939917450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.06466275153138200E-2 " " Order of pole (three term test) = 22.996308358352973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 0.4292255150664208 " " y[1] (numeric) = 0.4292255150664212 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.0530046555753810000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.070899315829984000E-2 " " Order of pole (three term test) = 22.99742195167973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 0.4292149887584089 " " y[1] (numeric) = 0.42921498875840935 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03465447731608910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.07510758801334470E-2 " " Order of pole (three term test) = 22.998336582858023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 0.4292085409175339 " " y[1] (numeric) = 0.42920854091753424 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.76002515410197500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.07768587149554600E-2 " " Order of pole (three term test) = 22.999051886047567 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 0.42920517219690746 " " y[1] (numeric) = 0.4292051721969079 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03467814140489150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.079033121664413700E-2 " " Order of pole (three term test) = 22.999567575136634 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 0.4292038829417326 " " y[1] (numeric) = 0.42920388294173295 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.76010937051012300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.079548786304687400E-2 " " Order of pole (three term test) = 22.99988344385646 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 0.4292036732892668 " " y[1] (numeric) = 0.42920367328926706 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.46676096756579200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.9632645824230410000E-4 " " Order of pole (three term test) = 22.999999365863776 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 0.42920354326880816 " " y[1] (numeric) = 0.42920354326880866 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.16401732678246580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.203153466528015000E-3 " " Order of pole (three term test) = 22.999915294791297 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 0.42920249290169243 " " y[1] (numeric) = 0.429202492901693 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.29335575047492800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.91989522526188100E-2 " " Order of pole (three term test) = 22.99963126426636 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 0.42919952230128877 " " y[1] (numeric) = 0.42919952230128916 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.05355291486162100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.918707171379117400E-2 " " Order of pole (three term test) = 22.99914738789738 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 0.4291936317729874 " " y[1] (numeric) = 0.429193631772988 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.4227206983975280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.916351673543377000E-2 " " Order of pole (three term test) = 22.998463859228444 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 0.42918382191417037 " " y[1] (numeric) = 0.42918382191417087 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.1640708143496430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.91242968725554730E-2 " " Order of pole (three term test) = 22.997580951661917 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 0.42916909371414835 " " y[1] (numeric) = 0.4291690937141487 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.76073841909475700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.906542794591003000E-2 " " Order of pole (three term test) = 22.99649901834904 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 0.4291484486540622 " " y[1] (numeric) = 0.4291484486540625 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.46759313768433700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.89829336356147400E-2 " " Order of pole (three term test) = 22.995218492048735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 0.42912088880673416 " " y[1] (numeric) = 0.4291208888067344 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.17440680975646800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.88728470716254600E-2 " " Order of pole (three term test) = 22.99373988495443 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 0.4290854169364591 " " y[1] (numeric) = 0.42908541693645946 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.05596049833469900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.8731212420431400E-2 " " Order of pole (three term test) = 22.99206378848926 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 0.4290410365987283 " " y[1] (numeric) = 0.4290410365987285 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.17536985938024100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.85540864673362200E-2 " " Order of pole (three term test) = 22.990190873069448 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 0.42898675223987115 " " y[1] (numeric) = 0.4289867522398716 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03520495104181420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10833754019369103 " " Order of pole (three term test) = 22.988121887836215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 0.4289215692966124 " " y[1] (numeric) = 0.4289215692966127 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.47101419057689800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11807766034844973 " " Order of pole (three term test) = 22.98585766035603 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 0.4288444942955245 " " y[1] (numeric) = 0.42884449429552507 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.29443544151004300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12777055101341683 " " Order of pole (three term test) = 22.983399096289727 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 0.4287545349523776 " " y[1] (numeric) = 0.428754534952378 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.06294923882180600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1374123351615633 " " Order of pole (three term test) = 22.98074717903015 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 0.42865070027136354 " " y[1] (numeric) = 0.42865070027136404 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.1655185930293390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14699915620778514 " " Order of pole (three term test) = 22.97790296930883 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 0.4285320006441977 " " y[1] (numeric) = 0.42853200064419816 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.03630349468062650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15652717955148637 " " Order of pole (three term test) = 22.974867604771752 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 0.4283974479490771 " " y[1] (numeric) = 0.4283974479490774 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.77471735609261000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16599259411036824 " " Order of pole (three term test) = 22.97164229952424 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 0.42824605564949225 " " y[1] (numeric) = 0.4282460556494925 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.184977234367543000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17539161384481136 " " Order of pole (three term test) = 22.968228343645396 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 0.4280768388928802 " " y[1] (numeric) = 0.4280768388928805 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.78054024714221800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1847204792722396 " " Order of pole (three term test) = 22.964627102672058 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 0.4278888146091089 " " y[1] (numeric) = 0.4278888146091094 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.1675938795869730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19397545897086632 " " Order of pole (three term test) = 22.960840017052597 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 0.42768100160878375 " " y[1] (numeric) = 0.42768100160878414 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.08569838634665600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2031528510722095 " " Order of pole (three term test) = 22.956868601570772 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 0.4274524206813646 " " y[1] (numeric) = 0.42745242068136496 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 9.09055697940384500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21224898474179243 " " Order of pole (three term test) = 22.952714444739815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 0.4272020946930868 " " y[1] (numeric) = 0.4272020946930874 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.42935315891305150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22126022164742734 " " Order of pole (three term test) = 22.94837920816707 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 0.4269290486846744 " " y[1] (numeric) = 0.42692904868467496 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.30024301232914750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23018295741450043 " " Order of pole (three term test) = 22.943864625889375 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 0.42663230996883406 " " y[1] (numeric) = 0.4266323099688343 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.204589519749498000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23901362306767268 " " Order of pole (three term test) = 22.939172503679433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 0.4263109082275225 " " y[1] (numeric) = 0.42631090822752293 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.04170266647986370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24774868645842363 " " Order of pole (three term test) = 22.93430471832358 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 0.4259638756089801 " " y[1] (numeric) = 0.4259638756089806 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.17287025893232320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2563846536778632 " " Order of pole (three term test) = 22.929263216871053 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 0.42559024682451296 " " y[1] (numeric) = 0.42559024682451313 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.91299976764837700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2649180704542478 " " Order of pole (three term test) = 22.924050015855205 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 0.4251890592450207 " " y[1] (numeric) = 0.42518905924502104 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.83338376530551500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2733455235346447 " " Order of pole (three term test) = 22.91866720048694 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 0.42475935299726064 " " y[1] (numeric) = 0.4247593529972612 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 1.30688472989589080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2816636420501862 " " Order of pole (three term test) = 22.913116923820635 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 0.4243001710598333 " " y[1] (numeric) = 0.4243001710598336 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.54149526885647300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28986909886437257 " " Order of pole (three term test) = 22.90740140589296 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 0.42381055935888234 " " y[1] (numeric) = 0.4238105593588826 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.54905240152959900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2979586119038832 " " Order of pole (three term test) = 22.901522932834858 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 0.4232895668635035 " " y[1] (numeric) = 0.4232895668635037 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.245690475443094000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3059289454713606 " " Order of pole (three term test) = 22.895483855957213 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 0.422736245680845 " " y[1] (numeric) = 0.4227362456808455 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.1818252307101809000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31377691153964776 " " Order of pole (three term test) = 22.889286590810215 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 0.422149651150898 " " y[1] (numeric) = 0.4221496511508985 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.18346742611126210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3214993710269557 " " Order of pole (three term test) = 22.882933616217315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 0.42152884194095996 " " y[1] (numeric) = 0.42152884194096013 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.950701283616992500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32909323505245364 " " Order of pole (three term test) = 22.87642747328365 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 0.4208728801397672 " " y[1] (numeric) = 0.4208728801397674 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.275811661974816000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3365554661717818 " " Order of pole (three term test) = 22.869770764379624 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 0.4201808313512867 " " y[1] (numeric) = 0.42018083135128714 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.0569002122773840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34388307959198794 " " Order of pole (three term test) = 22.86296615210007 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 0.4194517647881544 " " y[1] (numeric) = 0.4194517647881547 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.94052940880493400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35107314436540377 " " Order of pole (three term test) = 22.85601635819915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 0.41868475336475175 " " y[1] (numeric) = 0.41868475336475225 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.19326141462351330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3581227845619863 " " Order of pole (three term test) = 22.848924162501778 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 0.41787887378991573 " " y[1] (numeric) = 0.41787887378991617 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.06272232865575270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3650291804196506 " " Order of pole (three term test) = 22.841692401791665 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 0.41703320665926524 " " y[1] (numeric) = 0.41703320665926574 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.19798700224252470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37178956947213837 " " Order of pole (three term test) = 22.834323968676674 