(%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_g,MAX_TERMS) (%o163) array_tmp2_g (%i164) array(array_tmp2,MAX_TERMS) (%o164) array_tmp2 (%i165) array(array_tmp3,MAX_TERMS) (%o165) array_tmp3 (%i166) array(array_tmp4,MAX_TERMS) (%o166) array_tmp4 (%i167) array(array_m1,MAX_TERMS) (%o167) array_m1 (%i168) array(array_y_higher,2,MAX_TERMS) (%o168) array_y_higher (%i169) array(array_y_higher_work,2,MAX_TERMS) (%o169) array_y_higher_work (%i170) array(array_y_higher_work2,2,MAX_TERMS) (%o170) array_y_higher_work2 (%i171) array(array_y_set_initial,2,MAX_TERMS) (%o171) array_y_set_initial (%i172) array(array_given_rad_poles,2,3) (%o172) array_given_rad_poles (%i173) array(array_given_ord_poles,2,3) (%o173) array_given_ord_poles (%i174) array(array_rad_test_poles,2,3) (%o174) array_rad_test_poles (%i175) array(array_ord_test_poles,2,3) (%o175) array_ord_test_poles (%i176) array(array_fact_2,MAX_TERMS,MAX_TERMS) (%o176) array_fact_2 (%i177) omniout_str(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a~%",string(str)) (%o177) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i178) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel then printf(true,"~a",string(str)) (%o178) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i179) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel then printf(true,"~a = ~a~%",string(label), string(str)) (%o179) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i180) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (if vallen = 4 then printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel) else printf(true,"~a = ~g ~s ~%",prelabel, value,postlabel)) (%o180) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i181) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if glob_iolevel >= iolevel then (printf(true,"~a = ~d ~a~%",prelabel,value, postlabel),newline()) (%o181) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i182) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen, postlabel):=if glob_iolevel >= iolevel then (sprint(prelabel,"[",elemnt,"]=",value, postlabel),newline()) (%o182) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i183) logitem_time(fd,secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp],convfloat]), secs:secs_in,printf(fd,"~%"), if secs >= 0 then (years_int :truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int :truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp, truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp, truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(fd,"~d Seconds~%", sec_int)) else printf(fd," 0.0 Seconds~%"), printf(fd,"~%")),0) (%o183) logitem_time(fd, secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs : secs_in, printf(fd, "~%"), secs if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if truncate(years_int) > 0.1 then printf(fd, "~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(fd, "~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(fd, "~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "~d Seconds~%", sec_int)) else printf(fd, " 0.0 Seconds~%"), printf(fd, "~%")), 0) (%i184) omniout_timestr(secs_in):=( block(mode_declare( [[days_int,hours_int,minutes_int,sec_int, years_int],fixnum,[secs,secs_temp], convfloat]),secs:secs_in, if secs >= 0 then ( years_int:truncate(secs/glob_sec_in_year), sec_temp :mod(truncate(secs), truncate(glob_sec_in_year)), days_int:truncate(sec_temp/glob_sec_in_day), sec_temp :mod(sec_temp,truncate(glob_sec_in_day)), hours_int :truncate(sec_temp/glob_sec_in_hour), sec_temp :mod(sec_temp,truncate(glob_sec_in_hour)), minutes_int :truncate(sec_temp/glob_sec_in_minute), sec_int :mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int,days_int, hours_int,minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,hours_int, minutes_int,sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int,sec_int) else printf(true,"= ~d Seconds~%", sec_int)) else printf(true,"= 0.0 Seconds~%")),0) (%o184) omniout_timestr(secs_in) := (block(mode_declare([[days_int, hours_int, minutes_int, sec_int, years_int], fixnum, [secs, secs_temp], convfloat]), secs secs : secs_in, if secs >= 0 then (years_int : truncate(----------------), glob_sec_in_year sec_temp : mod(truncate(secs), truncate(glob_sec_in_year)), sec_temp days_int : truncate(---------------), sec_temp : glob_sec_in_day mod(sec_temp, truncate(glob_sec_in_day)), sec_temp hours_int : truncate(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, truncate(glob_sec_in_hour)), sec_temp minutes_int : truncate(------------------), glob_sec_in_minute sec_int : mod(sec_temp, truncate(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0.1 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0.1 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0.1 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, "= 0.0 Seconds~%")), 0) (%i185) zero_ats_ar(arr_a):=( block(modedcclare([iii],fixnum),iii:1, while iii <= MAX_TERMS do (arr_a[iii]:0.0,iii:1+iii)),0) (%o185) zero_ats_ar(arr_a) := (block(modedcclare([iii], fixnum), iii : 1, while iii <= MAX_TERMS do (arr_a : 0.0, iii : 1 + iii)), 0) iii (%i186) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block( mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats], convfloat]),ret_ats:0.0, if jjj_ats <= mmm_ats then (ma_ats:1+mmm_ats,iii_ats:jjj_ats, while iii_ats <= mmm_ats do (lll_ats:ma_ats-iii_ats, if lll_ats <= MAX_TERMS and iii_ats <= MAX_TERMS then ret_ats :arr_a[iii_ats]*arr_b[lll_ats]+ret_ats, iii_ats:1+iii_ats)),ret_ats) (%o186) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block(mode_declare([[iii_ats, lll_ats, ma_ats], fixnum, [ret_ats], convfloat]), ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, if (lll_ats <= MAX_TERMS) and (iii_ats <= MAX_TERMS) then ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i187) att(mmm_att,arr_aa,arr_bb,jjj_att):=block( mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att], fixnum]),ret_att:0.0, if jjj_att < mmm_att then (ma_att:2+mmm_att,iii_att:jjj_att, while iii_att < mmm_att and iii_att <= MAX_TERMS do (lll_att:ma_att-iii_att,al_att:lll_att-1, if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS then ret_att :arr_aa[iii_att]*arr_bb[lll_att]*al_att +ret_att,iii_att:1+iii_att), ret_att:ret_att/mmm_att),ret_att) (%o187) att(mmm_att, arr_aa, arr_bb, jjj_att) := block(mode_declare([[al_att, iii_att, lll_att, ma_att], convfloat, [ret_att], fixnum]), ret_att : 0.0, if jjj_att < mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while (iii_att < mmm_att) and (iii_att <= MAX_TERMS) do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if (lll_att <= MAX_TERMS) and (iii_att <= MAX_TERMS) then ret_att : arr_aa arr_bb al_att + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : -------), ret_att) mmm_att (%i188) logditto(file):=(printf(file,""),printf(file,"ditto"), printf(file,""),0) (%o188) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, ""), 0) (%i189) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n), printf(file,""),0) (%o189) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, ""), 0) (%i190) logitem_str(file,str):=(printf(file,""),printf(file,str), printf(file,""),0) (%o190) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, ""), 0) (%i191) logitem_good_digits(file,rel_error):=( block(mode_declare([[good_digits],fixnum]), printf(file,""), if rel_error # -1.0 then (if rel_error > +1.0E-34 then ( good_digits :3-floor(log10(rel_error)), printf(file,"~d",good_digits)) else (good_digits:16, printf(file,"~d", good_digits))) else printf(file,"Unknown"), printf(file,"")),0) (%o191) logitem_good_digits(file, rel_error) := (block(mode_declare([[good_digits], fixnum]), printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 3 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")), 0) (%i192) log_revs(file,revs):=printf(file,revs) (%o192) log_revs(file, revs) := printf(file, revs) (%i193) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x), printf(file,""),0) (%o193) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, ""), 0) (%i194) logitem_pole(file,pole):=(printf(file,""), if pole = 0 then printf(file,"NA") elseif pole = 1 then printf(file,"Real") elseif pole = 2 then printf(file,"Complex") elseif pole = 4 then printf(file,"Yes") else printf(file,"No"), printf(file,""),0) (%o194) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, ""), 0) (%i195) logstart(file):=(printf(file,""),0) (%o195) logstart(file) := (printf(file, ""), 0) (%i196) logend(file):=(printf(file,"~%"),0) (%o196) logend(file) := (printf(file, "~%"), 0) (%i197) chk_data():=( block(mode_declare([[errflag],boolean]),errflag:false, if glob_max_iter < 2 then (omniout_str(ALWAYS,"Illegal max_iter"), errflag:true),if errflag then quit()),0) (%o197) chk_data() := (block(mode_declare([[errflag], boolean]), errflag : false, if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()), 0) (%i198) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block( mode_declare([[ms2,rrr,sec_left,sub1,sub2], convfloat]),ms2:clock_sec2, sub1:t_end2-t_start2,sub2:t2-t_start2, if sub1 = 0.0 then sec_left:0.0 else (if sub2 > 0.0 then (rrr:sub1/sub2, sec_left:rrr*ms2-ms2) else sec_left:0.0),sec_left) (%o198) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block(mode_declare([[ms2, rrr, sec_left, sub1, sub2], convfloat]), ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i199) comp_percent(t_end2,t_start2,t2):=block( mode_declare([[rrr,sub1,sub2],convfloat]), sub1:t_end2-t_start2,sub2:t2-t_start2, if sub2 > glob_small_float then rrr:100.0*sub2/sub1 else rrr:0.0,rrr) (%o199) comp_percent(t_end2, t_start2, t2) := block(mode_declare([[rrr, sub1, sub2], convfloat]), sub1 : t_end2 - t_start2, 100.0 sub2 sub2 : t2 - t_start2, if sub2 > glob_small_float then rrr : ---------- sub1 else rrr : 0.0, rrr) (%i200) comp_rad_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret:abs(term1*glob_h/term2) else ret:glob_larger_float,ret) (%o200) comp_rad_from_ratio(term1, term2, last_no) := !term1 glob_h! (if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret) ! term2 ! (%i201) comp_ord_from_ratio(term1,term2,last_no):=( if term2 > 0.0 then ret :abs(term2)*convfloat(last_no) *log(abs(term1*glob_h/term2)) /log(convfloat(last_no)) +1.0 else ret:glob_larger_float,ret) (%o201) comp_ord_from_ratio(term1, term2, last_no) := !term1 glob_h! mabs(term2) convfloat(last_no) log(!------------!) ! term2 ! (if term2 > 0.0 then ret : -------------------------------------------------- log(convfloat(last_no)) + 1.0 else ret : glob_larger_float, ret) (%i202) comp_rad_from_three_terms(term1,term2,term3,last_no):=( temp:abs( term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no)), if temp > 0.0 then ret:abs(term2*glob_h*term1/temp) else ret:glob_larger_float,ret) (%o202) comp_rad_from_three_terms(term1, term2, term3, last_no) := (temp : mabs(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no)), if temp > 0.0 !term2 glob_h term1! then ret : !------------------! else ret : glob_larger_float, ret) ! temp ! (%i203) comp_ord_from_three_terms(term1,term2,term3,last_no):=( ret:abs( (-term1*term3*convfloat(last_no*last_no) +term2*term2*convfloat(last_no*last_no) +4.0*term2*term2 -4.0*term2*term2*convfloat(last_no) -3.0*term1*term3 +4.0*term1*term3*convfloat(last_no)) /(term1*term3 -term1*term3*convfloat(last_no) -2.0*term2*term2 +term2*term2*convfloat(last_no))),ret) (%o203) comp_ord_from_three_terms(term1, term2, term3, last_no) := (ret : mabs((- term1 term3 convfloat(last_no last_no) + term2 term2 convfloat(last_no last_no) + 4.0 term2 term2 - 4.0 term2 term2 convfloat(last_no) - 3.0 term1 term3 + 4.0 term1 term3 convfloat(last_no))/(term1 term3 - term1 term3 convfloat(last_no) - 2.0 term2 term2 + term2 term2 convfloat(last_no))), ret) (%i204) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):= ( if term5 # 0.0 and term4 # 0.0 and term3 # 0.0 and term2 # 0.0 and term1 # 0.0 then (rm0:term6/term5,rm1:term5/term4, rm2:term4/term3,rm3:term3/term2, rm4:term2/term1, nr1 :convfloat(last_no-3)*rm2 -2.0*convfloat(last_no-2)*rm1 +convfloat(last_no-1)*rm0, nr2 :convfloat(last_no-4)*rm3 -2.0*convfloat(last_no-3)*rm2 +convfloat(last_no-2)*rm1, dr1:(-1.0)/rm3+2.0/rm2+(-1.0)/rm1, dr2:(-1.0)/rm4+2.0/rm3+(-1.0)/rm2, ds1:5.0/rm3-8.0/rm2+3.0/rm1, ds2:5.0/rm4-8.0/rm3+3.0/rm2, if abs(nr1*dr2-nr2*dr1) = 0.0 or abs(dr1) = 0.0 then (rad_c:glob_larger_float, ord_no:glob_larger_float) else (if abs(nr1*dr2-nr2*dr1) # 0.0 then ( rcs :(dr1*dr2-ds2*dr1+ds1*dr2) /(nr1*dr2-nr2*dr1), ord_no :(rcs*nr1-ds1)/(2.0*dr1) -convfloat(last_no)/2.0, if abs(rcs) # 0.0 then (if rcs > 0.0 then rad_c :sqrt(rcs) *abs(glob_h) else ( rad_c :glob_larger_float, ord_no :glob_larger_float)) else ( rad_c:glob_larger_float, ord_no:glob_larger_float)) else (rad_c:glob_larger_float, ord_no:glob_larger_float))) else (rad_c:glob_larger_float, ord_no:glob_larger_float), glob_six_term_ord_save:ord_no,rad_c) (%o204) comp_rad_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := (if (term5 # 0.0) and (term4 # 0.0) and (term3 # 0.0) term6 term5 and (term2 # 0.0) and (term1 # 0.0) then (rm0 : -----, rm1 : -----, term5 term4 term4 term3 term2 rm2 : -----, rm3 : -----, rm4 : -----, term3 term2 term1 nr1 : convfloat(last_no - 3) rm2 - 2.0 convfloat(last_no - 2) rm1 + convfloat(last_no - 1) rm0, nr2 : convfloat(last_no - 4) rm3 - 2.0 convfloat(last_no - 3) rm2 + convfloat(last_no - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (mabs(nr1 dr2 - nr2 dr1) = 0.0) or (mabs(dr1) = 0.0) rm4 rm3 rm2 then (rad_c : glob_larger_float, ord_no : glob_larger_float) else (if mabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(last_no) ord_no : ------------- - ------------------, 2.0 dr1 2.0 if mabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) mabs(glob_h) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float)) else (rad_c : glob_larger_float, ord_no : glob_larger_float))) else (rad_c : glob_larger_float, ord_no : glob_larger_float), glob_six_term_ord_save : ord_no, rad_c) (%i205) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save (%o205) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6, last_no) := glob_six_term_ord_save (%i206) factorial_2(nnn):=nnn! (%o206) factorial_2(nnn) := nnn! (%i207) factorial_1(nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS then (if array_fact_1[nnn] = 0 then (ret:factorial_2(nnn), array_fact_1[nnn]:ret) else ret:array_fact_1[nnn]) else ret:factorial_2(nnn),ret) (%o207) factorial_1(nnn) := block(mode_declare([[ret], convfloat]), if nnn <= MAX_TERMS then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i208) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]), if nnn <= MAX_TERMS and mmm <= MAX_TERMS then (if array_fact_2[mmm,nnn] = 0 then (ret:factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn]:ret) else ret:array_fact_2[mmm,nnn]) else ret:factorial_2(mmm)/factorial_2(nnn),ret) (%o208) factorial_3(mmm, nnn) := block(mode_declare([[ret], convfloat]), if (nnn <= MAX_TERMS) and (mmm <= MAX_TERMS) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i209) log10(x):=log(x)/glob_log_10 log(x) (%o209) log10(x) := ----------- glob_log_10 (%i210) expt(x,y):=(if x <= 0.0 and y < 0.0 then print("expt error x = ",x,"y = ",y),x^y) (%o210) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i211) estimated_needed_step_error(x_start,x_end,estimated_h, estimated_answer):=block( [desired_abs_gbl_error,range, estimated_steps,step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32,""), desired_abs_gbl_error :expt(10.0,-glob_desired_digits_correct) *abs(estimated_answer), omniout_float(ALWAYS,"estimated_h",32, estimated_h,32,""), omniout_float(ALWAYS,"estimated_answer", 32,estimated_answer,32,""), omniout_float(ALWAYS, "desired_abs_gbl_error",32, desired_abs_gbl_error,32, ""),range:x_end-x_start, omniout_float(ALWAYS,"range",32,range,32, ""), estimated_steps:range/estimated_h, omniout_float(ALWAYS,"estimated_steps",32, estimated_steps,32,""), step_error :abs( desired_abs_gbl_error/estimated_steps), omniout_float(ALWAYS,"step_error",32, step_error,32,""), step_error) (%o211) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) mabs(estimated_answer), omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""), omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, ""), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h !desired_abs_gbl_error! 32, estimated_steps, 32, ""), step_error : !---------------------!, ! estimated_steps ! omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i212) exact_soln_y(x):=block(x/2.0+(-sin(x)*cos(x))/2.0) x - sin(x) cos(x) (%o212) exact_soln_y(x) := block(--- + ---------------) 2.0 2.0 (%i213) display_poles():=( block(mode_declare([[rad_given],convfloat]), if glob_type_given_pole = 4 then (rad_given :sqrt( array_given_rad_poles[1,2] *array_given_rad_poles[1,2] +(array_x[1] -array_given_rad_poles[1,1]) *(array_x[1] -array_given_rad_poles[1,1])), if rad_given < glob_least_given_sing then glob_least_given_sing :rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,rad_given,4," "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[ 1,1],4," ")) elseif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles[1,1] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1,1], 4," "), if array_rad_test_poles[1,1] < glob_least_ratio_sing then glob_least_ratio_sing :array_rad_test_poles[1,1], omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1,1], 4," ")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if array_rad_test_poles[1,2] > 0.0 and array_rad_test_poles[1,2] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1,2], 4," "), if array_rad_test_poles[1,2] < glob_least_3_sing then glob_least_3_sing :array_rad_test_poles[1,2], omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1,2], 4," ")) else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1"), if array_rad_test_poles[1,3] > 0.0 and array_rad_test_poles[1,3] < glob_large_float then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1,3], 4," "), if array_rad_test_poles[1,3] < glob_least_6_sing then glob_least_6_sing :array_rad_test_poles[1,3], omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1,3], 4," ")) else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%o213) display_poles() := (block(mode_declare([[rad_given], convfloat]), if glob_type_given_pole = 4 then (rad_given : sqrt(array_given_rad_poles array_given_rad_poles 1, 2 1, 2 + (array_x - array_given_rad_poles ) 1 1, 1 (array_x - array_given_rad_poles )), 1 1, 1 if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given, omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "), omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\ 1, 1 dius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 1 1, 1 glob_least_ratio_sing then glob_least_ratio_sing : array_rad_test_poles , 1, 1 omniout_float(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 1 "NO POLE (ratio test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float) 1, 2 1, 2 then (omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 2 1, 2 glob_least_3_sing then glob_least_3_sing : array_rad_test_poles , 1, 2 omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO REAL POLE (three term test) for Equation 1"), if (array_rad_test_poles > 0.0) and (array_rad_test_poles < 1, 3 1, 3 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles , 4, " "), if array_rad_test_poles < 1, 3 1, 3 glob_least_6_sing then glob_least_6_sing : array_rad_test_poles , 1, 3 omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS, 1, 3 "NO COMPLEX POLE (six term test) for Equation 1")), 0) (%i214) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0 else ret:-1.0,ret) (%o214) my_check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i215) est_size_answer():=block([min_size], min_size:glob_estimated_size_answer, if abs(array_y[1]) < min_size then (min_size:abs(array_y[1]), omniout_float(ALWAYS,"min_size",32,min_size, 32,"")), if min_size < 1.0 then (min_size:1.0, omniout_float(ALWAYS,"min_size",32,min_size, 32,"")),min_size) (%o215) est_size_answer() := block([min_size], min_size : glob_estimated_size_answer, if !array_y ! < min_size then (min_size : !array_y !, ! 1! ! 1! omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i216) test_suggested_h():=block( [max_estimated_step_error,hn_div_ho,hn_div_ho_2, hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error:0.0,no_terms:MAX_TERMS, hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125, omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32, ""), omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32, ""), est_tmp:abs(array_y[no_terms]*hn_div_ho_3 +array_y[no_terms-1]*hn_div_ho_2 +array_y[no_terms-2]*hn_div_ho +array_y[no_terms-3]), if est_tmp >= max_estimated_step_error then max_estimated_step_error:est_tmp, omniout_float(ALWAYS,"max_estimated_step_error",32, max_estimated_step_error,32,""), max_estimated_step_error) (%o216) test_suggested_h() := block([max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0, no_terms : MAX_TERMS, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), est_tmp : mabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i217) reached_interval():=block(mode_declare([[ret],boolean]), if glob_check_sign*array_x[1] >= glob_check_sign*glob_next_display then ret:true else ret:false,return(ret)) (%o217) reached_interval() := block(mode_declare([[ret], boolean]), if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i218) display_alot(iter):=( block(mode_declare( [[abserr],convfloat,[analytic_val_y],convfloat, [ind_var],convfloat,[numeric_val],convfloat, [relerr],convfloat,[term_no],fixnum]), if reached_interval() then (if iter >= 0 then (ind_var:array_x[1], omniout_float(ALWAYS, "x[1] ", 33,ind_var,20, " "), analytic_val_y :exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20," "), term_no:1, numeric_val:array_y[term_no], abserr :abs( numeric_val-analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33,numeric_val, 20," "), if abs(analytic_val_y) # 0.0 then ( relerr :abserr*100.0 /abs(analytic_val_y), if relerr > 1.0E-34 then glob_good_digits :3-floor(log10(relerr)) else glob_good_digits :16) else (relerr:-1.0, glob_good_digits:-1), if glob_iter = 1 then array_1st_rel_error[1] :relerr else array_last_rel_error[ 1] :relerr, omniout_float(ALWAYS, "absolute error ", 4,abserr,20," "), omniout_float(ALWAYS, "relative error ", 4,relerr,20,"%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits,4, " "), omniout_float(ALWAYS, "h ", 4,glob_h,20, " ")))),0) (%o218) display_alot(iter) := (block(mode_declare([[abserr], convfloat, [analytic_val_y], convfloat, [ind_var], convfloat, [numeric_val], convfloat, [relerr], convfloat, [term_no], fixnum]), if reached_interval() then (if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : mabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if mabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : --------------------, if relerr > 1.0E-34 mabs(analytic_val_y) then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))), 0) (%i219) adjust_for_pole(h_param):=( block(mode_declare( [[hnew],convfloat,[sz2],convfloat,[tmp], convfloat]),hnew:h_param, glob_normmax:glob_small_float, if abs(array_y_higher[1,1]) > glob_small_float then (tmp:abs(array_y_higher[1,1]), if tmp < glob_normmax then glob_normmax:tmp), if glob_look_poles and glob_min_pole_est > glob_small_float and glob_min_pole_est < glob_large_float then (sz2:glob_min_pole_est/10.0, if sz2 < hnew then ( omniout_float(INFO, "glob_h adjusted to ", 20,h_param,12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h:true, glob_curr_iter_when_opt :glob_current_iter, glob_optimal_clock_start_sec :elapsed_time_seconds(), glob_optimal_start:array_x[1]), hnew:sz2),hnew) (%o219) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat, [sz2], convfloat, [tmp], convfloat]), hnew : h_param, glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (glob_min_pole_est > glob_small_float) and (glob_min_pole_est < glob_large_float) glob_min_pole_est then (sz2 : -----------------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), hnew) 1 (%i220) prog_report(x_start,x_end):=( block(mode_declare([[clock_sec],convfloat,[opt_clock_sec], convfloat,[clock_sec1],convfloat, [expect_sec],convfloat,[left_sec], convfloat,[percent_done],convfloat, [total_clock_sec],convfloat]), clock_sec1:elapsed_time_seconds(), total_clock_sec:clock_sec1-glob_orig_start_sec, glob_clock_sec:clock_sec1-glob_clock_start_sec, left_sec:-clock_sec1+glob_orig_start_sec +glob_max_sec, expect_sec:comp_expect_sec(x_end,x_start, glob_h+array_x[1], clock_sec1 -glob_orig_start_sec), opt_clock_sec:clock_sec1 -glob_optimal_clock_start_sec, glob_optimal_expect_sec :comp_expect_sec(x_end,x_start,glob_h+array_x[1], opt_clock_sec), glob_total_exp_sec :total_clock_sec+glob_optimal_expect_sec, percent_done:comp_percent(x_end,x_start, glob_h+array_x[1]), glob_percent_done:percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ",33, percent_done,4,"%")),0) (%o220) prog_report(x_start, x_end) := (block(mode_declare([[clock_sec], convfloat, [opt_clock_sec], convfloat, [clock_sec1], convfloat, [expect_sec], convfloat, [left_sec], convfloat, [percent_done], convfloat, [total_clock_sec], convfloat]), clock_sec1 : elapsed_time_seconds(), total_clock_sec : clock_sec1 - glob_orig_start_sec, glob_clock_sec : clock_sec1 - glob_clock_start_sec, left_sec : - clock_sec1 + glob_orig_start_sec + glob_max_sec, expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 clock_sec1 - glob_orig_start_sec), opt_clock_sec : clock_sec1 - glob_optimal_clock_start_sec, glob_optimal_expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x , 1 opt_clock_sec), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(x_end, x_start, glob_h + array_x ), 1 glob_percent_done : percent_done, omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(total_clock_sec), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(glob_clock_sec), if percent_done < 100.0 then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(expect_sec), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(left_sec), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")), 0) (%i221) check_for_pole():=( block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc], convfloat,[m,n],fixnum,[nr1,nr2], convfloat,[ord_no],fixnum, [term1,term2,term3,part1,part2, part3,part4,part5,part6,part7, part8,part9,part10,part11,part12, part13,part14,rad_c,rcs,rm0,rm1, rm2,rm3,rm4],convfloat, [found_sing],fixnum, [h_new,ratio,term,local_test, tmp_rad,tmp_ord,tmp_ratio, prev_tmp_rad],convfloat,[last_no], fixnum), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,1]:glob_larger_float, array_ord_test_poles[1,1]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-3 and found_sing = 1 do (tmp_rad :comp_rad_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,1] then ( array_rad_test_poles[1,1]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_ratio( array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,1]:rad_c, array_ord_test_poles[1,1] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,2]:glob_larger_float, array_ord_test_poles[1,2]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-4 and found_sing = 1 do (tmp_rad :comp_rad_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,2] then ( array_rad_test_poles[1,2]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_three_terms( array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,2]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,2] :tmp_ord)), glob_min_pole_est:glob_larger_float, tmp_rad:glob_larger_float, prev_tmp_rad:glob_larger_float, tmp_ratio:glob_larger_float, rad_c:glob_larger_float, array_rad_test_poles[1,3]:glob_larger_float, array_ord_test_poles[1,3]:glob_larger_float, found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0, while last_no < MAX_TERMS-7 and found_sing = 1 do (tmp_rad :comp_rad_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no],last_no), tmp_ratio:tmp_rad/prev_tmp_rad, if cnt > 0 and tmp_ratio < glob_upper_ratio_limit and tmp_ratio > glob_lower_ratio_limit then rad_c:tmp_rad elseif cnt = 0 then rad_c:tmp_rad elseif cnt > 0 then found_sing:0, prev_tmp_rad:tmp_rad,cnt:1+cnt, last_no:1+last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles[1,3] then ( array_rad_test_poles[1,3]:rad_c, last_no:last_no-1, tmp_ord :comp_ord_from_six_terms( array_y_higher[1,last_no-5], array_y_higher[1,last_no-4], array_y_higher[1,last_no-3], array_y_higher[1,last_no-2], array_y_higher[1,last_no-1], array_y_higher[1,last_no], last_no), array_rad_test_poles[1,3]:rad_c, if rad_c < glob_min_pole_est then glob_min_pole_est:rad_c, array_ord_test_poles[1,3] :tmp_ord)), if abs(glob_min_pole_est)*glob_ratio_of_radius < abs(glob_h) then (h_new :glob_check_sign*glob_min_pole_est *glob_ratio_of_radius, term:1,ratio:1.0, while term <= MAX_TERMS do ( array_y[term] :array_y[term]*ratio, array_y_higher[1,term] :array_y_higher[1,term]*ratio, array_x[term] :array_x[term]*ratio, ratio:ratio*h_new/abs(glob_h), term:1+term),glob_h:h_new), if reached_interval() then display_poles()),0) (%o221) check_for_pole() := (block(mode_declare([cnt], fixnum, [dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat, [ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum, [h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad], convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 1 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 1 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad : comp_rad_from_ratio(array_y_higher , array_y_higher , 1, last_no - 1 1, last_no tmp_rad last_no), tmp_ratio : ------------, if (cnt > 0) prev_tmp_rad and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 1 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 1 tmp_ord : comp_ord_from_ratio(array_y_higher , 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 1 array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float, 1, 1 tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 2 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 2 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad : comp_rad_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_higher , last_no), 1, last_no - 1 1, last_no tmp_rad tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) prev_tmp_rad and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 2 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 2 tmp_ord : comp_ord_from_three_terms(array_y_higher , 1, last_no - 2 array_y_higher , array_y_higher , last_no), 1, last_no - 1 1, last_no array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est 1, 2 then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), 1, 2 glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float, rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float, 1, 3 array_ord_test_poles : glob_larger_float, found_sing : 1, 1, 3 last_no : - 10 - 1 + MAX_TERMS, cnt : 0, while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad : comp_rad_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 tmp_rad array_y_higher , last_no), tmp_ratio : ------------, 1, last_no prev_tmp_rad if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0 then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0, prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no), if found_sing = 1 then (if rad_c < array_rad_test_poles 1, 3 then (array_rad_test_poles : rad_c, last_no : last_no - 1, 1, 3 tmp_ord : comp_ord_from_six_terms(array_y_higher , 1, last_no - 5 array_y_higher , array_y_higher , 1, last_no - 4 1, last_no - 3 array_y_higher , array_y_higher , 1, last_no - 2 1, last_no - 1 array_y_higher , last_no), array_rad_test_poles : rad_c, 1, last_no 1, 3 if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est) 1, 3 glob_ratio_of_radius < mabs(glob_h) then (h_new : glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0, while term <= MAX_TERMS do (array_y : array_y ratio, term term array_y_higher : array_y_higher ratio, 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ------------, term : 1 + term), term term mabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()), 0) (%i222) atomall():=( block(mode_declare([[kkk,order_d],fixnum, [adj2,adj3,temporary,term,temp,temp2], convfloat]),array_tmp1[1]:sin(array_x[1]), array_tmp1_g[1]:cos(array_x[1]), array_tmp2[1]:sin(array_x[1]), array_tmp2_g[1]:cos(array_x[1]), array_tmp3[1]:array_tmp1[1]*array_tmp2[1], array_tmp4[1]:array_tmp3[1]+array_const_0D0[1], if not array_y_set_initial[1,2] then (if 1 <= MAX_TERMS then ( temporary :array_tmp4[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_tmp2_g[1]*array_x[2]/1, array_tmp2_g[2]:(-array_tmp2[1]*array_x[2])/1, array_tmp3[2]:ats(2,array_tmp1,array_tmp2,1), array_tmp4[2]:array_tmp3[2], if not array_y_set_initial[1,3] then (if 2 <= MAX_TERMS then ( temporary :array_tmp4[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_tmp2_g[2]*array_x[2]/2, array_tmp2_g[3]:(-array_tmp2[2]*array_x[2])/2, array_tmp3[3]:ats(3,array_tmp1,array_tmp2,1), array_tmp4[3]:array_tmp3[3], if not array_y_set_initial[1,4] then (if 3 <= MAX_TERMS then ( temporary :array_tmp4[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_tmp2_g[3]*array_x[2]/3, array_tmp2_g[4]:(-array_tmp2[3]*array_x[2])/3, array_tmp3[4]:ats(4,array_tmp1,array_tmp2,1), array_tmp4[4]:array_tmp3[4], if not array_y_set_initial[1,5] then (if 4 <= MAX_TERMS then ( temporary :array_tmp4[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_tmp2_g[4]*array_x[2]/4, array_tmp2_g[5]:(-array_tmp2[4]*array_x[2])/4, array_tmp3[5]:ats(5,array_tmp1,array_tmp2,1), array_tmp4[5]:array_tmp3[5], if not array_y_set_initial[1,6] then (if 5 <= MAX_TERMS then ( temporary :array_tmp4[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_tmp2_g[kkk-1]*array_x[2]/(kkk-1), array_tmp2_g[kkk] :(-array_tmp2[kkk-1]*array_x[2])/(kkk-1), array_tmp3[kkk]:ats(kkk,array_tmp1,array_tmp2,1), array_tmp4[kkk]:array_tmp3[kkk],order_d:1, if order_d+kkk <= MAX_TERMS then (if not array_y_set_initial[1,order_d+kkk] then ( temporary :array_tmp4[kkk]*expt(glob_h,order_d) *factorial_3(kkk-1, -1+order_d +kkk), array_y[order_d+kkk]:temporary, array_y_higher[1,order_d+kkk]:temporary, term:-1+order_d+kkk,adj2:-1+order_d+kkk, adj3:2, while term >= 1 and term <= MAX_TERMS and adj3 < 1+order_d do ( if adj3 <= 1+order_d then ( if adj2 > 0 then temporary :temporary*adj2/glob_h else temporary:temporary, array_y_higher[adj3,term] :temporary),term:term-1, adj2:adj2-1,adj3:1+adj3))), kkk:1+kkk)),0) (%o222) atomall() := (block(mode_declare([[kkk, order_d], fixnum, [adj2, adj3, temporary, term, temp, temp2], convfloat]), array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : sin(array_x ), array_tmp2_g : cos(array_x ), 1 1 1 1 array_tmp3 : array_tmp1 array_tmp2 , 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= MAX_TERMS 1, 2 then (temporary : array_tmp4 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_g array_x - array_tmp2 array_x 1 2 1 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 2 1 2 1 array_tmp3 : ats(2, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 2 2 2 if not array_y_set_initial then (if 2 <= MAX_TERMS 1, 3 then (temporary : array_tmp4 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_g array_x - array_tmp2 array_x 2 2 2 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 3 2 3 2 array_tmp3 : ats(3, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 3 3 3 if not array_y_set_initial then (if 3 <= MAX_TERMS 1, 4 then (temporary : array_tmp4 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_g array_x - array_tmp2 array_x 3 2 3 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 4 3 4 3 array_tmp3 : ats(4, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 4 4 4 if not array_y_set_initial then (if 4 <= MAX_TERMS 1, 5 then (temporary : array_tmp4 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_g array_x - array_tmp2 array_x 4 2 4 2 array_tmp2 : ----------------------, array_tmp2_g : ----------------------, 5 4 5 4 array_tmp3 : ats(5, array_tmp1, array_tmp2, 1), array_tmp4 : array_tmp3 , 5 5 5 if not array_y_set_initial then (if 5 <= MAX_TERMS 1, 6 then (temporary : array_tmp4 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 : ----------------------------, kkk kkk - 1 array_tmp2_g array_x kkk - 1 2 array_tmp2 : ----------------------------, kkk kkk - 1 - array_tmp2 array_x kkk - 1 2 array_tmp2_g : ----------------------------, kkk kkk - 1 array_tmp3 : ats(kkk, array_tmp1, array_tmp2, 1), kkk array_tmp4 : array_tmp3 , 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_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while (term >= 1) and (term <= MAX_TERMS) and (adj3 < 1 + order_d) do (if adj3 <= 1 + order_d temporary adj2 then (if adj2 > 0 then temporary : -------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)), 0) (%i223) exact_soln_y(x):=block(x/2.0+(-sin(x)*cos(x))/2.0) x - sin(x) cos(x) (%o223) exact_soln_y(x) := block(--- + ---------------) 2.0 2.0 (%i224) main_prog():=block( mode_declare([[d1,d2,d3,d4,est_err_2],convfloat, [niii,done_once,term,ord,order_diff,term_no, html_log_file,iiif,jjjf,rows,r_order, sub_iter,calc_term,iii],fixnum,[temp_sum], convfloat,[current_iter],fixnum, [x_start,x_end],convfloat,[it,opt_iter], fixnum,[tmp],convfloat,[subiter],fixnum, [est_needed_step_err,estimated_step_error, min_value,est_answer,best_h,found_h], convfloat,[repeat_it],fixnum]),Digits:32, max_terms:30,glob_html_log:true,term:1, while term <= MAX_TERMS do (array_y_init[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_norms[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_fact_1[term]:0.0,term:1+term),term:1, while term <= 2 do (array_1st_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_last_rel_error[term]:0.0,term:1+term),term:1, while term <= 2 do (array_type_pole[term]:0,term:1+term), term:1, while term <= 2 do (array_type_real_pole[term]:0,term:1+term),term:1, while term <= 2 do (array_type_complex_pole[term]:0,term:1+term),term:1, while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term), term:1, while term <= MAX_TERMS do (array_tmp0[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp1_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_g[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp2[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp3[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_tmp4[term]:0.0,term:1+term),term:1, while term <= MAX_TERMS do (array_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_g), zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4),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_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/mult_sin_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; "), 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," (-(sin(x) * cos(x))/2.0 + x/2.0) "), omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false, glob_small_float:0.0,glob_smallish_float:0.0, glob_large_float:1.0E+100,glob_larger_float:1.1E+100, glob_almost_1:0.99,x_start:0.1,x_end:5.0, array_y_init[1+0]:exact_soln_y(x_start), glob_look_poles:true,glob_max_iter:1000000, glob_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 ) * sin ( x ) ; "), 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, "2014-01-09T00:13:10-06:00"), logitem_str(html_log_file,"Maxima"), logitem_str(html_log_file, "mult_sin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; "), logitem_float(html_log_file,x_start), logitem_float(html_log_file,x_end), logitem_float(html_log_file,array_x[1]), logitem_float(html_log_file,glob_h), logitem_str(html_log_file,"16"), logitem_good_digits(html_log_file, array_last_rel_error[ 1]), logitem_integer(html_log_file, MAX_TERMS), if glob_least_given_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_given_sing), 0) else ( logitem_str(html_log_file, "NOT GIVEN"),0), if glob_least_ratio_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_ratio_sing), 0) else ( logitem_str(html_log_file,"NONE"),0), if glob_least_3_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_3_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), if glob_least_6_sing < glob_large_float then ( logitem_float(html_log_file, glob_least_6_sing),0) else ( logitem_str(html_log_file,"NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then ( logitem_time(html_log_file, glob_total_exp_sec),0) else ( logitem_str(html_log_file,"Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "mult_sin_sin diffeq.max"), logitem_str(html_log_file, "mult_sin_sin maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o224) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2], convfloat, [niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii], fixnum, [temp_sum], convfloat, [current_iter], fixnum, [x_start, x_end], convfloat, [it, opt_iter], fixnum, [tmp], convfloat, [subiter], fixnum, [est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 30, glob_html_log : true, term : 1, while term <= MAX_TERMS do (array_y_init : 0.0, term : 1 + term), term : 1, term while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term), term term : 1, while term <= 2 do (array_type_complex_pole : 0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp1_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_g : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= MAX_TERMS do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1, while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), zero_ats_ar(array_y), zero_ats_ar(array_x), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1_g), zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2_g), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3), zero_ats_ar(array_tmp4), zero_ats_ar(array_m1), zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0), array_const_0D0 : 0.0, 1 1 zero_ats_ar(array_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/mult_sin_sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; "), 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, " (-(sin(x) * cos(x))/2.0 + x/2.0) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+100, glob_larger_float : 1.1E+100, glob_almost_1 : 0.99, x_start : 0.1, x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_look_poles : true, 1 + 0 glob_max_iter : 1000000, glob_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 ) * sin ( x ) ; "), 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, "2014-01-09T00:13:10-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_sin_sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; "), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, MAX_TERMS), 1 if glob_least_given_sing < glob_large_float then (logitem_float(html_log_file, glob_least_given_sing), 0) else (logitem_str(html_log_file, "NOT GIVEN"), 0), if glob_least_ratio_sing < glob_large_float then (logitem_float(html_log_file, glob_least_ratio_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_3_sing < glob_large_float then (logitem_float(html_log_file, glob_least_3_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), if glob_least_6_sing < glob_large_float then (logitem_float(html_log_file, glob_least_6_sing), 0) else (logitem_str(html_log_file, "NONE"), 0), logitem_integer(html_log_file, glob_iter), logitem_time(html_log_file, glob_clock_sec), if glob_percent_done < 100.0 then (logitem_time(html_log_file, glob_total_exp_sec), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 225 "), logitem_str(html_log_file, "mult_sin_sin diffeq.max"), logitem_str(html_log_file, "mult_sin_sin maxima results"), logitem_str(html_log_file, "All Tests - Maxima only - to save time"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i225) main():=(alias(convfloat,convfloat),compile(all),main_prog()) (%o225) main() := (alias(convfloat, convfloat), compile(all), main_prog()) (%i226) main() warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. warning: encountered undefined variable glob_iolevel in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable secs in translation. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable sec_temp in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable years_int in translation. warning: encountered undefined variable days_int in translation. warning: encountered undefined variable hours_int in translation. warning: encountered undefined variable minutes_int in translation. warning: encountered undefined variable sec_int in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_sec_in_year in translation. warning: encountered undefined variable glob_sec_in_day in translation. warning: encountered undefined variable glob_sec_in_hour in translation. warning: encountered undefined variable glob_sec_in_minute in translation. warning: encountered undefined variable iii in translation. warning: encountered undefined variable fixnum in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_ats in translation. warning: encountered undefined variable ma_ats in translation. warning: encountered undefined variable ret_ats in translation. warning: encountered undefined variable lll_ats in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable iii_att in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ma_att in translation. warning: encountered undefined variable lll_att in translation. warning: encountered undefined variable ret_att in translation. warning: encountered undefined variable al_att in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable good_digits in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable errflag in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable sub1 in translation. warning: encountered undefined variable sub2 in translation. warning: encountered undefined variable rrr in translation. warning: encountered undefined variable ms2 in translation. warning: encountered undefined variable sec_left in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable ret in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temp in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable rm0 in translation. warning: encountered undefined variable rm1 in translation. warning: encountered undefined variable rm2 in translation. warning: encountered undefined variable rm3 in translation. warning: encountered undefined variable rm4 in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable nr1 in translation. warning: encountered undefined variable dr2 in translation. warning: encountered undefined variable nr2 in translation. warning: encountered undefined variable dr1 in translation. warning: encountered undefined variable ds1 in translation. warning: encountered undefined variable ds2 in translation. warning: encountered undefined variable rcs in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable ord_no in translation. warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any. warning: encountered undefined variable rad_c in translation. warning: encountered undefined variable glob_six_term_ord_save in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_1 in translation. warning: encountered undefined variable MAX_TERMS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_fact_2 in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable glob_log_10 in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable glob_desired_digits_correct in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_x in translation. warning: encountered undefined variable array_given_rad_poles in translation. warning: encountered undefined variable rad_given in translation. warning: variable glob_least_given_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable array_given_ord_poles in translation. warning: encountered undefined variable glob_type_given_pole in translation. warning: encountered undefined variable array_rad_test_poles in translation. warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable array_ord_test_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: variable glob_least_3_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_3_sing in translation. warning: variable glob_least_6_sing (declared type convfloat) assigned type any. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_estimated_size_answer in translation. warning: encountered undefined variable array_y in translation. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable ALWAYS in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_next_display in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable ind_var in translation. warning: encountered undefined variable analytic_val_y in translation. warning: encountered undefined variable term_no in translation. warning: encountered undefined variable numeric_val in translation. warning: encountered undefined variable abserr in translation. warning: encountered undefined variable relerr in translation. warning: variable glob_good_digits (declared type fixnum) assigned type any. warning: encountered undefined variable array_1st_rel_error in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable array_last_rel_error in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_good_digits in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable glob_small_float in translation. warning: encountered undefined variable array_y_higher in translation. warning: encountered undefined variable tmp in translation. warning: variable glob_normmax (declared type convfloat) assigned type any. warning: encountered undefined variable glob_normmax in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable hnew in translation. warning: encountered undefined variable sz2 in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_current_iter in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_optimal_start (declared type convfloat) assigned type any. warning: encountered undefined variable glob_reached_optimal_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable clock_sec1 in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_clock_start_sec in translation. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_optimal_clock_start_sec in translation. warning: encountered undefined variable opt_clock_sec in translation. warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_optimal_expect_sec in translation. warning: encountered undefined variable total_clock_sec in translation. warning: variable glob_total_exp_sec (declared type convfloat) assigned type any. warning: encountered undefined variable percent_done in translation. warning: variable glob_percent_done (declared type convfloat) assigned type any. warning: encountered undefined variable INFO in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable expect_sec in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable left_sec in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable last_no in translation. warning: encountered undefined variable found_sing in translation. warning: variable tmp_rad (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_rad in translation. warning: encountered undefined variable prev_tmp_rad in translation. warning: encountered undefined variable cnt in translation. warning: encountered undefined variable tmp_ratio in translation. warning: encountered undefined variable glob_upper_ratio_limit in translation. warning: encountered undefined variable glob_lower_ratio_limit in translation. warning: variable tmp_ord (declared type convfloat) assigned type any. warning: encountered undefined variable tmp_ord in translation. warning: encountered undefined variable glob_min_pole_est in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_ratio_of_radius in translation. warning: encountered undefined variable term in translation. warning: encountered undefined variable ratio in translation. warning: encountered undefined variable h_new in translation. warning: encountered undefined variable glob_h in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable array_tmp1 in translation. warning: encountered undefined variable array_tmp1_g in translation. warning: encountered undefined variable array_tmp2 in translation. warning: encountered undefined variable array_tmp2_g in translation. warning: encountered undefined variable array_tmp3 in translation. warning: encountered undefined variable array_const_0D0 in translation. warning: encountered undefined variable array_tmp4 in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable temporary in translation. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_set_initial in translation. warning: encountered undefined variable kkk in translation. warning: encountered undefined variable order_d in translation. warning: encountered undefined variable adj3 in translation. warning: encountered undefined variable adj2 in translation. modedeclare: false is not a built-in type; assuming it is a Maxima extension type. warning: encountered undefined variable MAX_TERMS in translation. warning: encountered undefined variable array_y_init in translation. warning: encountered undefined variable array_norms in translation. warning: encountered undefined variable array_type_pole in translation. warning: encountered undefined variable array_type_real_pole in translation. warning: encountered undefined variable array_type_complex_pole in translation. warning: encountered undefined variable array_tmp0 in translation. warning: encountered undefined variable array_m1 in translation. warning: encountered undefined variable ord in translation. warning: encountered undefined variable array_y_higher_work in translation. warning: encountered undefined variable array_y_higher_work2 in translation. warning: encountered undefined variable array_const_1 in translation. warning: encountered undefined variable iiif in translation. warning: encountered undefined variable jjjf in translation. warning: encountered undefined variable INFO in translation. warning: variable glob_orig_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable ALWAYS in translation. warning: encountered undefined variable x_start in translation. warning: encountered undefined variable glob_h in translation. warning: encountered undefined variable glob_max_minutes in translation. warning: encountered undefined variable glob_max_hours in translation. warning: encountered undefined variable x_end in translation. warning: variable glob_check_sign (declared type convfloat) assigned type any. warning: encountered undefined variable glob_min_h in translation. warning: encountered undefined variable glob_check_sign in translation. warning: encountered undefined variable glob_max_h in translation. warning: encountered undefined variable glob_display_interval in translation. warning: encountered undefined variable glob_larger_float in translation. warning: encountered undefined variable est_answer in translation. warning: encountered undefined variable est_needed_step_err in translation. warning: encountered undefined variable opt_iter in translation. warning: encountered undefined variable found_h in translation. warning: variable glob_next_display (declared type convfloat) assigned type any. warning: encountered undefined variable order_diff in translation. warning: encountered undefined variable r_order in translation. warning: encountered undefined variable rows in translation. warning: encountered undefined variable it in translation. warning: encountered undefined variable estimated_step_error in translation. warning: encountered undefined variable best_h in translation. warning: encountered undefined variable glob_html_log in translation. warning: variable glob_clock_start_sec (declared type convfloat) assigned type any. warning: variable glob_clock_sec (declared type convfloat) assigned type any. warning: encountered undefined variable DEBUGL in translation. warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any. warning: encountered undefined variable glob_current_iter in translation. warning: encountered undefined variable glob_max_iter in translation. warning: encountered undefined variable glob_clock_sec in translation. warning: encountered undefined variable glob_orig_start_sec in translation. warning: encountered undefined variable glob_max_sec in translation. warning: encountered undefined variable glob_iter in translation. warning: encountered undefined variable current_iter in translation. warning: encountered undefined variable glob_look_poles in translation. warning: encountered undefined variable glob_next_display in translation. warning: encountered undefined variable calc_term in translation. warning: encountered undefined variable temp_sum in translation. warning: encountered undefined variable html_log_file in translation. warning: encountered undefined variable glob_least_given_sing in translation. warning: encountered undefined variable glob_large_float in translation. warning: encountered undefined variable glob_least_ratio_sing in translation. warning: encountered undefined variable glob_least_3_sing in translation. warning: encountered undefined variable glob_least_6_sing in translation. warning: encountered undefined variable glob_total_exp_sec in translation. warning: encountered undefined variable glob_percent_done in translation. WARNING: in $ADJUST_FOR_POLE : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $ADJUST_FOR_POLE : $GLOB_OPTIMAL_START is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound, it will be treated as if it were declared SPECIAL. WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound, it will be treated as if it were declared SPECIAL. Warning: modedcclare has a function or macro call which has not been translated properly. The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################" "##############temp/mult_sin_sinpostode.ode#################" "diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; " "!" "/* 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(" " (-(sin(x) * cos(x))/2.0 + x/2.0) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" estimated_h = 1.000000E-6 "" estimated_answer = 1. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900000. "" step_error = 2.040816326530612300000000000000000E-17 "" est_needed_step_err = 2.040816326530612300000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 8.26478913043485000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-177 "" estimated_step_error = 8.26478913043485000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-177 "" 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 = 5.5464071108108490000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-169 "" estimated_step_error = 5.5464071108108490000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-169 "" 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 = 3.72213216501669500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 "" estimated_step_error = 3.72213216501669500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 "" 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 = 2.4978824380652864000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 "" estimated_step_error = 2.4978824380652864000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 "" 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 = 1.67630297844455460000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 "" estimated_step_error = 1.67630297844455460000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 "" 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 = 1.124951174639118500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" estimated_step_error = 1.124951174639118500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 "" 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 = 7.5494636774678210000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 "" estimated_step_error = 7.5494636774678210000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-130 "" 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 = 5.06641855425318600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-122 "" estimated_step_error = 5.06641855425318600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-122 "" 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 = 3.400095450684845000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" estimated_step_error = 3.400095450684845000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 "" 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 = 2.2818721527065827000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" estimated_step_error = 2.2818721527065827000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 "" 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 = 1.531481717098862300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" estimated_step_error = 1.531481717098862300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 "" 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 = 1.0279522306717594000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" estimated_step_error = 1.0279522306717594000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" 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 = 6.90105089563419400000000000000000000000000000000000000000000000000000000000000000000000000000000000E-83 "" estimated_step_error = 6.90105089563419400000000000000000000000000000000000000000000000000000000000000000000000000000000000E-83 "" 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 = 4.634679859924863000000000000000000000000000000000000000000000000000000000000000000000000000E-75 "" estimated_step_error = 4.634679859924863000000000000000000000000000000000000000000000000000000000000000000000000000E-75 "" 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 = 3.1149285481487926000000000000000000000000000000000000000000000000000000000000000000E-67 "" estimated_step_error = 3.1149285481487926000000000000000000000000000000000000000000000000000000000000000000E-67 "" 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 = 2.096629870325225600000000000000000000000000000000000000000000000000000000000E-59 "" estimated_step_error = 2.096629870325225600000000000000000000000000000000000000000000000000000000000E-59 "" 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 = 1.41539221715502980000000000000000000000000000000000000000000000000E-51 "" estimated_step_error = 1.41539221715502980000000000000000000000000000000000000000000000000E-51 "" 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 = 9.6107630289087100000000000000000000000000000000000000000000E-44 "" estimated_step_error = 9.6107630289087100000000000000000000000000000000000000000000E-44 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 3.32667301234691740000E-4 " " y[1] (numeric) = 3.32667301234691740000E-4 " " 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 = 9.73545855771626800E-2 " " Order of pole (three term test) = 22.96053049700144 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 4.4259422978266960000E-4 " " y[1] (numeric) = 4.42594229782665660000E-4 " " absolute error = 3.957337929572091000000000000000000E-18 " " relative error = 8.9412325405039580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1064848662664999 " " Order of pole (three term test) = 22.952375831609977 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 5.7434339321635330000E-4 " " y[1] (numeric) = 5.7434339321634850000E-4 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 8.3059883952372580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1154447938853708 " " Order of pole (three term test) = 22.943497461389644 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 7.2986202696122270000E-4 " " y[1] (numeric) = 7.2986202696122130000E-4 " " absolute error = 1.4094628242311558000000000000000000E-18 " " relative error = 1.93113598483736400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12422003446093421 " " Order of pole (three term test) = 22.93390958983883 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 9.1108785897156540000E-4 " " y[1] (numeric) = 9.1108785897156240000E-4 " " absolute error = 3.0357660829594124000000000000000000E-18 " " relative error = 3.3320234191093057000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13279654948022085 " " Order of pole (three term test) = 22.923627555506712 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 1.1199483346651107000E-3 " " y[1] (numeric) = 1.119948334665102100E-3 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 7.7446584913023140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14116061834875882 " " Order of pole (three term test) = 22.91266780745484 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 1.358359845970561000E-3 " " y[1] (numeric) = 1.3583598459705543000E-3 " " absolute error = 6.7220534694101270000000000000000000E-18 " " relative error = 4.9486544300837726000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14929886034059803 " " Order of pole (three term test) = 22.901047878942144 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 1.628226964796406000E-3 " " y[1] (numeric) = 1.6282269647963968000E-3 " " absolute error = 9.107298248878237000000000000000000E-18 " " relative error = 5.5933837516423990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15719825600461715 " " Order of pole (three term test) = 22.888786359375462 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 1.931441681227497000E-3 " " y[1] (numeric) = 1.9314416812275018000E-3 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 2.4699112612628357000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16484616799286825 " " Order of pole (three term test) = 22.87590286457045 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 2.2698826467543315000E-3 " " y[1] (numeric) = 2.269882646754328200E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.52846974574413370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17223036127763788 " " Order of pole (three term test) = 22.862418005370458 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 2.645414422837389000E-3 " " y[1] (numeric) = 2.645414422837373000E-3 " " absolute error = 1.561251128379126400000000000000000E-17 " " relative error = 5.9017260770226590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17933902272488073 " " Order of pole (three term test) = 22.848353354673577 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 3.059886735107459000E-3 " " y[1] (numeric) = 3.0598867351074500000E-3 " " absolute error = 9.107298248878237000000000000000000E-18 " " relative error = 2.97635142647147800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1861607799927149 " " Order of pole (three term test) = 22.833731412920653 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 3.5151337335000976000E-3 " " y[1] (numeric) = 3.515133733500096000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 4.935014163030162000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19268471972474238 " " Order of pole (three term test) = 22.818575572099288 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 4.012973258620059000E-3 " " y[1] (numeric) = 4.0129732586200556000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 8.64557705312657200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19890040500909156 " " Order of pole (three term test) = 22.802910078321727 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 4.555206114629284400E-3 " " y[1] (numeric) = 4.555206114629275000E-3 " " absolute error = 9.540979117872439000000000000000000E-18 " " relative error = 2.0945219333173710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20479789207524954 " " Order of pole (three term test) = 22.786759993036224 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 5.143615348949249000E-3 " " y[1] (numeric) = 5.143615348949248000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.686288105049671700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21036774620197415 " " Order of pole (three term test) = 22.770151152934066 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 5.779965539065818000E-3 " " y[1] (numeric) = 5.7799655390658200000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 3.00126958240858400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21560105681083463 " " Order of pole (three term test) = 22.753110128616388 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 6.466002086721712000E-3 " " y[1] (numeric) = 6.466002086721723000E-3 " " absolute error = 1.127570259384924600000000000000000E-17 " " relative error = 1.7438445646351580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22048945172123688 " " Order of pole (three term test) = 22.73566418208686 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 7.203450519779164000E-3 " " y[1] (numeric) = 7.203450519779149000E-3 " " absolute error = 1.561251128379126400000000000000000E-17 " " relative error = 2.16736565912718950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22502511054412627 " " Order of pole (three term test) = 22.717841223138358 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 7.994015802031629000E-3 " " y[1] (numeric) = 7.994015802031611000E-3 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 2.17002757929992850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22920077719294188 " " Order of pole (three term test) = 22.699669764703142 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 8.83938165124117900E-3 " " y[1] (numeric) = 8.839381651241162000E-3 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 1.96249414769100540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23300977149180668 " " Order of pole (three term test) = 22.681178877238338 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 9.741209865673728000E-3 " " y[1] (numeric) = 9.741209865673733000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.342427172490126000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2364459998623848 " " Order of pole (three term test) = 22.662398142219388 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 1.070113965940200400E-2 " " y[1] (numeric) = 1.07011396594019900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.29685138681667950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23950396507230617 " " Order of pole (three term test) = 22.643357604815975 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 1.172078700664155900E-2 " " y[1] (numeric) = 1.172078700664155700E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.480040098837927500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2421787750295664 " " Order of pole (three term test) = 22.624087725826186 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 1.280174399538289200E-2 " " y[1] (numeric) = 1.280174399538287800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.0840544704549360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2444661506088291 " " Order of pole (three term test) = 22.60461933294571 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 1.394557819057723500E-2 " " y[1] (numeric) = 1.394557819057724300E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 6.21961833446578500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24636243249711506 " " Order of pole (three term test) = 22.584983571450124 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 1.515383200713174600E-2 " " y[1] (numeric) = 1.51538320071317200E-2 " " absolute error = 2.602085213965210600000000000000000E-17 " " relative error = 1.71711367312281730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24786458704792166 " " Order of pole (three term test) = 22.56521185436907 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 1.642802209296373400E-2 " " y[1] (numeric) = 1.64280220929637400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.2238157853946500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24897021113440995 " " Order of pole (three term test) = 22.545335812232157 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 1.776963872236220200E-2 " " y[1] (numeric) = 1.776963872236217400E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.5619662306752422000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2496775359938958 " " Order of pole (three term test) = 22.52538724246679 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 1.91801451998974700E-2 " " y[1] (numeric) = 1.918014519989746600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.808874185150673700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24998543005749155 " " Order of pole (three term test) = 22.505398058529128 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 2.06609772751193700E-2 " " y[1] (numeric) = 2.066097727511932400E-2 " " absolute error = 4.510281037539698400000000000000000E-17 " " relative error = 2.1829950139730940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2498934007603763 " " Order of pole (three term test) = 22.48540023884935 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 2.221354256827606800E-2 " " y[1] (numeric) = 2.221354256827604600E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 9.37116700217403100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2494015953297934 " " Order of pole (three term test) = 22.465425775672966 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 2.383922000728522200E-2 " " y[1] (numeric) = 2.383922000728519000E-2 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 1.45535254546640260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24851080054951893 " " Order of pole (three term test) = 22.445506623880064 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 2.553935927618081000E-2 " " y[1] (numeric) = 2.553935927618078000E-2 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 1.3584706313244832000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24722244150117537 " " Order of pole (three term test) = 22.42567464986432 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 2.73152802752577600E-2 " " y[1] (numeric) = 2.7315280275257700E-2 " " absolute error = 5.89805981832114400000000000000000E-17 " " relative error = 2.15925290126479870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2455385792844046 " " Order of pole (three term test) = 22.405961580553555 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 2.916827259312921000E-2 " " y[1] (numeric) = 2.916827259312917400E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.07051325949750630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24346190771954876 " " Order of pole (three term test) = 22.386398952653455 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 3.109959499090856000E-2 " " y[1] (numeric) = 3.10995949909085200E-2 " " absolute error = 3.816391647148975600000000000000000E-17 " " relative error = 1.22715155881117850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24099574903811194 " " Order of pole (three term test) = 22.36701806219551 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 3.31104748987214870E-2 " " y[1] (numeric) = 3.31104748987214600E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.3827174634395400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2381440485678988 " " Order of pole (three term test) = 22.34784991447008 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 3.52021079247505100E-2 " " y[1] (numeric) = 3.52021079247504700E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 1.1826951815624390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23491136842133117 " " Order of pole (three term test) = 22.328925174424548 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 3.73756573770074600E-2 " " y[1] (numeric) = 3.73756573770074200E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 1.11391655278430340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23130288019704193 " " Order of pole (three term test) = 22.31027411760592 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 3.96322537980259570E-2 " " y[1] (numeric) = 3.96322537980259070E-2 " " absolute error = 4.8572257327350600000000000000000E-17 " " relative error = 1.22557393719985540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22732435670642032 " " Order of pole (three term test) = 22.291926581726422 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 4.197299451265934500E-2 " " y[1] (numeric) = 4.197299451265930000E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 9.9190834265795500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2229821627383448 " " Order of pole (three term test) = 22.273911918929542 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 4.439894318916548500E-2 " " y[1] (numeric) = 4.439894318916543500E-2 " " absolute error = 4.8572257327350600000000000000000E-17 " " relative error = 1.09399579896314990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21828324487687897 " " Order of pole (three term test) = 22.25625894883282 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 4.69111294137535300E-2 " " y[1] (numeric) = 4.69111294137534700E-2 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.18332583173712550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21323512038821896 " " Order of pole (three term test) = 22.23899591242265 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 4.95105482787632200E-2 " " y[1] (numeric) = 4.951054827876317000E-2 " " absolute error = 4.8572257327350600000000000000000E-17 " " relative error = 9.81048665707968200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2078458651946706 " " Order of pole (three term test) = 22.222150426874695 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 5.21981599846412800E-2 " " y[1] (numeric) = 5.21981599846412100E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 1.32933687814837140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20212410095489744 " " Order of pole (three term test) = 22.205749441372326 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 5.497488945587387000E-2 " " y[1] (numeric) = 5.497488945587380000E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 1.26219333455446060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19607898127110482 " " Order of pole (three term test) = 22.18981919399366 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 5.78416259710293200E-2 " " y[1] (numeric) = 5.78416259710292300E-2 " " absolute error = 9.02056207507939700000000000000000E-17 " " relative error = 1.55952774902929830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1897201770452302 " " Order of pole (three term test) = 22.174385169736222 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 6.079922280705841000E-2 " " y[1] (numeric) = 6.079922280705832000E-2 " " absolute error = 9.02056207507939700000000000000000E-17 " " relative error = 1.48366404348710980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18305786100756252 " " Order of pole (three term test) = 22.15947205974642 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 6.38484968979950400E-2 " " y[1] (numeric) = 6.38484968979949700E-2 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 1.30412978992934550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17610269144254373 " " Order of pole (three term test) = 22.14510372181894 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 6.69902285081935300E-2 " " y[1] (numeric) = 6.69902285081934600E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 1.03580687190200240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16886579513778732 " " Order of pole (three term test) = 22.131303142229374 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 7.02251609202332500E-2 " " y[1] (numeric) = 7.02251609202331400E-2 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.58094764052762630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16135874958359228 " " Order of pole (three term test) = 22.118092398961114 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 7.3554000137615390E-2 " " y[1] (numeric) = 7.3554000137615300E-2 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 1.32072374681117650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15359356445142738 " " Order of pole (three term test) = 22.10549262638523 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 7.69774146023712300E-2 " " y[1] (numeric) = 7.69774146023711200E-2 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.44227112635575200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14558266238102013 " " Order of pole (three term test) = 22.09352398145006 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 8.04960349276939200E-2 " " y[1] (numeric) = 8.04960349276938200E-2 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 1.20682359996938840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13733885910678148 " " Order of pole (three term test) = 22.082205611434294 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 8.41104536457019700E-2 " " y[1] (numeric) = 8.41104536457018200E-2 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.64994803930933380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12887534295536582 " " Order of pole (three term test) = 22.071555623315525 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 8.7821224970433900E-2 " " y[1] (numeric) = 8.78212249704337500E-2 " " absolute error = 1.52655665885959020000000000000000E-16 " " relative error = 1.73825480044661670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1202056537471616 " " Order of pole (three term test) = 22.06159105480286 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 9.16288645761703400E-2 " " y[1] (numeric) = 9.16288645761702300E-2 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.21165205938161230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11134366113546744 " " Order of pole (three term test) = 22.052327847080253 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 9.55338493911711600E-2 " " y[1] (numeric) = 9.55338493911710300E-2 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.30739095165019970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10230354241800388 " " Order of pole (three term test) = 22.043780819304022 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 9.95366174069102800E-2 " " y[1] (numeric) = 9.95366174069101600E-2 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.25481549930246070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.30997598562635300E-2 " " Order of pole (three term test) = 22.035963644895332 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 0.10363756750288516 " " y[1] (numeric) = 0.10363756750288504 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.2051623101521851000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.37470375389758500E-2 " " Order of pole (three term test) = 22.028888829665668 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 0.10783705928707027 " " y[1] (numeric) = 0.10783705928707014 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.1582297504778650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.42603378267077200E-2 " " Order of pole (three term test) = 22.022567691810192 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 0.11213541295207863 " " y[1] (numeric) = 0.11213541295207848 " " absolute error = 1.52655665885959020000000000000000E-16 " " relative error = 1.36135108318722500000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.46548374152772400E-2 " " Order of pole (three term test) = 22.01701034380101 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 0.11653290914708905 " " y[1] (numeric) = 0.11653290914708889 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.42906801960614620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.4945903056278600E-2 " " Order of pole (three term test) = 22.012225676209464 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 0.12102978886559024 " " y[1] (numeric) = 0.12102978886559008 " " absolute error = 1.52655665885959020000000000000000E-16 " " relative error = 1.2613065536740790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.51490669735577440E-2 " " Order of pole (three term test) = 22.00822134348299 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 0.12562625334898667 " " y[1] (numeric) = 0.1256262533489865 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.32562620673839250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.52800020149663700E-2 " " Order of pole (three term test) = 22.005003751699775 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 0.13032246400610453 " " y[1] (numeric) = 