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 0.41614683654714213 " " y[1] (numeric) = 0.4161468365471426 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.0671454660926040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3784012476539652 " " Order of pole (three term test) = 22.826821810431806 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 0.41521885209815235 " " y[1] (numeric) = 0.41521885209815257 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.347652299576775000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38486157038201296 " " Order of pole (three term test) = 22.819188927820328 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 0.4142483461183004 " " y[1] (numeric) = 0.41424834611830064 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.36018084334415600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3911679536133269 " " Order of pole (three term test) = 22.811428373893516 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 0.41323441566570907 " " y[1] (numeric) = 0.4132344156657093 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.373332822904493000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.397317874878699 " " Order of pole (three term test) = 22.803543252769472 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 0.4121761621409119 " " y[1] (numeric) = 0.41217616214091213 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.38712874057768200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4033088742916204 " " Order of pole (three term test) = 22.795536718391514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 0.41107269137671265 " " y[1] (numeric) = 0.4110726913767131 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.08031795632732310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40913855553220535 " " Order of pole (three term test) = 22.787411973266632 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 0.40992311372760204 " " y[1] (numeric) = 0.4099231137276024 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 8.12510678792494800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4148045868056855 " " Order of pole (three term test) = 22.779172267184556 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 0.40872654415872 " " y[1] (numeric) = 0.4087265441587202 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.07444674376479600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4203047017750974 " " Order of pole (three term test) = 22.770820895917847 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 0.40748210233435955 " " y[1] (numeric) = 0.40748210233435955 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4256367004677872 " " Order of pole (three term test) = 22.762361199903673 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 0.406188912705999 " " y[1] (numeric) = 0.4061889127059992 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.466535347944074000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43079845015536994 " " Order of pole (three term test) = 22.753796562907635 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 0.4048461045998577 " " y[1] (numeric) = 0.40484610459985765 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.371166737200645900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43578788620679354 " " Order of pole (three term test) = 22.745130410670352 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 0.4034528123039598 " " y[1] (numeric) = 0.4034528123039598 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4406030129141622 " " Order of pole (three term test) = 22.736366209537156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 0.40200817515470755 " " y[1] (numeric) = 0.4020081751547075 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.38084632756274420000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4452419042909938 " " Order of pole (three term test) = 22.727507465071657 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 0.400511337622945 " " y[1] (numeric) = 0.40051133762294505 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.38600698698616880000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4497027048425882 " " Order of pole (three term test) = 22.718557720653514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 0.3989614493995117 " " y[1] (numeric) = 0.3989614493995116 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.782782713207466000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45398363030820194 " " Order of pole (three term test) = 22.70952055606118 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 0.3973576654802713 " " y[1] (numeric) = 0.3973576654802713 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45808296837472673 " " Order of pole (three term test) = 22.70039958603999 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 0.395699146250613 " " y[1] (numeric) = 0.3956991462506128 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.208587642195741000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46199907936159323 " " Order of pole (three term test) = 22.691198458856338 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 0.3939850575694104 " " y[1] (numeric) = 0.3939850575694103 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.408965902760871700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4657303968766204 " " Order of pole (three term test) = 22.68192085483843 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 0.39221457085243694 " " y[1] (numeric) = 0.3922145708524369 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.415326083133785800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46927542844255316 " " Order of pole (three term test) = 22.67257048490416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 0.3903868631552223 " " y[1] (numeric) = 0.3903868631552221 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.68780934712815500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47263275609403077 " " Order of pole (three term test) = 22.663151089076845 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 0.3885011172553461 " " y[1] (numeric) = 0.3885011172553459 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.2865630572773300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4758010369447572 " " Order of pole (three term test) = 22.65366643498921 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 0.38655652173416044 " " y[1] (numeric) = 0.38655652173416016 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.18021144517560500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4787790037246347 " " Order of pole (three term test) = 22.644120316376444 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 0.3845522710579301 " " y[1] (numeric) = 0.3845522710579298 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 8.66116084742541300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48156546528665733 " " Order of pole (three term test) = 22.6345165515587 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 0.3824875656583857 " " y[1] (numeric) = 0.3824875656583855 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.805276428864300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4841593070833526 " " Order of pole (three term test) = 22.624858981913864 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 0.3803616120126807 " " y[1] (numeric) = 0.38036161201267993 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.04320334306423200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.486559491612586 " " Order of pole (three term test) = 22.615151470341036 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 0.3781736227227399 " " y[1] (numeric) = 0.3781736227227394 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.32108727595632750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4887650588325477 " " Order of pole (three term test) = 22.6053978997154 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 0.3759228165940036 " " y[1] (numeric) = 0.3759228165940029 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 1.91966258538046640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4907751265457568 " " Order of pole (three term test) = 22.59560217133515 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 0.37360841871354156 " " y[1] (numeric) = 0.3736084187135409 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 1.78297324527325940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4925888907519289 " " Order of pole (three term test) = 22.58576820336106 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 0.3712296605275469 " " y[1] (numeric) = 0.3712296605275461 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.2429976831204190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49420562596956447 " " Order of pole (three term test) = 22.57589992924918 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 0.36878577991818906 " " y[1] (numeric) = 0.3687857799181881 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.5589098667002020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4956246855261329 " " Order of pole (three term test) = 22.56600129617759 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 0.3662760212798255 " " y[1] (numeric) = 0.36627602127982467 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.27333273294658550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49684550181673165 " " Order of pole (three term test) = 22.556076263467535 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 0.3636996355945623 " " y[1] (numeric) = 0.36369963559456137 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.59469484864529800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4978675865311221 " " Order of pole (three term test) = 22.54612880099976 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 0.3610558805071542 " " y[1] (numeric) = 0.36105588050715315 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 2.92118735723790550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49869053084904635 " " Order of pole (three term test) = 22.536162887626634 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 0.35834402039923985 " " y[1] (numeric) = 0.35834402039923885 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 2.78838396982153350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49931400560374906 " " Order of pole (three term test) = 22.526182509580618 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 0.3555633264629039 " " y[1] (numeric) = 0.35556332646290273 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 3.27855571454171400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4997377614136418 " " Order of pole (three term test) = 22.51619165887987 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 0.35271307677355557 " " y[1] (numeric) = 0.3527130767735545 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 2.99028287536680040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49996162878205047 " " Order of pole (three term test) = 22.506194331731457 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 0.3497925563621225 " " y[1] (numeric) = 0.3497925563621212 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 3.65003901625959360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49998551816501247 " " Order of pole (three term test) = 22.496194526932936 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 0.346801057286545 " " y[1] (numeric) = 0.34680105728654353 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 4.16172298696362500000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4998094200070929 " " Order of pole (three term test) = 22.486196244272904 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 0.34373787870257067 " " y[1] (numeric) = 0.34373787870256944 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 3.55283895885210400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49943340474520753 " " Order of pole (three term test) = 22.47620348293111 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 0.3406023269338392 " " y[1] (numeric) = 0.34060232693383796 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 3.585546047443460300000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4988576227804472 " " Order of pole (three term test) = 22.466220239878872 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 0.33739371554124764 " " y[1] (numeric) = 0.33739371554124636 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 3.78417385833863250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4980823044179209 " " Order of pole (three term test) = 22.45625050828028 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 0.3341113653915948 " " y[1] (numeric) = 0.33411136539159336 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 4.31978699773082340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4971077597746365 " " Order of pole (three term test) = 22.446298275895067 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 0.33075460472549345 " " y[1] (numeric) = 0.33075460472549195 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 4.5314594621830790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49593437865545725 " " Order of pole (three term test) = 22.436367523483476 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 0.3273227692245464 " " y[1] (numeric) = 0.32732276922454473 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 5.0877442497600890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.494562630397186 " " Order of pole (three term test) = 22.426462223214077 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 0.3238152020777769 " " y[1] (numeric) = 0.32381520207777525 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 5.1428547092663660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4929930636808364 " " Order of pole (three term test) = 22.416586337074897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 0.32023125404731045 " " y[1] (numeric) = 0.32023125404730857 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 5.8938005519721310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49122630631216796 " " Order of pole (three term test) = 22.40674381528872 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 0.3165702835332964 " " y[1] (numeric) = 0.31657028353329436 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 6.4880145180794010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4892630649705709 " " Order of pole (three term test) = 22.396938594733026 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 0.31283165663806844 " " y[1] (numeric) = 0.31283165663806656 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 6.0332102004829240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4871041249264064 " " Order of pole (three term test) = 22.38717459736531 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 0.3090147472295346 " " y[1] (numeric) = 0.30901474722953254 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 6.6466491129334470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4847503497269066 " " Order of pole (three term test) = 22.37745572865433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 0.30511893700378767 " " y[1] (numeric) = 