0.13032246400610437 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.2778568527216670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.535449657914984300E-2 " " Order of pole (three term test) = 22.002578048320274 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 0.13511854234863052 " " y[1] (numeric) = 0.13511854234863035 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.23249889170715550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.538842935747768100E-2 " " Order of pole (three term test) = 22.00094811395243 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 0.14001456994250872 " " y[1] (numeric) = 0.14001456994250855 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.18940088708020640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.397743931523397000E-3 " " Order of pole (three term test) = 22.00011655614354 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 0.1450105883753153 " " y[1] (numeric) = 0.1450105883753151 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.33982650154170130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.6015767332640717000E-3 " " Order of pole (three term test) = 22.0000847052087 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 0.15010659923962405 " " y[1] (numeric) = 0.15010659923962383 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.47924612275419250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.459353585689566700E-2 " " Order of pole (three term test) = 22.000852612102623 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 0.15530256413236931 " " y[1] (numeric) = 0.15530256413236912 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.25103555369377980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.456214843627765600E-2 " " Order of pole (three term test) = 22.002419048338083 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 0.1605984046702069 " " y[1] (numeric) = 0.16059840467020672 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.03695584047521760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.44914668178071150E-2 " " Order of pole (three term test) = 22.004781507951268 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 0.16599400252086619 " " y[1] (numeric) = 0.16599400252086596 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.33766643103337020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.43656062102158400E-2 " " Order of pole (three term test) = 22.007936211510742 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 0.17148919945048136 " " y[1] (numeric) = 0.17148919945048116 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.13295198725039630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.416877009684552000E-2 " " Order of pole (three term test) = 22.011878112163792 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 0.1770837973868832 " " y[1] (numeric) = 0.177083797386883 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.09715870213089070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.38852755067086200E-2 " " Order of pole (three term test) = 22.016600903710273 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 0.18277755849882502 " " y[1] (numeric) = 0.18277755849882482 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.06298076692304320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.34995781038926300E-2 " " Order of pole (three term test) = 22.02209703069117 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 0.18857020529111201 " " y[1] (numeric) = 0.18857020529111182 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.03032729380265400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.29962970551841700E-2 " " Order of pole (three term test) = 22.028357700475762 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 0.1944614207155958 " " y[1] (numeric) = 0.19446142071559558 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.1418439920264521000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.23602396361199700E-2 " " Order of pole (three term test) = 22.03537289732793 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 0.20045084829798926 " " y[1] (numeric) = 0.20045084829798904 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.10772594284530480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10157642553610459 " " Order of pole (three term test) = 22.043131398429228 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 0.2065380922804516 " " y[1] (numeric) = 0.20653809228045142 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.40693443830126100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1106301108237138 " " Order of pole (three term test) = 22.05162079183293 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 0.21272271777988636 " " y[1] (numeric) = 0.21272271777988613 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.04382177532533570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11950681153383617 " " Order of pole (three term test) = 22.06082749632056 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 0.2190042509618884 " " y[1] (numeric) = 0.2190042509618882 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.01388262533621780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12819232683893167 " " Order of pole (three term test) = 22.07073678312895 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 0.22538217923027193 " " y[1] (numeric) = 0.22538217923027168 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.10834042599898960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13667276176732238 " " Order of pole (three term test) = 22.081332799513056 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 0.23185595143210166 " " y[1] (numeric) = 0.2318559514321014 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.19710429877652080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1449345494321863 " " Order of pole (three term test) = 22.09259859410704 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 0.23842497807814686 " " y[1] (numeric) = 0.2384249780781466 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.04770977669455840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15296447273568045 " " Order of pole (three term test) = 22.10451614404279 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 0.24508863157866928 " " y[1] (numeric) = 0.245088631578669 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.13247095293034210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1607496855134779 " " Order of pole (three term test) = 22.11706638378268 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 0.2518462464944504 " " y[1] (numeric) = 0.25184624649445014 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.10208414864108470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16827773308589097 " " Order of pole (three term test) = 22.130229235620373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 0.25869711980295845 " " y[1] (numeric) = 0.25869711980295823 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.58318813499569700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1755365721827022 " " Order of pole (three term test) = 22.143983641800848 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 0.265640511179548 " " y[1] (numeric) = 0.26564051117954784 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.26912864134689600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1825145902098255 " " Order of pole (three term test) = 22.158307598208335 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 0.2726756432935801 " " y[1] (numeric) = 0.2726756432935799 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.10738281139664900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18920062382698247 " " Order of pole (three term test) = 22.173178189568198 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 0.27980170211934363 " " y[1] (numeric) = 0.2798017021193435 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.96789231879516600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1955839768066637 " " Order of pole (three term test) = 22.188571626106484 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 0.2870178372616556 " " y[1] (numeric) = 0.2870178372616555 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.868132500814010500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20165443714581058 " " Order of pole (three term test) = 22.204463281608483 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 0.29432316229600697 " " y[1] (numeric) = 0.29432316229600686 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.772122506310196500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20740229340284316 " " Order of pole (three term test) = 22.220827732815444 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 0.30171675512312146 " " y[1] (numeric) = 0.30171675512312124 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.35937269491121500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21281835023389398 " " Order of pole (three term test) = 22.23763880009633 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 0.3091976583377821 " " y[1] (numeric) = 0.3091976583377819 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.18131586502700300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2178939431033975 " " Order of pole (three term test) = 22.25486958932965 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 0.31676487961178146 " " y[1] (numeric) = 0.3167648796117813 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.257320631563461000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22262095214549757 " " Order of pole (three term test) = 22.272492534928347 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 0.32441739209083914 " " y[1] (numeric) = 0.3244173920908389 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.84441125347734900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2269918151541018 " " Order of pole (three term test) = 22.290479443938825 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 0.33215413480532974 " " y[1] (numeric) = 0.33215413480532957 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.013740195989915000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23099953968079726 " " Order of pole (three term test) = 22.308801541143662 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 0.339974013094657 " " y[1] (numeric) = 0.3399740130946568 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.5312228691787900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2346377142212772 " " Order of pole (three term test) = 22.327429515095844 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 0.3478758990451031 " " y[1] (numeric) = 0.3478758990451028 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.97858537823867100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23790051847237934 " " Order of pole (three term test) = 22.346333565010795 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 0.35585863194097894 " " y[1] (numeric) = 0.35585863194097866 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.79960723848124200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24078273264332936 " " Order of pole (three term test) = 22.3654834484413 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 0.3639210187288956 " " y[1] (numeric) = 0.3639210187288953 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.62681301359665000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24327974580629355 " " Order of pole (three term test) = 22.384848529658974 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 0.37206183449496916 " " y[1] (numeric) = 0.3720618344949689 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.45993623702465800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.245387563272879 " " Order of pole (three term test) = 22.40439782866485 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 0.38027982295477014 " " y[1] (numeric) = 0.38027982295476986 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.29872423942148400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24710281298478273 " " Order of pole (three term test) = 22.42410007075082 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 0.3885736969558206 " " y[1] (numeric) = 0.38857369695582034 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 7.14293732001747400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2484227509083662 " " Order of pole (three term test) = 22.44392373653248 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 0.3969421389924378 " " y[1] (numeric) = 0.3969421389924376 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 5.593878379570618000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24934526542452345 " " Order of pole (three term test) = 22.463837112373376 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 0.40538380173271915 " " y[1] (numeric) = 0.4053838017327189 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.84674017486493900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24986888070682095 " " Order of pole (three term test) = 22.483808341120135 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 0.41389730855745666 " " y[1] (numeric) = 0.4138973085574564 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 6.70590869806922800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24999275908250612 " " Order of pole (three term test) = 22.50380547306708 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 0.42248125411076665 " " y[1] (numeric) = 0.4224812541107663 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.88359019830553500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24971670237260346 " " Order of pole (three term test) = 22.52379651706889 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 0.431134204862213 " " y[1] (numeric) = 0.43113420486221266 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 7.72536494741799600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2490411522089601 " " Order of pole (three term test) = 22.543749491719726 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 0.4398546996802006 " " y[1] (numeric) = 0.4398546996802002 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.83423682641843200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24796718932772804 " " Order of pole (three term test) = 22.563632476516524 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 0.4486412504164081 " " y[1] (numeric) = 0.4486412504164077 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 9.89853718172101800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24649653184041748 " " Order of pole (three term test) = 22.58341366292511 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 0.4574923425010277 " " y[1] (numeric) = 0.4574923425010273 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.49365164222244600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24463153248528435 " " Order of pole (three term test) = 22.60306140526698 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 0.46640643554857286 " " y[1] (numeric) = 0.4664064355485725 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.33131854541782200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24237517486345203 " " Order of pole (three term test) = 22.622544271345685 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 0.47538196397401167 " " y[1] (numeric) = 0.4753819639740113 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.17401769664210000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23973106866578442 " " Order of pole (three term test) = 22.641831092731618 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 0.4844173376189803 " " y[1] (numeric) = 0.4844173376189799 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 8.02155555638765800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23670344389815193 " " Order of pole (three term test) = 22.660891014624866 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 0.4935109423878251 " " y[1] (numeric) = 0.4935109423878247 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 7.87374757566046100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2332971441143241 " " Order of pole (three term test) = 22.67969354521629 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 0.5026611408932191 " " y[1] (numeric) = 0.5026611408932188 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.62607232370685200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22951761866731646 " " Order of pole (three term test) = 22.69820860446797 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 0.5118662731110956 " " y[1] (numeric) = 0.5118662731110951 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.67588339335022800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22537091399158832 " " Order of pole (three term test) = 22.716406572234728 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 0.5211246570446348 " " y[1] (numeric) = 0.5211246570446344 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.5217462625650800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22086366393003787 " " Order of pole (three term test) = 22.73425833565019 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 0.5304345893970412 " " y[1] (numeric) = 0.5304345893970408 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.37217667789859500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21600307912126818 " " Order of pole (three term test) = 22.751735335701053 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 0.5397943462528388 " " y[1] (numeric) = 0.5397943462528384 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.22700743223516300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21079693546410375 " " Order of pole (three term test) = 22.76880961291548 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 0.5492021837674146 " " y[1] (numeric) = 0.5492021837674141 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 8.08607873340381800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20525356167781136 " " Order of pole (three term test) = 22.785453852092232 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 0.5586563388645331 " " y[1] (numeric) = 0.5586563388645327 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.9492378221765500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19938182597792556 " " Order of pole (three term test) = 22.801641425999204 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 0.5681550299415434 " " y[1] (numeric) = 0.568155029941543 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.81633861264511400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1931911218889962 " " Order of pole (three term test) = 22.817346437971317 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 0.5776964575819966 " " y[1] (numeric) = 0.5776964575819961 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.60905169188764300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18669135321695243 " " Order of pole (three term test) = 22.83254376333964 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 0.5872788052753879 " " y[1] (numeric) = 0.5872788052753873 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.45226538615290700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1798929182051263 " " Order of pole (three term test) = 22.84720908962551 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 0.5969002401437371 " " y[1] (numeric) = 0.5969002401437365 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.29990432201709500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17280669289928102 " " Order of pole (three term test) = 22.861318955435298 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 0.6065589136747153 " " y[1] (numeric) = 0.6065589136747147 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.15181526143184900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16544401374825857 " " Order of pole (three term test) = 22.87485078799366 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 0.6162529624610248 " " y[1] (numeric) = 0.6162529624610242 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 9.0078514202304800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15781665946807952 " " Order of pole (three term test) = 22.887782939255125 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 0.6259805089457375 " " y[1] (numeric) = 0.6259805089457371 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.09429772179309200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14993683219851006 " " Order of pole (three term test) = 22.9000947205364 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 0.6357396621732929 " " y[1] (numeric) = 0.6357396621732925 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.98539412079359500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14181713798224133 " " Order of pole (three term test) = 22.91176643561381 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 0.6455285185458544 " " y[1] (numeric) = 0.6455285185458539 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.87946693432595800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13347056659791015 " " Order of pole (three term test) = 22.922779412233062 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 0.6553451625847234 " " y[1] (numeric) = 0.6553451625847229 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.47052124598254200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12491047077922464 " " Order of pole (three term test) = 22.93311603198087 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 0.6651876676965055 " " y[1] (numeric) = 0.665187667696505 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.34518646797658500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1161505448534384 " " Order of pole (three term test) = 22.942759758470658 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 0.6750540969437219 " " y[1] (numeric) = 0.6750540969437213 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.22321521824430900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.107204802833348 " " Order of pole (three term test) = 22.95169516379728 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 0.6849425038195585 " " y[1] (numeric) = 0.6849425038195579 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.10449795737624500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.80875559978625200E-2 " " Order of pole (three term test) = 22.95990795321832 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 0.6948509330264429 " " y[1] (numeric) = 0.6948509330264423 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.9889295088771700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.88133899970096700E-2 " " Order of pole (three term test) = 22.967384988022683 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 0.7047774212581371 " " y[1] (numeric) = 0.7047774212581366 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.87640885716256300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.93971415180076700E-2 " " Order of pole (three term test) = 22.97411430654968 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 0.7147199979850343 " " y[1] (numeric) = 0.7147199979850337 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.76683895620060600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.98538745497304100E-2 " " Order of pole (three term test) = 22.980085143325187 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 0.7246766862423437 " " y[1] (numeric) = 0.724676686242343 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.19215185780556300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.01988562835387400E-2 " " Order of pole (three term test) = 22.985287946284075 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 0.7346455034208507 " " y[1] (numeric) = 0.73464550342085 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.0674183898664800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.044753268903115000E-2 " " Order of pole (three term test) = 22.98971439205149 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 0.7446244620599338 " " y[1] (numeric) = 0.7446244620599332 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 8.9459029177244210000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.06155038037874560E-2 " " Order of pole (three term test) = 22.993357399258443 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 0.7546115706425228 " " y[1] (numeric) = 0.7546115706425222 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 8.82750597380724700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.071849877663640500E-2 " " Order of pole (three term test) = 22.996211139870557 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 0.7646048343916785 " " y[1] (numeric) = 0.7646048343916778 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 8.71213187273491000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.077235070437300E-2 " " Order of pole (three term test) = 22.998271048511608 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 0.7746022560684771 " " y[1] (numeric) = 0.7746022560684764 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 8.59968854410625200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.079297130218105800E-2 " " Order of pole (three term test) = 22.999533829767195 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 0.7846018367708795 " " y[1] (numeric) = 0.7846018367708787 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.90510193598432600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.9632544828338770000E-4 " " Order of pole (three term test) = 22.999997463456687 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 0.7946015767332646 " " y[1] (numeric) = 0.7946015767332638 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.7804502280579900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.201594356457846000E-3 " " Order of pole (three term test) = 22.99966120786509 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 0.80459947612631 " " y[1] (numeric) = 0.8045994761263092 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.65891900625110300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.918479357313083200E-2 " " Order of pole (three term test) = 22.998525600929604 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 0.8145935358568962 " " y[1] (numeric) = 0.8145935358568954 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.54041596242345500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.913730121262452000E-2 " " Order of pole (three term test) = 22.996592459379098 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 0.8245817583677175 " " y[1] (numeric) = 0.8245817583677167 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.42485216718851100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.904319538580408600E-2 " " Order of pole (three term test) = 22.99386487582765 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 0.8345621484362783 " " y[1] (numeric) = 0.8345621484362776 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.98183593664331600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.888662877513716400E-2 " " Order of pole (three term test) = 22.990347213827107 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 0.8445327139729556 " " y[1] (numeric) = 0.8445327139729549 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.88760226517910300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.8651853987021310E-2 " " Order of pole (three term test) = 22.986045100886265 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 0.854491466817808 " " y[1] (numeric) = 0.8544914668178073 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.79567544724381600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.83232487442543400E-2 " " Order of pole (three term test) = 22.980965419468095 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 0.8644364235358133 " " y[1] (numeric) = 0.8644364235358126 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.70598966723775700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.78853408783457400E-2 " " Order of pole (three term test) = 22.975116295979266 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 0.8743656062102163 " " y[1] (numeric) = 0.8743656062102156 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.61848144579169300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.73228330816849300E-2 " " Order of pole (three term test) = 22.968507087769602 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 0.8842770432336687 " " y[1] (numeric) = 0.8842770432336681 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.53308954328546600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.6620627379971100E-2 " " Order of pole (three term test) = 22.96114836816235 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 0.8941687700968461 " " y[1] (numeric) = 0.8941687700968455 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.44975486789754400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10576384928575036 " " Order of pole (three term test) = 22.953051909539116 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 0.9040388301742255 " " y[1] (numeric) = 0.9040388301742248 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.36842038794636000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11473787159442378 " " Order of pole (three term test) = 22.94423066450654 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 0.9138852755067091 " " y[1] (numeric) = 0.9138852755067084 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.2890310482981800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12352833778465322 " " Order of pole (three term test) = 22.934698745174906 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 0.9237061675807823 " " y[1] (numeric) = 0.9237061675807816 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.21153369062935700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13212118498573386 " " Order of pole (three term test) = 22.924471400581787 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 0.9334995781038932 " " y[1] (numeric) = 0.9334995781038925 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.13587697734296100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14050266647518692 " " Order of pole (three term test) = 22.913564992296795 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 0.9432635897757439 " " y[1] (numeric) = 0.9432635897757431 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.23901320544318300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1486593736705833 " " Order of pole (three term test) = 22.90199696824663 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 0.9529962970551848 " " y[1] (numeric) = 0.9529962970551841 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.1548702722042900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15657825758041502 " " Order of pole (three term test) = 22.889785834802044 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 0.9626958069224063 " " y[1] (numeric) = 0.9626958069224055 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.07270699269025300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16424664967969832 " " Order of pole (three term test) = 22.876951127171655 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 0.9723602396361206 " " y[1] (numeric) = 0.9723602396361198 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.99247115995239800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17165228217691053 " " Order of pole (three term test) = 22.863513378149744 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 0.9819877294854339 " " y[1] (numeric) = 0.9819877294854331 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.91411230407983800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17878330763984032 " " Order of pole (three term test) = 22.849494085268166 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 0.9915764255361055 " " y[1] (numeric) = 0.9915764255361047 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.8375816248095300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1856283179489513 " " Order of pole (three term test) = 22.834915676404933 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 1.0011244923708968 " " y[1] (numeric) = 1.0011244923708962 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.6538559375121600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19217636254793985 " " Order of pole (three term test) = 22.819801473904313 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 1.0106301108237143 " " y[1] (numeric) = 1.0106301108237137 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.5912721938609300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19841696596228908 " " Order of pole (three term test) = 22.804175657266125 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 1.0200914787072508 " " y[1] (numeric) = 1.0200914787072501 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.53013801879099100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20434014455779406 " " Order of pole (three term test) = 22.788063224463663 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 1.029506811533837 " " y[1] (numeric) = 1.0295068115338364 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.47041677929879300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20993642251224573 " " Order of pole (three term test) = 22.771489951952255 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 1.0388743432292125 " " y[1] (numeric) = 1.0388743432292118 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.4120730203471900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21519684697472607 " " Order of pole (three term test) = 22.7544823534325 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 1.0481923268389322 " " y[1] (numeric) = 1.0481923268389315 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.35507242057357300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22011300238825926 " " Order of pole (three term test) = 22.73706763743393 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 1.0574590352271247 " " y[1] (numeric) = 1.0574590352271238 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.39917566650096400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22467702395290726 " " Order of pole (three term test) = 22.719273663787195 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 1.066672761767323 " " y[1] (numeric) = 1.0666727617673222 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.32662510504666400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22888161020777292 " " Order of pole (three term test) = 22.70112889905428 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 1.0758318210250937 " " y[1] (numeric) = 1.0758318210250928 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.25573665272175100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23272003471177885 " " Order of pole (three term test) = 22.6826623709881 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 1.0849345494321871 " " y[1] (numeric) = 1.084934549432186 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.02330875646480650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23618615680453903 " " Order of pole (three term test) = 22.663903622094228 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 1.0939793059519423 " " y[1] (numeric) = 1.0939793059519414 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.11878629575413800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23927443143010468 " " Order of pole (three term test) = 22.644882662369245 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 1.102964472735681 " " y[1] (numeric) = 1.1029644727356802 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.05264758435217500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24197991800787208 " " Order of pole (three term test) = 22.62562992129112 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 1.1118884557698248 " " y[1] (numeric) = 1.1118884557698239 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98801727899214400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.244298288336456 " " Order of pole (three term test) = 22.606176199138556 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 1.1207496855134784 " " y[1] (numeric) = 1.1207496855134778 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.94364489578152900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2462258335178905 " " Order of pole (three term test) = 22.58655261771709 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 1.1295466175262276 " " y[1] (numeric) = 1.1295466175262268 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.86314089138956700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24775946989107267 " " Order of pole (three term test) = 22.56679057057084 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 1.1382777330858918 " " y[1] (numeric) = 1.1382777330858909 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.80282697169395800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24889674396496383 " " Order of pole (three term test) = 22.54692167275958 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 1.1469415397959948 " " y[1] (numeric) = 1.146941539795994 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.74388570718351200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24963583634365133 " " Order of pole (three term test) = 22.526977710281322 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 1.1555365721827027 " " y[1] (numeric) = 1.1555365721827018 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.68628567092807500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2499755646369939 " " Order of pole (three term test) = 22.50699058922156 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 1.164061392280994 " " y[1] (numeric) = 1.164061392280993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.62999636951903100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24991538535219346 " " Order of pole (three term test) = 22.48699228471028 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 1.1725145902098262 " " y[1] (numeric) = 1.1725145902098253 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.57498821009282500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2494553947632685 " " Order of pole (three term test) = 22.467014789768626 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 1.18089478473607 " " y[1] (numeric) = 1.1808947847360691 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.52123246863718800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2485963287570349 " " Order of pole (three term test) = 22.447090064126886 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 1.1892006238269832 " " y[1] (numeric) = 1.1892006238269826 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.601525944641699000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24733956165584525 " " Order of pole (three term test) = 22.427249983095688 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 1.1974307851910069 " " y[1] (numeric) = 1.1974307851910064 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.70868375310080430000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24568710401896526 " " Order of pole (three term test) = 22.407526286572363 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 1.2055839768066638 " " y[1] (numeric) = 1.2055839768066636 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.841801228257698000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24364159942610855 " " Order of pole (three term test) = 22.38795052826385 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 1.2136589374393498 " " y[1] (numeric) = 1.2136589374393496 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.82954698453845900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2412063202482726 " " Order of pole (three term test) = 22.3685540252075 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 1.2216544371458105 " " y[1] (numeric) = 1.2216544371458105 " " 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 = 0.23838516241264343 " " Order of pole (three term test) = 22.349367807670504 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 1.229569277766103 " " y[1] (numeric) = 1.229569277766103 " " 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 = 0.23518263916994311 " " Order of pole (three term test) = 22.33042256950808 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 1.2374022934028428 " " y[1] (numeric) = 1.237402293402843 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.79444151759579400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23160387387419154 " " Order of pole (three term test) = 22.31174861905986 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 1.2451523508875486 " " y[1] (numeric) = 1.245152350887549 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.56654516640886900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22765459178643255 " " Order of pole (three term test) = 22.29337583066299 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 1.2528183502338934 " " y[1] (numeric) = 1.252818350233894 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.3170821983149500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22334111091553815 " " Order of pole (three term test) = 22.27533359685958 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 1.2603992250776848 " " y[1] (numeric) = 1.2603992250776856 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.04680233078834400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21867033191074156 " " Order of pole (three term test) = 22.257650781374924 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 1.2678939431033964 " " y[1] (numeric) = 1.2678939431033975 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.75643448463589800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21364972702207055 " " Order of pole (three term test) = 22.24035567294166 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 1.2753015064570805 " " y[1] (numeric) = 1.2753015064570818 