0.3051189370037856 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 6.7315146536809120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48220268085076773 " " Order of pole (three term test) = 22.36778587601798 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 0.3011436155469376 " " y[1] (numeric) = 0.30114361554693525 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 7.742048083863280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4794621373315719 " " Order of pole (three term test) = 22.358168907268393 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 0.29708818039615004 " " y[1] (numeric) = 0.29708818039614765 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 8.034582526175180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47652981535018674 " " Order of pole (three term test) = 22.348608669064845 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 0.2929520370998939 " " y[1] (numeric) = 0.29295203709989165 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 7.769043775945790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4734068877963075 " " Order of pole (three term test) = 22.339108985375145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 0.2887345992773862 " " y[1] (numeric) = 0.2887345992773835 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 9.4205766026623490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4700946037993176 " " Order of pole (three term test) = 22.329673655946113 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 0.2844352886772268 " " y[1] (numeric) = 0.2844352886772241 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 9.3678083035753460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4665942882286527 " " Order of pole (three term test) = 22.320306454783715 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 0.2800535352352269 " " y[1] (numeric) = 0.28005353523522414 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 9.910810657082411000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4629073411638701 " " Order of pole (three term test) = 22.31101112864352 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 0.2755887771314125 " " y[1] (numeric) = 0.2755887771314096 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.0474228646288315000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45903523733463775 " " Order of pole (three term test) = 22.30179139553205 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 0.27104046084620625 " " y[1] (numeric) = 0.2710404608462036 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 9.8307656752852330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4549795255308598 " " Order of pole (three term test) = 22.29265094321962 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 0.26640804121578077 " " y[1] (numeric) = 0.2664080412157777 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.1460289651115561000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45074182798318213 " " Order of pole (three term test) = 22.283593427765286 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 0.2616909814865709 " " y[1] (numeric) = 0.26169098148656794 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.1242615234746417000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4463238397141223 " " Order of pole (three term test) = 22.27462247205446 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 0.25688875336895256 " " y[1] (numeric) = 0.2568887533689496 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.145278248530846000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4417273278600822 " " Order of pole (three term test) = 22.265741664349825 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 0.2520008370900695 " " y[1] (numeric) = 0.252000837090066 " " absolute error = 3.497202527569243000000000000000E-15 " " relative error = 1.3877741708926475000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43695413096451674 " " Order of pole (three term test) = 22.256954556856037 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = 0.2470267214458084 " " y[1] (numeric) = 0.24702672144580498 " " absolute error = 3.4139358007223564000000000000000E-15 " " relative error = 1.382010731770688000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43200615824254324 " " Order of pole (three term test) = 22.24826466429895 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = 0.24196590385192263 " " y[1] (numeric) = 0.24196590385191927 " " absolute error = 3.3584246494910985000000000000000E-15 " " relative error = 1.3879743368910252000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4268853888172781 " " Order of pole (three term test) = 22.23967546251972 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = 0.2368178903942879 " " y[1] (numeric) = 0.2368178903942842 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.5705093590277094000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.421593870928215 " " Order of pole (three term test) = 22.231190387084528 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = 0.23158219587829265 " " y[1] (numeric) = 0.23158219587828882 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.6539567821395806000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4161337211119574 " " Order of pole (three term test) = 22.222812831910428 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = 0.22625834387735866 " " y[1] (numeric) = 0.22625834387735502 " " absolute error = 3.635980405647387700000000000000E-15 " " relative error = 1.6070038979946918000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4105071233556311 " " Order of pole (three term test) = 22.214546147907782 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = 0.2208458667805835 " " y[1] (numeric) = 0.22084586678057963 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.7469310459885012000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4047163282233173 " " Order of pole (three term test) = 22.206393641639973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = 0.21534430583949904 " " y[1] (numeric) = 0.21534430583949526 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.7528944027611967000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3987636519558602 " " Order of pole (three term test) = 22.198358574000807 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = 0.20975321121394908 " " y[1] (numeric) = 0.20975321121394472 " " absolute error = 4.3576253716537394000000000000000E-15 " " relative error = 2.07750114834186980000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39265147554439855 " " Order of pole (three term test) = 22.190444158910207 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = 0.2040721420170688 " " y[1] (numeric) = 0.20407214201706464 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 2.0401296821768605000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38638224377800245 " " Order of pole (three term test) = 22.182653562028694 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = 0.19830066635937804 " " y[1] (numeric) = 0.1983006663593738 " " absolute error = 4.246603069191224000000000000000E-15 " " relative error = 2.1414971251257187000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37995846426578944 " " Order of pole (three term test) = 22.174989899491134 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = 0.19243836139196624 " " y[1] (numeric) = 0.19243836139196172 " " absolute error = 4.524158825347513000000000000000E-15 " " relative error = 2.350965157166623000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37338270643391563 " " Order of pole (three term test) = 22.167456236660367 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = 0.18648481334877776 " " y[1] (numeric) = 0.1864848133487732 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 2.4409035348362726000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3666576004978378 " " Order of pole (three term test) = 22.160055586901084 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = 0.18043961758798943 " " y[1] (numeric) = 0.1804396175879846 " " absolute error = 4.829470157119431000000000000000E-15 " " relative error = 2.6765021017429236000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.35978583641026407 " " Order of pole (three term test) = 22.1527909103745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = 0.17430237863247244 " " y[1] (numeric) = 0.17430237863246767 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 2.738894926932906000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3527701627852064 " " Order of pole (three term test) = 22.14566511285438 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = 0.168072710209342 " " y[1] (numeric) = 0.16807271020933692 " " absolute error = 5.079270337660091000000000000000E-15 " " relative error = 3.022067253710394300000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34561338579857404 " " Order of pole (three term test) = 22.138681044564713 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = 0.16175023528858157 " " y[1] (numeric) = 0.16175023528857657 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 3.0887148954681530000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.33831836806573956 " " Order of pole (three term test) = 22.1318414990397 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = 0.15533458612074869 " " y[1] (numeric) = 0.15533458612074333 " " absolute error = 5.35682609381638000000000000000E-15 " " relative error = 3.4485726763080790000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3308880274965303 " " Order of pole (three term test) = 22.125149212006363 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = 0.14882540427374646 " " y[1] (numeric) = 0.14882540427374089 " " absolute error = 5.578870698741412000000000000000E-15 " " relative error = 3.748601071144916400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3233253361281034 " " Order of pole (three term test) = 22.118606860290267 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = 0.14222234066866868 " " y[1] (numeric) = 0.142222340668663 " " absolute error = 5.689893001203927000000000000000E-15 " " relative error = 4.00070268457999000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3156333189361729 " " Order of pole (three term test) = 22.112217060744886 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = 0.1355250556147065 " " y[1] (numeric) = 0.13552505561470088 " " absolute error = 5.6343818499726690000000000000000E-15 " " relative error = 4.1574466244758757000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30781505262505593 " " Order of pole (three term test) = 22.10598236920484 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = 0.12873321884311828 " " y[1] (numeric) = 0.12873321884311223 " " absolute error = 6.050715484207103000000000000000E-15 " " relative error = 4.700197461527668000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29987366439703433 " " Order of pole (three term test) = 22.099905279463606 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = 0.12184650954025367 " " y[1] (numeric) = 0.12184650954024764 " " absolute error = 6.022959908591474000000000000000E-15 " " relative error = 4.9430713537195790000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29181233070151685 " " Order of pole (three term test) = 22.093988222276067 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = 0.1148646163796383 " " y[1] (numeric) = 0.11486461637963183 " " absolute error = 6.467049118441537000000000000000E-15 " " relative error = 5.630149059190983000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28363427596449786 " " Order of pole (three term test) = 22.0882335643862 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = 0.10778723755310216 " " y[1] (numeric) = 0.10778723755309591 " " absolute error = 6.2450045135165060000000000000000E-15 " " relative error = 5.793825554198715000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27534277129883283 " " Order of pole (three term test) = 22.08264360758043 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y[1] (analytic) = 0.10061408080096479 " " y[1] (numeric) = 0.10061408080095806 " " absolute error = 6.7307270867900120000000000000000E-15 " " relative error = 6.68964724739151000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2669411331958364 " " Order of pole (three term test) = 22.077220587766952 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y[1] (analytic) = 9.33448634412559200E-2 " " y[1] (numeric) = 9.33448634412491700E-2 " " absolute error = 6.744604874597826000000000000000E-15 " " relative error = 7.2254697537185440000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25843272219872915 " " Order of pole (three term test) = 22.071966674081384 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y[1] (analytic) = 8.59793123979879500E-2 " " y[1] (numeric) = 8.59793123979808900E-2 " " absolute error = 7.0637939941775580000000000000000E-15 " " relative error = 8.2156902598616990000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24982094155846624 " " Order of pole (three term test) = 22.066883968019145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y[1] (analytic) = 7.85171642284598900E-2 " " y[1] (numeric) = 7.85171642284528700E-2 " " absolute error = 7.022160630754115000000000000000E-15 " " relative error = 8.943472041758752000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24110923587248131 " " Order of pole (three term test) = 22.061974502594893 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y[1] (analytic) = 7.09581651496038500E-2 " " y[1] (numeric) = 7.09581651495969600E-2 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 9.700621116912294000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23230108970689434 " " Order of pole (three term test) = 22.05724024152935 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y[1] (analytic) = 6.3302071063362500E-2 " " y[1] (numeric) = 6.33020710633552100E-2 " " absolute error = 7.28583859910259000000000000000E-15 " " relative error = 1.150963700983779300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2234000262027314 " " Order of pole (three term test) = 22.052683078463804 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y[1] (analytic) = 5.55486475810966800E-2 " " y[1] (numeric) = 5.554864758108947000E-2 " " absolute error = 7.202571872255703000000000000000E-15 " " relative error = 1.296624163844945200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21440960566671463 " " Order of pole (three term test) = 22.04830483620273 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y[1] (analytic) = 4.76976700470275200E-2 " " y[1] (numeric) = 4.76976700470201300E-2 " " absolute error = 7.389922007661198000000000000000E-15 " " relative error = 1.549325575101489200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2053334241471875 " " Order of pole (three term test) = 22.04410726598465 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y[1] (analytic) = 3.97489235606993700E-2 " " y[1] (numeric) = 3.97489235606914300E-2 " " absolute error = 7.93809462606986900000000000000E-15 " " relative error = 1.99705901820154880000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19617511199574417 " " Order of pole (three term test) = 22.040092046781687 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y[1] (analytic) = 3.170220299846926400E-2 " " y[1] (numeric) = 3.170220299846137600E-2 " " absolute error = 7.889522368742519000000000000000E-15 " " relative error = 2.488635369953142700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18693833241513558 " " Order of pole (three term test) = 22.036260784627988 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y[1] (analytic) = 2.355731303402208700E-2 " " y[1] (numeric) = 2.355731303401392400E-2 " " absolute error = 8.163608677946854000000000000000E-15 " " relative error = 3.465424374230098300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17762677999403914 " " Order of pole (three term test) = 22.032615011977327 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y[1] (analytic) = 1.531406815789981800E-2 " " y[1] (numeric) = 1.531406815789143300E-2 " " absolute error = 8.383918559395909000000000000000E-15 " " relative error = 5.47465145965870300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1682441792292705 " " Order of pole (three term test) = 22.02915618709017 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y[1] (analytic) = 6.972292696053817000E-3 " " y[1] (numeric) = 6.97229269604548000E-3 " " absolute error = 8.337081025544535000000000000000E-15 " " relative error = 1.19574455476649170000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.158794283036036 " " Order of pole (three term test) = 22.025885693450338 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y[1] (analytic) = -1.4681791725874582000E-3 " " y[1] (numeric) = -1.468179172595908000E-3 " " absolute error = 8.449838051483027000000000000000E-15 " " relative error = 5.755318021976420000000000E-10 "%" Correct digits = 13 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14928087124681594 " " Order of pole (three term test) = 22.022804839211677 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y[1] (analytic) = -1.000750339953748700E-2 " " y[1] (numeric) = -1.000750339954626100E-2 " " absolute error = 8.77423134149069000000000000000E-15 " " relative error = 8.76765262142824200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13970774909948208 " " Order of pole (three term test) = 22.01991485667482 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y[1] (analytic) = -1.86458260511566100E-2 " " y[1] (numeric) = -1.86458260511656600E-2 " " absolute error = 9.048317650695026000000000000000E-15 " " relative error = 4.85273091461332900000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13007874571525377 " " Order of pole (three term test) = 22.017216901794253 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y[1] (analytic) = -2.738328329404504700E-2 " " y[1] (numeric) = -2.738328329405421000E-2 " " absolute error = 9.166278847061449000000000000000E-15 " " relative error = 3.34739948772133140000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12039771256709944 " " Order of pole (three term test) = 22.01471205371593 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y[1] (analytic) = -3.622000138142622600E-2 " " y[1] (numeric) = -3.62200013814355200E-2 " " absolute error = 9.291178937331779000000000000000E-15 " " relative error = 2.565206676688956400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11066852193919968 " " Order of pole (three term test) = 22.01240131434571 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y[1] (analytic) = -4.51560966405217800E-2 " " y[1] (numeric) = -4.51560966405314350E-2 " " absolute error = 9.652001420334955000000000000000E-15 " " relative error = 2.137474701848681700000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10089506537808485 " " Order of pole (three term test) = 22.010285607948514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y[1] (analytic) = -5.41916754609195200E-2 " " y[1] (numeric) = -5.41916754609294700E-2 " " absolute error = 9.950373858202965000000000000000E-15 " " relative error = 1.83614434755365820000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.1081252136068500E-2 " " Order of pole (three term test) = 22.008365780778714 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y[1] (analytic) = -6.33268342839339300E-2 " " y[1] (numeric) = -6.33268342839439100E-2 " " absolute error = 9.978129433818594000000000000000E-15 " " relative error = 1.575655809523081600000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.12310076075980700E-2 " " Order of pole (three term test) = 22.00664260074155 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y[1] (analytic) = -7.25616595929614600E-2 " " y[1] (numeric) = -7.25616595929717400E-2 " " absolute error = 1.028344076559051200000000000000E-14 " " relative error = 1.417200326353618100000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.13482717591504700E-2 " " Order of pole (three term test) = 22.0051167570861 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y[1] (analytic) = -8.18962279048340800E-2 " " y[1] (numeric) = -8.18962279048444300E-2 " " absolute error = 1.035282970462958500000000000000E-14 " " relative error = 1.264139993927423400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.14369975532966600E-2 " " Order of pole (three term test) = 22.003788860129443 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y[1] (analytic) = -9.13306057621654500E-2 " " y[1] (numeric) = -9.13306057621762800E-2 " " absolute error = 1.082467449009527600000000000000E-14 " " relative error = 1.185218733606549400000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.15011493675705800E-2 " " Order of pole (three term test) = 22.002659441012685 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y[1] (analytic) = -0.10086484972669929 " " y[1] (numeric) = -0.10086484972671017 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 1.078689520760423200000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.15447014087703400E-2 " " Order of pole (three term test) = 22.001728951488392 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y[1] (analytic) = -0.1104990063736504 " " y[1] (numeric) = -0.11049900637366154 " " absolute error = 1.114386360967500900000000000000E-14 " " relative error = 1.008503512872526300000000000E-11 "%" Correct digits = 14 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.157163612332855600E-2 " " Order of pole (three term test) = 22.000997763739985 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y[1] (analytic) = -0.12023311228704969 " " y[1] (numeric) = -0.12023311228706082 " " absolute error = 1.112998582186719400000000000000E-14 " " relative error = 9.257005503854037000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.15859426043869800E-2 " " Order of pole (three term test) = 22.000466170232805 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999999772 " " y[1] (analytic) = -0.13006719405608358 " " y[1] (numeric) = -0.1300671940560951 " " absolute error = 1.151856388048599900000000000000E-14 " " relative error = 8.855856362611557000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.159161499621236500E-2 " " Order of pole (three term test) = 22.00013438359717 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999977 " " y[1] (analytic) = -0.14000126827243742 " " y[1] (numeric) = -0.1400012682724492 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 8.405898179526379000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5926508965920890000E-3 " " Order of pole (three term test) = 22.000002536543313 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999977 " " y[1] (analytic) = -0.15003534152863462 " " y[1] (numeric) = -0.15003534152864653 " " absolute error = 1.190714193910480400000000000000E-14 " " relative error = 7.936224770636654000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.406950242151767000E-3 " " Order of pole (three term test) = 22.000070681808293 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1599999999999766 " " y[1] (analytic) = -0.16016941041737764 " " y[1] (numeric) = -0.1601694104173899 " " absolute error = 1.22679644221079800000000000000E-14 " " relative error = 7.65936790935265900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.84031887128899500E-2 " " Order of pole (three term test) = 22.000338792134915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1699999999999764 " " y[1] (analytic) = -0.1704034615318899 " " y[1] (numeric) = -0.17040346153190217 " " absolute error = 1.22679644221079800000000000000E-14 " " relative error = 7.199363388408697000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.839206615351552700E-2 " " Order of pole (three term test) = 22.000806760282615 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999976 " " y[1] (analytic) = -0.18073747146725427 " " y[1] (numeric) = -0.1807374714672669 " " absolute error = 1.262878690511115600000000000000E-14 " " relative error = 6.987365045327204000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.836958714623557300E-2 " " Order of pole (three term test) = 22.001474399070393 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999976 " " y[1] (analytic) = -0.19117140682275613 " " y[1] (numeric) = -0.1911714068227689 " " absolute error = 1.2767564783189300000000000000E-14 " " relative error = 6.67859540052802000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.833176081568479000E-2 " " Order of pole (three term test) = 22.002341441451613 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999758 " " y[1] (analytic) = -0.20170522420522152 " " y[1] (numeric) = -0.20170522420523423 " " absolute error = 1.271205363195804200000000000000E-14 " " relative error = 6.302292705628874000000000000E-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 = 5.82746024252225800E-2 " " Order of pole (three term test) = 22.003407540620906 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999999755 " " y[1] (analytic) = -0.2123388702333564 " " y[1] (numeric) = -0.2123388702333695 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 6.169681357058884000000000000E-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 = 6.81941349707746200E-2 " " Order of pole (three term test) = 22.0046722701528 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999999753 " " y[1] (analytic) = -0.22307228154308634 " " y[1] (numeric) = -0.22307228154309994 " " absolute error = 1.360023205165816800000000000000E-14 " " relative error = 6.096782602293548000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.80863907715813300E-2 " " Order of pole (three term test) = 22.006135124172342 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.229999999999975 " " y[1] (analytic) = -0.2339053847938919 " " y[1] (numeric) = -0.2339053847939057 " " absolute error = 1.382227665658320000000000000000E-14 " " relative error = 5.909345211852579000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.79474130572175500E-2 " " Order of pole (three term test) = 22.00779551755744 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999975 " " y[1] (analytic) = -0.24483809667614187 " " y[1] (numeric) = -0.24483809667615603 " " absolute error = 1.415534356397074600000000000000E-14 " " relative error = 5.781511846456903000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.77732575502473900E-2 " " Order of pole (three term test) = 22.009652786172882 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999747 " " y[1] (analytic) = -0.25587032391942577 " " y[1] (numeric) = -0.25587032391943987 " " absolute error = 1.409983241273948800000000000000E-14 " " relative error = 5.510538383958729000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10755999404388317 " " Order of pole (three term test) = 22.01170618713598 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2599999999999745 " " y[1] (analytic) = -0.26700196330187875 " " y[1] (numeric) = -0.26700196330189313 " " absolute error = 1.437738816889577700000000000000E-14 " " relative error = 5.3847499812727440000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11730370797401542 " " Order of pole (three term test) = 22.013954899113724 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2699999999999743 " " y[1] (analytic) = -0.27823290166050585 " " y[1] (numeric) = -0.2782329016605206 " " absolute error = 1.476596622751458200000000000000E-14 " " relative error = 5.307052523044782000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12700050198498672 " " Order of pole (three term test) = 22.01639802265131 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999974 " " y[1] (analytic) = -0.28956301590249733 " " y[1] (numeric) = -0.2895630159025122 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 5.1377378024638790000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13664649748848143 " " Order of pole (three term test) = 22.01903458053189 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999974 " " y[1] (analytic) = -0.3009921730175371 " " y[1] (numeric) = -0.30099217301755216 " " absolute error = 1.50435219836708700000000000000E-14 " " relative error = 4.997977798842752000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14623783621490985 " " Order of pole (three term test) = 22.021863518167475 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999999736 " " y[1] (analytic) = -0.3125202300911045 " " y[1] (numeric) = -0.3125202300911199 " " absolute error = 1.537658889105841800000000000000E-14 " " relative error = 4.920189930288962000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15577068175666406 " " Order of pole (three term test) = 22.024883704020727 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999999734 " " y[1] (analytic) = -0.324147034318766 " " y[1] (numeric) = -0.32414703431878145 " " absolute error = 1.543210004228967600000000000000E-14 " " relative error = 4.760833328221586000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16524122110263043 " " Order of pole (three term test) = 22.02809393005757 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.319999999999973 " " y[1] (analytic) = -0.33587242302145404 " " y[1] (numeric) = -0.33587242302146975 " " absolute error = 1.570965579844596500000000000000E-14 " " relative error = 4.67726872516785960000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17464566616334262 " " Order of pole (three term test) = 22.031492912230387 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.329999999999973 " " y[1] (analytic) = -0.34769622366173625 " " y[1] (numeric) = -0.3476962236617523 " " absolute error = 1.604272270583351200000000000000E-14 " " relative error = 4.614005449032722600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18398025528616735 " " Order of pole (three term test) = 22.035079290991643 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999728 " " y[1] (analytic) = -0.3596182538610688 " " y[1] (numeric) = -0.3596182538610849 " " absolute error = 1.60982338570647700000000000000E-14 " " relative error = 4.476478511372783400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19324125475991474 " " Order of pole (three term test) = 22.038851631837638 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3499999999999726 " " y[1] (analytic) = -0.371638321418033 " " y[1] (numeric) = -0.37163832141804937 " " absolute error = 1.63757896132210600000000000000E-14 " " relative error = 4.4063781018968023000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20242496030827395 " " Order of pole (three term test) = 22.042808425882328 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3599999999999723 " " y[1] (analytic) = -0.3837562243275565 " " y[1] (numeric) = -0.38375622432757334 " " absolute error = 1.681987882307112200000000000000E-14 " " relative error = 4.382959221715308000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2115276985714734 " " Order of pole (three term test) = 22.046948090460866 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999972 " " y[1] (analytic) = -0.3959717508011136 " " y[1] (numeric) = -0.3959717508011308 " " absolute error = 1.720845688168992600000000000000E-14 " " relative error = 4.345879938878088000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22054582857557606 " " Order of pole (three term test) = 22.051268969762603 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999972 " " y[1] (analytic) = -0.40828467928790335 " " y[1] (numeric) = -0.4082846792879206 " " absolute error = 1.726396803292118400000000000000E-14 " " relative error = 4.22841436593496050000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2294757431888202 " " Order of pole (three term test) = 22.05576933549344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999717 " " y[1] (analytic) = -0.4206947784970039 " " y[1] (numeric) = -0.4206947784970216 " " absolute error = 1.770805724277124700000000000000E-14 " " relative error = 4.209241033614911000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23831387056442466 " " Order of pole (three term test) = 22.06044738756708 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999999715 " " y[1] (analytic) = -0.4332018074205033 " " y[1] (numeric) = -0.43320180742052117 " " absolute error = 1.78745906964650200000000000000E-14 " " relative error = 4.1261579223085715000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24705667556927938 " " Order of pole (three term test) = 22.065301254825073 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999999713 " " y[1] (analytic) = -0.44580551535759794 " " y[1] (numeric) = -0.4458055153576162 " " absolute error = 1.826316875508382500000000000000E-14 " " relative error = 4.096667296822074600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.25570066119795143 " " Order of pole (three term test) = 22.070328995785232 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.419999999999971 " " y[1] (analytic) = -0.45850564193966425 " " y[1] (numeric) = -0.45850564193968274 " " absolute error = 1.848521336000885600000000000000E-14 " " relative error = 4.0316217880785343000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.26424236997144096 " " Order of pole (three term test) = 22.0755285994182 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.429999999999971 " " y[1] (analytic) = -0.471301917156294 " " y[1] (numeric) = -0.4713019171563127 " " absolute error = 1.870725796493388800000000000000E-14 " " relative error = 3.9692726220611046000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27267838532012667 " " Order of pole (three term test) = 22.080897985951857 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999999706 " " y[1] (analytic) = -0.4841940613822957 " " y[1] (numeric) = -0.48419406138231463 " " absolute error = 1.89293025698589200000000000000E-14 " " relative error = 3.909445422733774000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2810053329503472 " " Order of pole (three term test) = 22.08643500770318 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4499999999999704 " " y[1] (analytic) = -0.49718178540565683 " " y[1] (numeric) = -0.49718178540567604 " " absolute error = 1.920685832601520800000000000000E-14 " " relative error = 3.863146014157396000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.28921988219407585 " " Order of pole (three term test) = 22.0921374499373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999997 " " y[1] (analytic) = -0.5102647904564646 " " y[1] (numeric) = -0.5102647904564843 " " absolute error = 1.976196983832778600000000000000E-14 " " relative error = 3.872885256427243700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.29731874734114033 " " Order of pole (three term test) = 22.098003031753354 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.46999999999997 " " y[1] (analytic) = -0.5234427682367837 " " y[1] (numeric) = -0.5234427682368036 " " absolute error = 1.987299214079030200000000000000E-14 " " relative error = 3.796593122822663000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3052986889534658 " " Order of pole (three term test) = 22.104029406996816 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.47999999999997 " " y[1] (analytic) = -0.5367154009514841 " " y[1] (numeric) = -0.536715400951504 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 3.72339128108217950000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31315651516080456 " " Order of pole (three term test) = 22.110214165197938 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999999696 " " y[1] (analytic) = -0.5500823613400212 " " y[1] (numeric) = -0.5500823613400415 " " absolute error = 2.031708135064036500000000000000E-14 " " relative error = 3.693461702925211500000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32088908293744345 " " Order of pole (three term test) = 22.11655483253591 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999999694 " " y[1] (analytic) = -0.5635433127091622 " " y[1] (numeric) = -0.5635433127091829 " " absolute error = 2.065014825802791200000000000000E-14 " " relative error = 3.6643409286067063000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3284932993593715 " " Order of pole (three term test) = 22.12304887282833 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.509999999999969 " " y[1] (analytic) = -0.5770979089666546 " " y[1] (numeric) = -0.5770979089666755 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 3.6167507347802510000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3359661228414083 " " Order of pole (three term test) = 22.12969368854567 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.519999999999969 " " y[1] (analytic) = -0.5907457946558341 " " y[1] (numeric) = -0.5907457946558554 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 3.6083679758095910000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3433045643537967 " " Order of pole (three term test) = 22.136486621850242 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999687 " " y[1] (analytic) = -0.6044866049911723 " " y[1] (numeric) = -0.6044866049911939 " " absolute error = 2.153832667772803700000000000000E-14 " " relative error = 3.5630775768873440000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3505056886177768 " " Order of pole (three term test) = 22.143424955659288 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999999685 " " y[1] (analytic) = -0.6183199658947527 " " y[1] (numeric) = -0.6183199658947747 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 3.555184548467231000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.357566615279657 " " Order of pole (three term test) = 22.15050591473181 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5499999999999683 " " y[1] (analytic) = -0.6322454940336799 " " y[1] (numeric) = -0.6322454940337019 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 3.4768798030226994000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3644845200629164 " " Order of pole (three term test) = 22.157726666778572 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999968 " " y[1] (analytic) = -0.6462627968584105 " " y[1] (numeric) = -0.6462627968584328 " " absolute error = 2.231548279496564600000000000000E-14 " " relative error = 3.4530043975059170000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3712566358978797 " " Order of pole (three term test) = 22.165084323595046 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999968 " " y[1] (analytic) = -0.66037147264201 " " y[1] (numeric) = -0.6603714726420328 " " absolute error = 2.27595720048157100000000000000E-14 " " relative error = 3.4464801929979440000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37788025402850584 " " Order of pole (three term test) = 22.17257594221659 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999999677 " " y[1] (analytic) = -0.6745711105203243 " " y[1] (numeric) = -0.6745711105203472 " " absolute error = 2.29816166097407400000000000000E-14 " " relative error = 3.406848625938647000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38435272509585733 " " Order of pole (three term test) = 22.180198526095666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999999674 " " y[1] (analytic) = -0.6888612905330649 " " y[1] (numeric) = -0.6888612905330881 " " absolute error = 2.320366121466577200000000000000E-14 " " relative error = 3.3684083477400756000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39067146019780474 " " Order of pole (three term test) = 22.18794902630032 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999999672 " " y[1] (analytic) = -0.7032415836658057 " " y[1] (numeric) = -0.7032415836658292 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 3.3468908364836460000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3968339319245565 " " Order of pole (three term test) = 22.19582434273385 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.609999999999967 " " y[1] (analytic) = -0.7177115518928838 " " y[1] (numeric) = -0.7177115518929076 " " absolute error = 2.37587727269783500000000000000E-14 " " relative error = 3.3103511660523300000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4028376753695873 " " Order of pole (three term test) = 22.20382132537465 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.619999999999967 " " y[1] (analytic) = -0.7322707482212016 " " y[1] (numeric) = -0.7322707482212255 " " absolute error = 2.386979502944086600000000000000E-14 " " relative error = 3.2596952817553165000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4086802891155673 " " Order of pole (three term test) = 22.211936775536316 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999999666 " " y[1] (analytic) = -0.7469187167349252 " " y[1] (numeric) = -0.7469187167349494 " " absolute error = 2.420286193682841300000000000000E-14 " " relative error = 3.2403608845991466000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41435943619489923 " " Order of pole (three term test) = 22.22016744714697 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999999664 " " y[1] (analytic) = -0.7616549926410765 " " y[1] (numeric) = -0.761654992641101 " " absolute error = 2.45359288442159600000000000000E-14 " " relative error = 3.221396706025178600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41987284502447153 " " Order of pole (three term test) = 22.228510048047713 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999966 " " y[1] (analytic) = -0.7764791023160118 " " y[1] (numeric) = -0.7764791023160369 " " absolute error = 2.509104035652854000000000000000E-14 " " relative error = 3.2313864316102325000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4252183103142644 " " Order of pole (three term test) = 22.236961241309423 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999966 " " y[1] (analytic) = -0.7913905633527842 " " y[1] (numeric) = -0.7913905633528096 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 3.1985578466102530000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4303936939494332 " " Order of pole (three term test) = 22.24551764656746 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999657 " " y[1] (analytic) = -0.8063888846093823 " " y[1] (numeric) = -0.806388884609408 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 3.1941380471508485000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43539692584552875 " " Order of pole (three term test) = 22.25417584137383 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999999655 " " y[1] (analytic) = -0.8214735662578461 " " y[1] (numeric) = -0.8214735662578722 " " absolute error = 2.60902410786911800000000000000E-14 " " relative error = 3.176029290576334300000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44022600477650065 " " Order of pole (three term test) = 22.262932362566037 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999999653 " " y[1] (analytic) = -0.8366440998342477 " " y[1] (numeric) = -0.8366440998342741 " " absolute error = 2.642330798607872600000000000000E-14 " " relative error = 3.158249486408090700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.444878999175164 " " Order of pole (three term test) = 22.27178370765236 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.699999999999965 " " y[1] (analytic) = -0.8518999682895383 " " y[1] (numeric) = -0.8518999682895652 " " absolute error = 2.686739719592879000000000000000E-14 " " relative error = 3.153820659234638000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.44935404790579814 " " Order of pole (three term test) = 22.28072633621277 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.709999999999965 " " y[1] (analytic) = -0.8672406460412527 " " y[1] (numeric) = -0.8672406460412795 " " absolute error = 2.675637489346627000000000000000E-14 " " relative error = 3.0852307275498170000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4536493610085773 " " Order of pole (three term test) = 22.289756671315097 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999647 " " y[1] (analytic) = -0.882665599026065 " " y[1] (numeric) = -0.8826655990260927 " " absolute error = 2.764455331316640000000000000000E-14 " " relative error = 3.131939586596493000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45776322041553064 " " Order of pole (three term test) = 22.298871100945682 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999999645 " " y[1] (analytic) = -0.8981742847531993 " " y[1] (numeric) = -0.8981742847532268 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 3.0654998120180604000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4616939806377458 " " Order of pole (three term test) = 22.3080659794542 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999999642 " " y[1] (analytic) = -0.9137661523586718 " " y[1] (numeric) = -0.9137661523586998 " " absolute error = 2.80886425230164600000000000000E-14 " " relative error = 3.0739421076729810000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46544006942354377 " " Order of pole (three term test) = 22.317337629011863 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999964 " " y[1] (analytic) = -0.9294406426603827 " " y[1] (numeric) = -0.9294406426604112 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 3.0579370134978370000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.468999988387357 " " Order of pole (three term test) = 22.326682341082453 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999964 " " y[1] (analytic) = -0.9451971882140304 " " y[1] (numeric) = -0.9451971882140592 " " absolute error = 2.875477633779155400000000000000E-14 " " relative error = 3.042198675191184000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4723723136090652 " " Order of pole (three term test) = 22.33609637790574 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7699999999999636 " " y[1] (analytic) = -0.9610352133698568 " " y[1] (numeric) = -0.9610352133698857 " " absolute error = 2.897682094271658600000000000000E-14 " " relative error = 3.015167450639999500000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4755556962035432 " " Order of pole (three term test) = 22.345575973992503 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999999634 " " y[1] (analytic) = -0.9769541343302106 " " y[1] (numeric) = -0.9769541343302403 " " absolute error = 2.96429547574916800000000000000E-14 " " relative error = 3.0342217424377427000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4785488628601978 " " Order of pole (three term test) = 22.35511733763072 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.789999999999963 " " y[1] (analytic) = -0.9929533592079292 " " y[1] (numeric) = -0.992953359207959 " " absolute error = 2.98649993624167100000000000000E-14 " " relative error = 3.007694076007737000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4813506163522751 " " Order of pole (three term test) = 22.364716652402137 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.799999999999963 " " y[1] (analytic) = -1.0090322880855234 " " y[1] (numeric) = -1.0090322880855538 " " absolute error = 3.04201108747292900000000000000E-14 " " relative error = 3.014780719499726000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48395983601573395 " " Order of pole (three term test) = 22.374370078708836 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999627 " " y[1] (analytic) = -1.0251903130751718 " " y[1] (numeric) = -1.0251903130752023 " " absolute error = 3.04201108747292900000000000000E-14 " " relative error = 2.967264759211468000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4863754781974983 " " Order of pole (three term test) = 22.38407375530901 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999999625 " " y[1] (analytic) = -1.0414268183795063 " " y[1] (numeric) = -1.0414268183795374 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 2.984966791797774000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4885965766729035 " " Order of pole (three term test) = 22.393823800861398 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999999623 " " y[1] (analytic) = -1.0577411803531946 " " y[1] (numeric) = -1.0577411803532257 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 2.938927335619499000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4906222430321738 " " Order of pole (three term test) = 22.40361631547778 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999962 " " y[1] (analytic) = -1.0741327675653003 " " y[1] (numeric) = -1.0741327675653318 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 2.9354224032121434000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49245166703577403 " " Order of pole (three term test) = 22.413447382282875 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999962 " " y[1] (analytic) = -1.090600940862429 " " y[1] (numeric) = -1.0906009408624608 " " absolute error = 3.17523785042794770000000000000E-14 " " relative error = 2.911457098062855700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49408411693849436 " " Order of pole (three term test) = 22.42331306898103 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999617 " " y[1] (analytic) = -1.107145053432641 " " y[1] (numeric) = -1.1071450534326732 " " absolute error = 3.21964677141295400000000000000E-14 " " relative error = 2.908062282743007000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49551893978213973 " " Order of pole (three term test) = 22.433209429429116 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8699999999999615 " " y[1] (analytic) = -1.1237644508701328 " " y[1] (numeric) = -1.1237644508701654 " " absolute error = 3.2640556923979600000000000000E-14 " " relative error = 2.904572830961681000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4967555616567036 " " Order of pole (three term test) = 22.443132505214905 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999999613 " " y[1] (analytic) = -1.140458471240677 " " y[1] (numeric) = -1.1404584712407095 " " absolute error = 3.2640556923979600000000000000E-14 " " relative error = 2.8620557211934900000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4977934879299238 " " Order of pole (three term test) = 22.453078327240377 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.889999999999961 " " y[1] (analytic) = -1.1572264451478138 " " y[1] (numeric) = -1.1572264451478471 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 2.878148082288285000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4986323034451301 " " Order of pole (three term test) = 22.463042917309348 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.899999999999961 " " y[1] (analytic) = -1.1740676957997938 " " y[1] (numeric) = -1.1740676957998273 " " absolute error = 3.35287353436797300000000000000E-14 " " relative error = 2.8557753069629780000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4992716726873003 " " Order of pole (three term test) = 22.47302228971863 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999999606 " " y[1] (analytic) = -1.190981539077252 " " y[1] (numeric) = -1.190981539077286 " " absolute error = 3.39728245535297900000000000000E-14 " " relative error = 2.852506393999292300000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49971133991726263 " " Order of pole (three term test) = 22.48301245285234 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999999604 " " y[1] (analytic) = -1.2079672836016226 " " y[1] (numeric) = -1.2079672836016568 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 2.8307777555449093000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49995112927398716 " " Order of pole (three term test) = 22.493009410778406 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.92999999999996 " " y[1] (analytic) = -1.2250242308042743 " " y[1] (numeric) = -1.225024230804309 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 2.827614139972000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4999909448449281 " " Order of pole (three term test) = 22.503009164846954 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.93999999999996 " " y[1] (analytic) = -1.2421516749963675 " " y[1] (numeric) = -1.2421516749964026 " " absolute error = 3.508304757815494700000000000000E-14 " " relative error = 2.8243771098451030000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49983077070438814 " " Order of pole (three term test) = 22.51300771528968 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999598 " " y[1] (analytic) = -1.259348903439423 " " y[1] (numeric) = -1.2593489034394583 " " absolute error = 3.53050921830799800000000000000E-14 " " relative error = 2.8034401019969780000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4994706709198879 " " Order of pole (three term test) = 22.52300106281973 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9599999999999596 " " y[1] (analytic) = -1.2766151964165937 " " y[1] (numeric) = -1.2766151964166295 " " absolute error = 3.57491813929300400000000000000E-14 " " relative error = 2.8003098735841875000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4989107895265397 " " Order of pole (three term test) = 22.532985210231317 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9699999999999593 " " y[1] (analytic) = -1.2939498273046373 " " y[1] (numeric) = -1.2939498273046735 " " absolute error = 3.619327060278010300000000000000E-14 " " relative error = 2.797115455254746000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4981513504694364 " " Order of pole (three term test) = 22.54295616399863 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999959 " " y[1] (analytic) = -1.3113520626465776 " " y[1] (numeric) = -1.3113520626466137 " " absolute error = 3.619327060278010300000000000000E-14 " " relative error = 2.759996467290000700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49719265751407454 " " Order of pole (three term test) = 22.55290993587307 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.989999999999959 " " y[1] (analytic) = -1.328821162225048 " " y[1] (numeric) = -1.3288211622250847 " " absolute error = 3.663735981263016600000000000000E-14 " " relative error = 2.757132476072449000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4960350941248543 " " Order of pole (three term test) = 22.56284254447862 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999587 " " y[1] (analytic) = -1.3463563791363158 " " y[1] (numeric) = -1.3463563791363526 " " absolute error = 3.6859404417555197000000000000E-14 " " relative error = 2.737715287626922300000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49467912331169683 " " Order of pole (three term test) = 22.572750016904266 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999959 " " y[1] (analytic) = -1.3639569598649688 " " y[1] (numeric) = -1.3639569598650056 " " absolute error = 3.6859404417555197000000000000E-14 " " relative error = 2.702387648742543000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4931252874448486 " " Order of pole (three term test) = 22.582628390293145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999959 " " y[1] (analytic) = -1.3816221443592678 " " y[1] (numeric) = -1.3816221443593049 " " absolute error = 3.70814490224802300000000000000E-14 " " relative error = 2.6839066798308220000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.49137420803793863 " " Order of pole (three term test) = 22.592473713427594 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999999585 " " y[1] (analytic) = -1.399351166107151 " " y[1] (numeric) = -1.3993511661071882 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 2.6657707179520695000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48942658549938217 " " Order of pole (three term test) = 22.60228204830964 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999958 " " y[1] (analytic) = -1.4171432522128842 " " y[1] (numeric) = -1.417143252212922 " " absolute error = 3.77475828372553200000000000000E-14 " " relative error = 2.663639175384145000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.487283198852227 " " Order of pole (three term test) = 22.612049471736114 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999958 " " y[1] (analytic) = -1.4349976234743504 " " y[1] (numeric) = -1.4349976234743889 " " absolute error = 3.841371665203041600000000000000E-14 " " relative error = 2.676918485692324000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4849449054225534 " " Order of pole (three term test) = 22.621772076867856 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999958 " " y[1] (analytic) = -1.4529134944609696 " " y[1] (numeric) = -1.452913494461008 " " absolute error = 3.841371665203041600000000000000E-14 " " relative error = 2.6439094136352480000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.48241264049655663 " " Order of pole (three term test) = 22.63144597479246 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999958 " " y[1] (analytic) = -1.4708900735922388 " " y[1] (numeric) = -1.4708900735922774 " " absolute error = 3.86357612569554500000000000000E-14 " " relative error = 2.6266926366970694000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4796874169464442 " " Order of pole (three term test) = 22.64106729607974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999957 " " y[1] (analytic) = -1.4889265632168915 " " y[1] (numeric) = -1.4889265632169308 " " absolute error = 3.93018950717305400000000000000E-14 " " relative error = 2.6396127278982157000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4767703248253001 " " Order of pole (three term test) = 22.650632192329454 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999957 " " y[1] (analytic) = -1.5070221596926636 " " y[1] (numeric) = -1.5070221596927031 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 2.6226515265519340000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4736625309310787 " " Order of pole (three term test) = 22.660136837710642 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999957 " " y[1] (analytic) = -1.525176053466653 " " y[1] (numeric) = -1.525176053466693 " " absolute error = 3.996802888650563500000000000000E-14 " " relative error = 2.6205518238802794000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.47036527833990116 " " Order of pole (three term test) = 22.669577430491877 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999957 " " y[1] (analytic) = -1.5433874291562772 " " y[1] (numeric) = -1.5433874291563177 " " absolute error = 4.0412118096355700000000000000E-14 " " relative error = 2.6184039945464480000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46687988590884094 " " Order of pole (three term test) = 22.67895019456191 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999957 " " y[1] (analytic) = -1.5616554656308104 " " y[1] (numeric) = -1.5616554656308512 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 2.6162113350464555000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.46320774774839946 " " Order of pole (three term test) = 22.688251380940102 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999956 " " y[1] (analytic) = -1.579979336093495 " " y[1] (numeric) = -1.5799793360935361 " " absolute error = 4.10782519111307900000000000000E-14 " " relative error = 2.5999233643584810000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45935033266487957 " " Order of pole (three term test) = 22.697477269275897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999956 " " y[1] (analytic) = -1.5983582081642211 " " y[1] (numeric) = -1.5983582081642627 " " absolute error = 4.152234112098085500000000000000E-14 " " relative error = 2.5978119866303900000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.45530918357288336 " " Order of pole (three term test) = 22.70662416933698 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999956 " " y[1] (analytic) = -1.6167912439627639 " " y[1] (numeric) = -1.616791243962806 " " absolute error = 4.21884749357559500000000000000E-14 " " relative error = 2.6093953126782016000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4510859168781657 " " Order of pole (three term test) = 22.715688422485268 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999956 " " y[1] (analytic) = -1.6352776001925715 " " y[1] (numeric) = -1.6352776001926141 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 2.6070536366782965000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4466822218310959 " " Order of pole (three term test) = 22.724666403140382 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.1699999999999555 " " y[1] (analytic) = -1.6538164282250927 " " y[1] (numeric) = -1.6538164282251357 " " absolute error = 4.307665335545607400000000000000E-14 " " relative error = 2.6046816696389186000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4420998598509774 " " Order of pole (three term test) = 22.733554520229745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999955 " " y[1] (analytic) = -1.6724068741846398 " " y[1] (numeric) = -1.6724068741846831 " " absolute error = 4.329869796038110500000000000000E-14 " " relative error = 2.5890050219681630000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.43734066382150427 " " Order of pole (three term test) = 22.742349218625037 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999955 " " y[1] (analytic) = -1.6910480790337754 " " y[1] (numeric) = -1.6910480790338194 " " absolute error = 4.3964831775156200000000000000E-14 " " relative error = 2.5998569952119077000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4324065373576337 " " Order of pole (three term test) = 22.75104698056416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999955 " " y[1] (analytic) = -1.7097391786592162 " " y[1] (numeric) = -1.7097391786592602 " " absolute error = 4.3964831775156200000000000000E-14 " " relative error = 2.5714350073929740000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4272994540441637 " " Order of pole (three term test) = 22.7596443270583 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999955 " " y[1] (analytic) = -1.7284793039582413 " " y[1] (numeric) = -1.7284793039582858 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 2.5692480600322626000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4220214566463265 " " Order of pole (three term test) = 22.76813781928351 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.2199999999999545 " " y[1] (analytic) = -1.7472675809256044 " " y[1] (numeric) = -1.7472675809256497 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 2.592453491337058400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.4165746562927081 " " Order of pole (three term test) = 22.776524059956113 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999954 " " y[1] (analytic) = -1.766103130740933 " " y[1] (numeric) = -1.7661031307409787 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 2.5899500328367940000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.41096123163082754 " " Order of pole (three term test) = 22.784799694691678 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999954 " " y[1] (analytic) = -1.7849850698566083 " " y[1] (numeric) = -1.784985069856654 " " absolute error = 4.57411886145564500000000000000E-14 " " relative error = 2.562553008817656000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.40518342795570444 " " Order of pole (three term test) = 22.79296141334665 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999954 " " y[1] (analytic) = -1.8039125100861195 " " y[1] (numeric) = -1.803912510086166 " " absolute error = 4.640732242933154300000000000000E-14 " " relative error = 2.5725927488088673000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3992435563117728 " " Order of pole (three term test) = 22.801005951342372 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999954 " " y[1] (analytic) = -1.8228845586928841 " " y[1] (numeric) = -1.822884558692931 " " absolute error = 4.685141163918160600000000000000E-14 " " relative error = 2.5701798512560130000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.39314399256849303 " " Order of pole (three term test) = 22.80893009097092 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999953 " " y[1] (analytic) = -1.8419003184795177 " " y[1] (numeric) = -1.841900318479565 " " absolute error = 4.72955008490316700000000000000E-14 " " relative error = 2.5677557235059245000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38688717647003606 " " Order of pole (three term test) = 22.8167306626821 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999953 " " y[1] (analytic) = -1.8609588878775547 " " y[1] (numeric) = -1.8609588878776024 " " absolute error = 4.77395900588817300000000000000E-14 " " relative error = 2.5653221234419255000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.38047561065941765 " " Order of pole (three term test) = 22.824404546351225 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999953 " " y[1] (analytic) = -1.8800593610376044 " " y[1] (numeric) = -1.8800593610376524 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 2.5510702298961846000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.37391185967747603 " " Order of pole (three term test) = 22.831948672527144 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999953 " " y[1] (analytic) = -1.899200827919934 " " y[1] (numeric) = -1.8992008279199826 " " absolute error = 4.862776847858185600000000000000E-14 " " relative error = 2.5604331971485370000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36719854893708864 " " Order of pole (three term test) = 22.839360023659975 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3099999999999525 " " y[1] (analytic) = -1.9183823743854735 " " y[1] (numeric) = -1.9183823743855226 " " absolute error = 4.90718576884319200000000000000E-14 " " relative error = 2.557981054436626000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.36033836367304156 " " Order of pole (three term test) = 22.84663563530808 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999952 " " y[1] (analytic) = -1.9376030822872279 " " y[1] (numeric) = -1.9376030822872772 " " absolute error = 4.92939022933569500000000000000E-14 " " relative error = 2.5440660548066620000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3533340478679729 " " Order of pole (three term test) = 22.853772597323815 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999952 " " y[1] (analytic) = -1.9568620295620902 " " y[1] (numeric) = -1.95686202956214 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 2.5417219380733480000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.34618840315481464 " " Order of pole (three term test) = 22.860768055017513 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999952 " " y[1] (analytic) = -1.976158290323049 " " y[1] (numeric) = -1.9761582903230992 " " absolute error = 5.018208071305708000000000000000E-14 " " relative error = 2.539375563121193400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3389042876961786 " " Order of pole (three term test) = 22.867619210299384 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999952 " " y[1] (analytic) = -1.9954909349517749 " " y[1] (numeric) = -1.9954909349518257 " " absolute error = 5.08482145278321700000000000000E-14 " " relative error = 2.5481556261272126000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3314846150411275 " " Order of pole (three term test) = 22.874323322798666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3599999999999515 " " y[1] (analytic) = -2.0148590301915825 " " y[1] (numeric) = -2.0148590301916336 " " absolute error = 5.1070259132757200000000000000E-14 " " relative error = 2.53468150215458000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.32393235295979605 " " Order of pole (three term test) = 22.88087771095974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999951 " " y[1] (analytic) = -2.0342616392407544 " " y[1] (numeric) = -2.034261639240806 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 2.5323364187231057000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.31625052225632116 " " Order of pole (three term test) = 22.887279753114726 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999951 " " y[1] (analytic) = -2.0536978218462214 " " y[1] (numeric) = -2.0536978218462734 " " absolute error = 5.195843755245733000000000000000E-14 " " relative error = 2.5299942863915603000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.3084421955605607 " " Order of pole (three term test) = 22.89352688853213 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999950 " " y[1] (analytic) = -2.073166634397586 " " y[1] (numeric) = -2.0731666343976385 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 2.5276562864197520000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.30051049609908437 " " Order of pole (three term test) = 22.899616618441087 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999950 " " y[1] (analytic) = -2.092667130021484 " " y[1] (numeric) = -2.0926671300215367 " " absolute error = 5.28466159721574500000000000000E-14 " " relative error = 2.52532355547702040000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2924585964459211 " " Order of pole (three term test) = 22.9055465070308 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.40999999999995 " " y[1] (analytic) = -2.11219835867627 " " y[1] (numeric) = -2.112198358676323 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 2.522997187414026000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2842897172535757 " " Order of pole (three term test) = 22.911314182424924 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999995 " " y[1] (analytic) = -2.131759367247021 " " y[1] (numeric) = -2.1317593672470747 " " absolute error = 5.373479439185758000000000000000E-14 " " relative error = 2.5206782349572276000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27600712596480786 " " Order of pole (three term test) = 22.91691733763019 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.42999999999995 " " y[1] (analytic) = -2.1513491996408476 " " y[1] (numeric) = -2.1513491996409018 " " absolute error = 5.41788836017076400000000000000E-14 " " relative error = 2.518367711329821400000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2676141355056999 " " Order of pole (three term test) = 22.922353731459232 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.43999999999995 " " y[1] (analytic) = -2.170966896882502 " " y[1] (numeric) = -2.1709668968825566 " " absolute error = 5.4622972811557700000000000000E-14 " " relative error = 2.51606659180275970000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2591141029605311 " " Order of pole (three term test) = 22.927621189426997 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4499999999999496 " " y[1] (analytic) = -2.1906114972102744 " " y[1] (numeric) = -2.1906114972103294 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 2.513775815179241600000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.250510428228986 " " Order of pole (three term test) = 22.932717604620525 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999950 " " y[1] (analytic) = -2.2102820361721696 " " y[1] (numeric) = -2.210282036172225 " " absolute error = 5.55111512312578300000000000000E-14 " " relative error = 2.5114962852158740000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24180655266624426 " " Order of pole (three term test) = 22.93764093854171 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999950 " " y[1] (analytic) = -2.22997754672235 " " y[1] (numeric) = -2.229977546722406 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 2.5092288719835604000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23300595770648033 " " Order of pole (three term test) = 22.942389221922603 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999949 " " y[1] (analytic) = -2.2496970593178403 " " y[1] (numeric) = -2.249697059317896 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 2.4872344571617477000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2241121634703385 " " Order of pole (three term test) = 22.946960555513172 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999949 " " y[1] (analytic) = -2.26943960201548 " " y[1] (numeric) = -2.2694396020155363 " " absolute error = 5.63993296509579500000000000000E-14 " " relative error = 2.4851654831822773000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21512872735693092 " " Order of pole (three term test) = 22.951353110840927 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999999485 " " y[1] (analytic) = -2.2892042005691184 " " y[1] (numeric) = -2.2892042005691753 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 2.4831082717162667000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20605924262092526 " " Order of pole (three term test) = 22.955565130942315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999948 " " y[1] (analytic) = -2.3089898785270373 " " y[1] (numeric) = -2.3089898785270946 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 2.4810636288801416000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19690733693529117 " " Order of pole (three term test) = 22.95959493106544 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999948 " " y[1] (analytic) = -2.328795657329596 " " y[1] (numeric) = -2.3287956573296533 " " absolute error = 5.72875080706580800000000000000E-14 " " relative error = 2.4599628520584338000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18767667094027926 " " Order of pole (three term test) = 22.963440899344 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999948 " " y[1] (analytic) = -2.348620556407085 " " y[1] (numeric) = -2.348620556407143 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 2.4770151283762606000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1783709367792133 " " Order of pole (three term test) = 22.967101497441945 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999948 " " y[1] (analytic) = -2.3684635932777844 " " y[1] (numeric) = -2.3684635932778426 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 2.4562626445039504000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16899385662168323 " " Order of pole (three term test) = 22.97057526116885 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999947 " " y[1] (analytic) = -2.388323783646209 " " y[1] (numeric) = -2.388323783646268 " " absolute error = 5.90638649100583300000000000000E-14 " " relative error = 2.4730258650226494000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15954918117472566 " " Order of pole (three term test) = 22.973860801065538 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999947 " " y[1] (analytic) = -2.4082001415015397 " " y[1] (numeric) = -2.4082001415015992 " " absolute error = 5.95079541199083900000000000000E-14 " " relative error = 2.4710551708050527000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15004068818259247 " " Order of pole (three term test) = 22.97695680295986 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999947 " " y[1] (analytic) = -2.428091679216221 " " y[1] (numeric) = -2.4280916792162808 " " absolute error = 5.99520433297584500000000000000E-14 " " relative error = 2.4691013046554633000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14047218091570202 " " Order of pole (three term test) = 22.97986202849234 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999947 " " y[1] (analytic) = -2.4479974076447237 " " y[1] (numeric) = -2.447997407644784 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 2.4671648895950862000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13084748664938273 " " Order of pole (three term test) = 22.982575315611502 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999947 " " y[1] (analytic) = -2.4679163362224603 " " y[1] (numeric) = -2.467916336222521 " " absolute error = 6.08402217494585800000000000000E-14 " " relative error = 2.465246526249112700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1211704551330136 " " Order of pole (three term test) = 22.985095579038664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999946 " " y[1] (analytic) = -2.4878474730648383 " " y[1] (numeric) = -2.4878474730649 " " absolute error = 6.1728400169158700000000000000E-14 " " relative error = 2.4811971327612792000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11144495705017576 " " Order of pole (three term test) = 22.987421810702063 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999946 " " y[1] (analytic) = -2.50778982506645 " " y[1] (numeric) = -2.5077898250665123 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 2.479174640457014700000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10167488247043083 " " Order of pole (three term test) = 22.989553080140066 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999946 " " y[1] (analytic) = -2.52774239800038 " " y[1] (numeric) = -2.5277423980004428 " " absolute error = 6.26165785888588300000000000000E-14 " " relative error = 2.4771740442535956000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.18641392933447400E-2 " " Order of pole (three term test) = 22.99148853487329 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999946 " " y[1] (analytic) = -2.5477041966176293 " " y[1] (numeric) = -2.5477041966176923 " " absolute error = 6.30606677987088900000000000000E-14 " " relative error = 2.47519582070906020000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.2016651685380200E-2 " " Order of pole (three term test) = 22.99322740074566 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.6399999999999455 " " y[1] (analytic) = -2.567674224746637 " " y[1] (numeric) = -2.5676742247467006 " " absolute error = 6.35047570085589500000000000000E-14 " " relative error = 2.473240428887556200000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.21363585102822600E-2 " " Order of pole (three term test) = 22.99476898223401 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999945 " " y[1] (analytic) = -2.5876514853928985 " " y[1] (numeric) = -2.587651485392963 " " absolute error = 6.43929354282590800000000000000E-14 " " relative error = 2.488470174277813100000000000E-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 = 6.222721175358543000E-2 " " Order of pole (three term test) = 22.996112662726294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999945 " " y[1] (analytic) = -2.607634980838664 " " y[1] (numeric) = -2.607634980838729 " " absolute error = 6.48370246381091400000000000000E-14 " " relative error = 2.48643023715138020000000000E-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 = 5.22931749418723400E-2 " " Order of pole (three term test) = 22.997257904768233 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999945 " " y[1] (analytic) = -2.6276237127427082 " " y[1] (numeric) = -2.6276237127427735 " " absolute error = 6.5281113847959200000000000000E-14 " " relative error = 2.4844163771006206000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.233822155741559500E-2 " " Order of pole (three term test) = 22.998204250278288 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999945 " " y[1] (analytic) = -2.647616682240165 " " y[1] (numeric) = -2.6476166822402303 " " absolute error = 6.5281113847959200000000000000E-14 " " relative error = 2.4656557834015627000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.23663334488378860E-2 " " Order of pole (three term test) = 22.99895132073087 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999944 " " y[1] (analytic) = -2.6676128900424114 " " y[1] (numeric) = -2.667612890042477 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 2.4638208678308013000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.238149923842604200E-2 " " Order of pole (three term test) = 22.999498817307742 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999944 " " y[1] (analytic) = -2.687611336536998 " " y[1] (numeric) = -2.687611336537064 " " absolute error = 6.61692922676593300000000000000E-14 " " relative error = 2.462011205568095000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.23877127267348200E-2 " " Order of pole (three term test) = 22.999846521017606 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999944 " " y[1] (analytic) = -2.7076110218876064 " " y[1] (numeric) = -2.707611021887673 " " absolute error = 6.66133814775093900000000000000E-14 " " relative error = 2.4602271500235653000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.3889712951202105000E-3 " " Order of pole (three term test) = 22.999994292783576 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999944 " " y[1] (analytic) = -2.7276109461340354 " " y[1] (numeric) = -2.7276109461341025 " " absolute error = 6.70574706873594600000000000000E-14 " " relative error = 2.4584690416499097000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.610725693159915000E-3 " " Order of pole (three term test) = 22.999942073498936 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999944 " " y[1] (analytic) = -2.747610109292194 " " y[1] (numeric) = -2.7476101092922613 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 2.4567372084170436000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.760737849263779600E-2 " " Order of pole (three term test) = 22.999689884050717 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999943 " " y[1] (analytic) = -2.767607511454098 " " y[1] (numeric) = -2.767607511454166 " " absolute error = 6.79456491070595800000000000000E-14 " " relative error = 2.4550319662689815000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.759698857548050000E-2 " " Order of pole (three term test) = 22.999237825311315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999943 " " y[1] (analytic) = -2.787602152887863 " " y[1] (numeric) = -2.7876021528879313 " " absolute error = 6.83897383169096400000000000000E-14 " " relative error = 2.4533536195636865000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.757556023084797000E-2 " " Order of pole (three term test) = 22.998586078098196 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999943 " " y[1] (analytic) = -2.807593034137674 " " y[1] (numeric) = -2.8075930341377426 " " absolute error = 6.8833827526759700000000000000E-14 " " relative error = 2.451702461496574000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.753910216312385300E-2 " " Order of pole (three term test) = 22.99773490310156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999943 " " y[1] (analytic) = -2.827579156123732 " " y[1] (numeric) = -2.827579156123801 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 2.4500787745083463000000000000E-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 = 5.74836290883807900E-2 " " Order of pole (three term test) = 22.996684640780064 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.7799999999999425 " " y[1] (analytic) = -2.84755952024216 " " y[1] (numeric) = -2.8475595202422297 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 2.448482830677779200000000000E-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 = 6.74051633284405400E-2 " " Order of pole (three term test) = 22.99543571122464 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999942 " " y[1] (analytic) = -2.8675331284648635 " " y[1] (numeric) = -2.8675331284649332 " " absolute error = 6.97220059464598300000000000000E-14 " " relative error = 2.4314280889855167000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.72997364018924700E-2 " " Order of pole (three term test) = 22.993988613990442 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999942 " " y[1] (analytic) = -2.8874989834393308 " " y[1] (numeric) = -2.8874989834394014 " " absolute error = 7.06101843661599600000000000000E-14 " " relative error = 2.4453752112513444000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.71633906114329200E-2 " " Order of pole (three term test) = 22.992343927897075 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999942 " " y[1] (analytic) = -2.9074560885883702 " " y[1] (numeric) = -2.907456088588441 " " absolute error = 7.06101843661599600000000000000E-14 " " relative error = 2.4285898811439197000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.69921806268919600E-2 " " Order of pole (three term test) = 22.99050231079704 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999942 " " y[1] (analytic) = -2.9274034482097635 " " y[1] (numeric) = -2.9274034482098346 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 2.4272115146773787000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10678217506331215 " " Order of pole (three term test) = 22.98846449931264 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.8299999999999415 " " y[1] (analytic) = -2.9473400675758388 " " y[1] (numeric) = -2.94734006757591 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 2.410793187989723200000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11652945805345027 " " Order of pole (three term test) = 22.986231308541285 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999941 " " y[1] (analytic) = -2.9672649530329394 " " y[1] (numeric) = -2.967264953033011 " " absolute error = 7.14983627858600800000000000000E-14 " " relative error = 2.4095712353822413000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12623013081407236 " " Order of pole (three term test) = 22.98380363172951 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999941 " " y[1] (analytic) = -2.98717711210079 " " y[1] (numeric) = -2.9871771121008623 " " absolute error = 7.23865412055602100000000000000E-14 " " relative error = 2.4232423619051155000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13588031320541483 " " Order of pole (three term test) = 22.98118243991567 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999940 " " y[1] (analytic) = -3.0070755535717453 " " y[1] (numeric) = -3.0070755535718177 " " absolute error = 7.23865412055602100000000000000E-14 " " relative error = 2.407207265530156000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14547614528318847 " " Order of pole (three term test) = 22.978368781541544 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999940 " " y[1] (analytic) = -3.0269592876099054 " " y[1] (numeric) = -3.0269592876099782 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 2.406065741073033000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15501378884250486 " " Order of pole (three term test) = 22.97536378203297 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.87999999999994 " " y[1] (analytic) = -3.0468273258501033 " " y[1] (numeric) = -3.046827325850177 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 2.419526968583358000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16448942895310736 " " Order of pole (three term test) = 22.972168643349683 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.88999999999994 " " y[1] (analytic) = -3.0666786814967386 " " y[1] (numeric) = -3.0666786814968128 " " absolute error = 7.41628980449604600000000000000E-14 " " relative error = 2.41834589624381980000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17389927548529177 " " Order of pole (three term test) = 22.968784643504545 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999994 " " y[1] (analytic) = -3.086512369422456 " " y[1] (numeric) = -3.0865123694225307 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 2.4171938526451095000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18323956462590796 " " Order of pole (three term test) = 22.965213136052398 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90999999999994 " " y[1] (analytic) = -3.106327406266658 " " y[1] (numeric) = -3.106327406266733 " " absolute error = 7.50510764646605800000000000000E-14 " " relative error = 2.416071026938553800000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19250656038383562 " " Order of pole (three term test) = 22.961455549548585 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9199999999999395 " " y[1] (analytic) = -3.126122810533839 " " y[1] (numeric) = -3.1261228105339143 " " absolute error = 7.54951656745106400000000000000E-14 " " relative error = 2.4149776016515026000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2016965560843294 " " Order of pole (three term test) = 22.957513386977606 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999940 " " y[1] (analytic) = -3.1458976026917345 " " y[1] (numeric) = -3.1458976026918104 " " absolute error = 7.59392548843607100000000000000E-14 " " relative error = 2.4139137529264953000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21080587585164134 " " Order of pole (three term test) = 22.95338822515193 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999939 " " y[1] (analytic) = -3.165650805269275 " " y[1] (numeric) = -3.1656508052693515 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 2.4128796507520506000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21983087607932 " " Order of pole (three term test) = 22.949081714081302 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999939 " " y[1] (analytic) = -3.1853814429543306 " " y[1] (numeric) = -3.1853814429544074 " " absolute error = 7.68274333040608300000000000000E-14 " " relative error = 2.4118754591853858000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22876794688760604 " " Order of pole (three term test) = 22.944595576312707 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999939 " " y[1] (analytic) = -3.205088542691241 " " y[1] (numeric) = -3.2050885426913185 " " absolute error = 7.7271522513910900000000000000E-14 " " relative error = 2.4109013365673737000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2376135135673361 " " Order of pole (three term test) = 22.93993160624145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999385 " " y[1] (analytic) = -3.2247711337781224 " " y[1] (numeric) = -3.2247711337782 " " absolute error = 7.77156117237609600000000000000E-14 " " relative error = 2.4099574357300146000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24636403800977658 " " Order of pole (three term test) = 22.935091669393373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999938 " " y[1] (analytic) = -3.244428247963934 " " y[1] (numeric) = -3.2444282479640125 " " absolute error = 7.86037901434610800000000000000E-14 " " relative error = 2.4227316536523655000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2550160201218238 " " Order of pole (three term test) = 22.930077701678695 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999938 " " y[1] (analytic) = -3.2640589195453056 " " y[1] (numeric) = -3.2640589195453846 " " absolute error = 7.90478793533111500000000000000E-14 " " relative error = 2.42176631310083000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2635659992259904 " " Order of pole (three term test) = 22.924891708617626 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999938 " " y[1] (analytic) = -3.2836621854631045 " " y[1] (numeric) = -3.283662185463184 " " absolute error = 7.94919685631612100000000000000E-14 " " relative error = 2.4208327188794002000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.27201055544463265 " " Order of pole (three term test) = 22.91953576453826 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = sin ( x ) - 1 , 0 ; " Iterations = 491 "Total Elapsed Time "= 15 Seconds "Elapsed Time(since restart) "= 14 Seconds "Time to Timeout "= 9 Minutes 44 Seconds Percent Done = 100.40816326530484 "%" (%o224) true (%o224) diffeq.max