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.04466874915827960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2082873281463419 " " Order of pole (three term test) = 22.223475940043844 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 1.2826209521454963 " " y[1] (numeric) = 1.2826209521454977 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.03870720911087970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20259171397783943 " " Order of pole (three term test) = 22.207038586653315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 1.2898513524212933 " " y[1] (numeric) = 1.289851352421295 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.2050320616848469000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19657199628423297 " " Order of pole (three term test) = 22.191069909029032 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 1.2969918151541002 " " y[1] (numeric) = 1.2969918151541018 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.19839787446194950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19023780532969473 " " Order of pole (three term test) = 22.175595453648743 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 1.3040414841873624 " " y[1] (numeric) = 1.3040414841873642 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.36219350453196700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18359927446852958 " " Order of pole (three term test) = 22.16063997634 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 1.3109995396807954 " " y[1] (numeric) = 1.3109995396807974 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.5243342074794750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17666702393397105 " " Order of pole (three term test) = 22.146227402676164 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 1.3178651984383092 " " y[1] (numeric) = 1.3178651984383112 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.51639291081775180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1694521438480735 " " Order of pole (three term test) = 22.13238078970058 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 1.3246377142212753 " " y[1] (numeric) = 1.3246377142212775 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.6762666693026050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16196617647988124 " " Order of pole (three term test) = 22.11912228904023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 1.331316378047014 " " y[1] (numeric) = 1.3313163780470165 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.8346432857367660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15422109778026327 " " Order of pole (three term test) = 22.10647311146784 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 1.3379005184723771 " " y[1] (numeric) = 1.3379005184723798 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.9915795100690730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14622929822294276 " " Order of pole (three term test) = 22.094453492969176 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 1.3443895018623158 " " y[1] (numeric) = 1.3443895018623186 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.14713061953159560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13800356298238575 " " Order of pole (three term test) = 22.083082662369783 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 1.350782732643327 " " y[1] (numeric) = 1.35078273264333 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 2.13696828828771060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12955705148024674 " " Order of pole (three term test) = 22.07237881057298 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 1.3570796535416745 " " y[1] (numeric) = 1.3570796535416776 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.29067207723409850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1209032763331032 " " Order of pole (three term test) = 22.06235906145827 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 1.363279745806291 " " y[1] (numeric) = 1.3632797458062942 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 2.28025427540690830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11205608173514998 " " Order of pole (three term test) = 22.053039444486807 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 1.3693825294162718 " " y[1] (numeric) = 1.3693825294162751 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.43224154122605730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10302962131044277 " " Order of pole (three term test) = 22.044434869057664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 1.3753875632728763 " " y[1] (numeric) = 1.3753875632728798 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.58306369322291450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.38383354701195500E-2 " " Order of pole (three term test) = 22.036559100655985 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 1.3812944453759624 " " y[1] (numeric) = 1.381294445375966 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.57201763946391550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.44969283108210200E-2 " " Order of pole (three term test) = 22.029424738831135 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 1.38710281298478 " " y[1] (numeric) = 1.3871028129847838 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.7213255199180040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.50203440912755500E-2 " " Order of pole (three term test) = 22.02304319704012 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 1.3928123427630639 " " y[1] (numeric) = 1.3928123427630679 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.86959180783945300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.54237433246703100E-2 " " Order of pole (three term test) = 22.017424684388487 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 1.3984227509083633 " " y[1] (numeric) = 1.3984227509083673 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.85807913669481550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.57224785250666200E-2 " " Order of pole (three term test) = 22.012578189297916 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 1.4039337932655584 " " y[1] (numeric) = 1.4039337932655627 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.0050188362248410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.59320696466509200E-2 " " Order of pole (three term test) = 22.0085114651267 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 1.4093452654245204 " " y[1] (numeric) = 1.4093452654245247 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.9934804459039360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.606817925511940400E-2 " " Order of pole (three term test) = 22.00523101776598 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 1.4146570028018717 " " y[1] (numeric) = 1.4146570028018761 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 3.1392005904646770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.614658747091474500E-2 " " Order of pole (three term test) = 22.00274209523175 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 1.4198688807068178 " " y[1] (numeric) = 1.4198688807068225 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 3.2840614839761990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.618316672439715500E-2 " " Order of pole (three term test) = 22.001048679269132 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 1.424980814391022 " " y[1] (numeric) = 1.4249808143910268 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 3.2722803397310330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.193856363345719000E-3 " " Order of pole (three term test) = 22.000153478982398 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 1.429992759082503 " " y[1] (numeric) = 1.4299927590825077 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 3.26081140887555470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.805362846601675300E-3 " " Order of pole (three term test) = 22.000057926501057 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 1.4349047100035432 " " y[1] (numeric) = 1.434904710003548 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 3.24964903308049170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.379849428776211100E-2 " " Order of pole (three term test) = 22.000762174688695 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 1.4397167023726003 " " y[1] (numeric) = 1.4397167023726052 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.39301565391331440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.376955108158338200E-2 " " Order of pole (three term test) = 22.002265096898437 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 1.4444288113902202 " " y[1] (numeric) = 1.444428811390225 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 3.38194673896669100000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.37025816642417150E-2 " " Order of pole (three term test) = 22.004564288775363 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 1.4490411522089568 " " y[1] (numeric) = 1.449041152208962 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.52441744355599160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.35816953057380200E-2 " " Order of pole (three term test) = 22.007656072102936 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 1.4535538798873144 " " y[1] (numeric) = 1.4535538798873195 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.5134754782338290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.3391087531677610E-2 " " Order of pole (three term test) = 22.01153550068737 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 1.4579671893277248 " " y[1] (numeric) = 1.45796718932773 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.5028400849202873000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.31150654070572200E-2 " " Order of pole (three term test) = 22.016196368270506 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 1.4622813151985892 " " y[1] (numeric) = 1.4622813151985943 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 3.4925057580881050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.27380726416150500E-2 " " Order of pole (three term test) = 22.021631218458467 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 1.4664965318404142 " " y[1] (numeric) = 1.4664965318404195 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.63387870512923040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.2244714476574400E-2 " " Order of pole (three term test) = 22.02783135665033 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 1.4706131531560798 " " y[1] (numeric) = 1.470613153156085 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 3.623706551763150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.16197823129741900E-2 " " Order of pole (three term test) = 22.03478686394762 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 1.4746315324852812 " " y[1] (numeric) = 1.4746315324852868 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.76440826120825600000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10084827804218482 " " Order of pole (three term test) = 22.042486613022415 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 1.478552062463199 " " y[1] (numeric) = 1.4785520624632045 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.75442655287895830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1099154380396797 " " Order of pole (three term test) = 22.050918285918723 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 1.4823751748634488 " " y[1] (numeric) = 1.4823751748634544 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.7447437175525640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11880675678368725 " " Order of pole (three term test) = 22.060068393758566 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 1.4861013404253793 " " y[1] (numeric) = 1.4861013404253849 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.73535436118834200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12750801006093052 " " Order of pole (three term test) = 22.069922298321327 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 1.4897310686657812 " " y[1] (numeric) = 1.489731068665787 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.8753033010322574000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13600527772233456 " " Order of pole (three term test) = 22.080464235461765 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 1.4932649076750886 " " y[1] (numeric) = 1.4932649076750943 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.86613232412943300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14428496595229473 " " Order of pole (three term test) = 22.091677340329266 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 1.496703443898149 " " y[1] (numeric) = 1.4967034438981548 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.85725024659172200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15233382901588252 " " Order of pole (three term test) = 22.103543674348057 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 1.5000473018996539 " " y[1] (numeric) = 1.5000473018996598 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.99667685504553300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16013899044919513 " " Order of pole (three term test) = 22.11604425391505 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 1.5032971441143212 " " y[1] (numeric) = 1.5032971441143272 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.9880368006073510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16768796365895133 " " Order of pole (three term test) = 22.129159080769586 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 1.5064536705819298 " " y[1] (numeric) = 1.506453670581936 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 4.1270760988615124000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1749686718983783 " " Order of pole (three term test) = 22.142867173986385 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 1.5095176186673136 " " y[1] (numeric) = 1.5095176186673198 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 4.11869915330290160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18196946758742663 " " Order of pole (three term test) = 22.15714660354053 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 1.5124897627654246 " " y[1] (numeric) = 1.5124897627654308 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 4.110605632485940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1886791509464181 " " Order of pole (three term test) = 22.171974525390855 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 1.5153709139915856 " " y[1] (numeric) = 1.515370913991592 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 4.2493184232132253000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19508698791330104 " " Order of pole (three term test) = 22.187327218025516 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 1.5181619198570555 " " y[1] (numeric) = 1.5181619198570622 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 4.3877652710312650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20118272731586037 " " Order of pole (three term test) = 22.20318012041137 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 1.5208636639300352 " " y[1] (numeric) = 1.520863663930042 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 4.3799706086326640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20695661727140693 " " Order of pole (three term test) = 22.21950787128637 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 1.5234770654822525 " " y[1] (numeric) = 1.5234770654822594 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.5182056944828730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21239942078770982 " " Order of pole (three term test) = 22.236284349732177 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = 1.5260030791212658 " " y[1] (numeric) = 1.5260030791212724 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 4.3652193359837826000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2175024305402123 " " Order of pole (three term test) = 22.253482716962075 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = 1.528442694408633 " " y[1] (numeric) = 1.5284426944086398 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.5035268759874630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22225748280189433 " " Order of pole (three term test) = 22.271075459257286 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = 1.5307969354641013 " " y[1] (numeric) = 1.5307969354641082 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.49660081831107950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2266569705034942 " " Order of pole (three term test) = 22.28903443198305 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = 1.5330668605559725 " " y[1] (numeric) = 1.5330668605559794 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.48994295668206260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23069385540319695 " " Order of pole (three term test) = 22.307330904614062 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = 1.5352535616778091 " " y[1] (numeric) = 1.535253561677816 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.4835478154849110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23436167934631877 " " Order of pole (three term test) = 22.325935606697136 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = 1.5373581641116523 " " y[1] (numeric) = 1.5373581641116592 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 4.4774099577852560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23765457459697856 " " Order of pole (three term test) = 22.344818774677744 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = 1.5393818259779235 " " y[1] (numeric) = 1.5393818259779306 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.6157666913386710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24056727322522184 " " Order of pole (three term test) = 22.363950199515305 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = 1.5413257377721925 " " y[1] (numeric) = 1.5413257377721996 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.6099453110223620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2430951155345859 " " Order of pole (three term test) = 22.38329927501123 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = 1.5431911218889944 " " y[1] (numeric) = 1.5431911218890015 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.6043728847424725000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24523405751662028 " " Order of pole (three term test) = 22.402835046772307 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = 1.544979232132888 " " y[1] (numeric) = 1.544979232132895 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.5990439287599727000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24698067732043683 " " Order of pole (three term test) = 22.422526261731132 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = 1.5466913532169508 " " y[1] (numeric) = 1.546691353216958 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.5939529841053806000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2483321807269418 " " Order of pole (three term test) = 22.442341418144338 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = 1.5483288002489117 " " y[1] (numeric) = 1.548328800248919 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.7325038204727950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24928640561899026 " " Order of pole (three term test) = 22.46224881598867 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = 1.5498929182051246 " " y[1] (numeric) = 1.549892918205132 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.7277278813633880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2498418254403119 " " Order of pole (three term test) = 22.482216607674268 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = 1.5513850813925958 " " y[1] (numeric) = 1.5513850813926031 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.7231806276933850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24999755163767595 " " Order of pole (three term test) = 22.50221284899399 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = 1.5528066928992796 " " y[1] (numeric) = 1.552806692899287 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.7188565041825960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24975333508238634 " " Order of pole (three term test) = 22.52220555022738 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = 1.5541591840328621 " " y[1] (numeric) = 1.5541591840328697 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8576211787141055000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24910956646883503 " " Order of pole (three term test) = 22.542162727317343 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = 1.5554440137482575 " " y[1] (numeric) = 1.5554440137482648 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.7108554841961390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24806727568947348 " " Order of pole (three term test) = 22.562052453037822 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = 1.556662668064044 " " y[1] (numeric) = 1.5566626680640514 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 4.7071675275921550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24662813018720514 " " Order of pole (three term test) = 22.581842908070595 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = 1.5578166594680785 " " y[1] (numeric) = 1.557816659468086 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8462163513059825000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2447944322878325 " " Order of pole (three term test) = 22.601502431909346 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = 1.5589075263125198 " " y[1] (numeric) = 1.5589075263125274 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8428251451892640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24256911551682644 " " Order of pole (three term test) = 22.620999573509735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = 1.5599368321985092 " " y[1] (numeric) = 1.5599368321985168 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8396296642416570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23995573990631153 " " Order of pole (three term test) = 22.64030314160438 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = 1.5609061653507503 " " y[1] (numeric) = 1.5609061653507579 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8366242219016525000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23695848629977442 " " Order of pole (three term test) = 22.659382254602185 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = 1.5618171379822408 " " y[1] (numeric) = 1.5618171379822483 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8338031283255830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23358214966360538 " " Order of pole (three term test) = 22.678206389992376 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = 1.562671385649408 " " y[1] (numeric) = 1.5626713856494157 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 4.8311606885370023000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22983213141617562 " " Order of pole (three term test) = 22.696745433173916 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y[1] (analytic) = 1.5634705665979096 " " y[1] (numeric) = 1.5634705665979174 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.9707115301101606000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2257144307867197 " " Order of pole (three term test) = 22.714969725632486 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y[1] (analytic) = 1.564216361099356 " " y[1] (numeric) = 1.5642163610993638 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.9683415706725637000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22123563521784903 " " Order of pole (three term test) = 22.73285011238782 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y[1] (analytic) = 1.5649104707792243 " " y[1] (numeric) = 1.5649104707792323 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.1080275367579510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21640290982704813 " " Order of pole (three term test) = 22.75035798863536 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y[1] (analytic) = 1.5655546179362319 " " y[1] (numeric) = 1.5655546179362398 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.1059258397759220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.211223985944016 " " Order of pole (three term test) = 22.76746534550795 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y[1] (analytic) = 1.5661505448534383 " " y[1] (numeric) = 1.5661505448534463 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.1039830133629820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20570714874218723 " " Order of pole (three term test) = 22.784144814883952 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y[1] (analytic) = 1.5667000131013566 " " y[1] (numeric) = 1.5667000131013646 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.1021929600149850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19986122398422246 " " Order of pole (three term test) = 22.800369713170472 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y[1] (analytic) = 1.567204802833348 " " y[1] (numeric) = 1.567204802833356 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.1005495662401590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19369556390267004 " " Order of pole (three term test) = 22.816114083991376 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y[1] (analytic) = 1.5676667120735845 " " y[1] (numeric) = 1.5676667120735925 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0990467015325100000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18722003223838973 " " Order of pole (three term test) = 22.831352739711964 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y[1] (analytic) = 1.5680875559978626 " " y[1] (numeric) = 1.5680875559978709 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2392803901808130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18044498846067164 " " Order of pole (three term test) = 22.84606130173383 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y[1] (analytic) = 1.5684691662075585 " " y[1] (numeric) = 1.5684691662075665 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0964379469626870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1733812711942943 " " Order of pole (three term test) = 22.860216239495394 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y[1] (analytic) = 1.56881338999701 " " y[1] (numeric) = 1.568813389997018 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0953197035858820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16604018088003814 " " Order of pole (three term test) = 22.873794908115798 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y[1] (analytic) = 1.5691220896146256 " " y[1] (numeric) = 1.5691220896146336 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0943172811137640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1584334616963899 " " Order of pole (three term test) = 22.886775584621876 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y[1] (analytic) = 1.5693971415180081 " " y[1] (numeric) = 1.5693971415180163 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2349084657306840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1505732827713633 " " Order of pole (three term test) = 22.899137502700285 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y[1] (analytic) = 1.569640435623398 " " y[1] (numeric) = 1.5696404356234062 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2340970554592230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14247221871448995 " " Order of pole (three term test) = 22.91086088591917 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y[1] (analytic) = 1.569853874549731 " " y[1] (numeric) = 1.5698538745497392 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2333854223104630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13414322950012558 " " Order of pole (three term test) = 22.92192697936622 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y[1] (analytic) = 1.5700393728576167 " " y[1] (numeric) = 1.570039372857625 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2327671039694480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12559963973425717 " " Order of pole (three term test) = 22.932318079652582 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y[1] (analytic) = 1.5701988562835396 " " y[1] (numeric) = 1.5701988562835476 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0908238439435450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11685511733797482 " " Order of pole (three term test) = 22.942017563234444 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y[1] (analytic) = 1.5703342609695896 " " y[1] (numeric) = 1.5703342609695976 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0903848791820560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10792365168171382 " " Order of pole (three term test) = 22.951009913007173 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y[1] (analytic) = 1.5704475326890321 " " y[1] (numeric) = 1.5704475326890401 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.090017724828989000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.88195312052466100E-2 " " Order of pole (three term test) = 22.95928074312941 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y[1] (analytic) = 1.5705406260680237 " " y[1] (numeric) = 1.570540626068032 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2310970158057660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.95573205592266500E-2 " " Order of pole (three term test) = 22.9668168220373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y[1] (analytic) = 1.5706155038037883 " " y[1] (numeric) = 1.5706155038037966 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.230847627779760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.01518373048547100E-2 " " Order of pole (three term test) = 22.97360609361222 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y[1] (analytic) = 1.5706741358795644 " " y[1] (numeric) = 1.5706741358795726 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2306523641999510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.06181282089417800E-2 " " Order of pole (three term test) = 22.97963769646793 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y[1] (analytic) = 1.5707184987766374 " " y[1] (numeric) = 1.5707184987766456 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2305046312403910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.09714451722917200E-2 " " Order of pole (three term test) = 22.984901981326544 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y[1] (analytic) = 1.5707505746837744 " " y[1] (numeric) = 1.5707505746837824 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0890357171509610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.12272208299139400E-2 " " Order of pole (three term test) = 22.989390526455274 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y[1] (analytic) = 1.570772350704374 " " y[1] (numeric) = 1.5707723507043823 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.230325310056579000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.14010438620992400E-2 " " Order of pole (three term test) = 22.993096151139426 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y[1] (analytic) = 1.5707858180616532 " " y[1] (numeric) = 1.5707858180616612 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0889215355695160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.15086340558568600E-2 " " Order of pole (three term test) = 22.996012927169982 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y[1] (analytic) = 1.5707929713021822 " " y[1] (numeric) = 1.5707929713021902 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0888983611089470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.156581715660853500E-2 " " Order of pole (three term test) = 22.998136188327525 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999999772 " " y[1] (analytic) = 1.5707958074980948 " " y[1] (numeric) = 1.5707958074981028 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0888891727009670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.158849955037192800E-2 " " Order of pole (three term test) = 22.999462537847112 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999977 " " y[1] (analytic) = 1.5707963254482846 " " y[1] (numeric) = 1.5707963254482926 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0888874947042270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.5926428169361265000E-3 " " Order of pole (three term test) = 22.99998985385248 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999977 " " y[1] (analytic) = 1.5707965248789124 " " y[1] (numeric) = 1.5707965248789206 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2302448166286050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.405761805261094000E-3 " " Order of pole (three term test) = 22.9997172927505 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1599999999999766 " " y[1] (analytic) = 1.5707984056435433 " " y[1] (numeric) = 1.5707984056435513 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.088880755532860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.839071900170346500E-2 " " Order of pole (three term test) = 22.99864529058079 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1699999999999764 " " y[1] (analytic) = 1.5708039669232305 " " y[1] (numeric) = 1.5708039669232385 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0888627388421890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.834625497088722500E-2 " " Order of pole (three term test) = 22.996775562318142 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999976 " " y[1] (analytic) = 1.5708152064268703 " " y[1] (numeric) = 1.5708152064268783 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0888263269898980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.82564429789961500E-2 " " Order of pole (three term test) = 22.994111099128915 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999976 " " y[1] (analytic) = 1.5708341195921456 " " y[1] (numeric) = 1.5708341195921536 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0887650564762390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.8105428839277903E-2 " " Order of pole (three term test) = 22.99065616358582 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999758 " " y[1] (analytic) = 1.5708626987873766 " " y[1] (numeric) = 1.5708626987873846 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0886724749857330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.78774562753610000E-2 " " Order of pole (three term test) = 22.986416282848733 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999999755 " " y[1] (analytic) = 1.5709029325146004 " " y[1] (numeric) = 1.5709029325146084 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0885421446794790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.75568921279356500E-2 " " Order of pole (three term test) = 22.981398239822354 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999999753 " " y[1] (analytic) = 1.570956804614197 " " y[1] (numeric) = 1.570956804614205 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0883676456427030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.71282513644739900E-2 " " Order of pole (three term test) = 22.975610062305076 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.229999999999975 " " y[1] (analytic) = 1.5710262934713788 " " y[1] (numeric) = 1.5710262934713868 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0881425794843050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.65762218519786600E-2 " " Order of pole (three term test) = 22.969061010146174 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999975 " " y[1] (analytic) = 1.5711133712248637 " " y[1] (numeric) = 1.5711133712248717 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0878605730846720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.58856888531291400E-2 " " Order of pole (three term test) = 22.961761560432045 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999747 " " y[1] (analytic) = 1.5712200029780459 " " y[1] (numeric) = 1.5712200029780536 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.9461954135296770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10504175920663733 " " Order of pole (three term test) = 22.953723390725123 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2599999999999745 " " y[1] (analytic) = 1.5713481460129795 " " y[1] (numeric) = 1.5713481460129874 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0871003969320880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11402978515312837 " " Order of pole (three term test) = 22.944959360382185 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2699999999999743 " " y[1] (analytic) = 1.5714997490074938 " " y[1] (numeric) = 1.5714997490075018 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0866096430175180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12283538776843116 " " Order of pole (three term test) = 22.935483489982246 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999974 " " y[1] (analytic) = 1.5716767512557464 " " y[1] (numeric) = 1.5716767512557543 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0860367889989820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1314444799667897 " " Order of pole (three term test) = 22.925310938896516 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999974 " " y[1] (analytic) = 1.571881081892532 " " y[1] (numeric) = 1.5718810818925402 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2266360839043770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13984328903719492 " " Order of pole (three term test) = 22.914457981036726 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999999736 " " y[1] (analytic) = 1.5721146591216548 " " y[1] (numeric) = 1.572114659121663 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2258595354719650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1480183786767847 " " Order of pole (three term test) = 22.90294197882025 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999999734 " " y[1] (analytic) = 1.5723793894486715 " " y[1] (numeric) = 1.5723793894486797 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2249796946949540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15595667048606163 " " Order of pole (three term test) = 22.89078135539405 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.319999999999973 " " y[1] (analytic) = 1.5726771669183153 " " y[1] (numeric) = 1.5726771669183235 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2239903745311240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1636454648915427 " " Order of pole (three term test) = 22.87799556516145 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.329999999999973 " " y[1] (analytic) = 1.573009872356903 " " y[1] (numeric) = 1.573009872356911 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0817263882292040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1710724614623681 " " Order of pole (three term test) = 22.864605062659347 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999728 " " y[1] (analytic) = 1.5733793726200291 " " y[1] (numeric) = 1.5733793726200371 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0805329702460660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1782257785883657 " " Order of pole (three term test) = 22.850631269835258 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3499999999999726 " " y[1] (analytic) = 1.5737875198458493 " " y[1] (numeric) = 1.5737875198458573 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0792153810471770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1850939724880936 " " Order of pole (three term test) = 22.836096541776776 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3599999999999723 " " y[1] (analytic) = 1.5742361507142495 " " y[1] (numeric) = 1.5742361507142575 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0777678899536980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1916660555164489 " " Order of pole (three term test) = 22.82102413094822 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999972 " " y[1] (analytic) = 1.574727085712198 " " y[1] (numeric) = 1.574727085712206 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0761848512219370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19793151374255574 " " Order of pole (three term test) = 22.80543814999165 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999972 " " y[1] (analytic) = 1.575262128405576 " " y[1] (numeric) = 1.5752621284055839 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0744607092103280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20388032376981208 " " Order of pole (three term test) = 22.78936353315175 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999717 " " y[1] (analytic) = 1.5758430647177735 " " y[1] (numeric) = 1.5758430647177815 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0725900035818260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20950296877118618 " " Order of pole (three term test) = 22.772825996386416 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999999715 " " y[1] (analytic) = 1.576471662215346 " " y[1] (numeric) = 1.576471662215354 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 5.0705673745305810000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21479045371410949 " " Order of pole (three term test) = 22.75585199622662 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999999713 " " y[1] (analytic) = 1.5771496694010099 " " y[1] (numeric) = 1.577149669401018 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2091761115775430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2197343197506098 " " Order of pole (three term test) = 22.738468687451725 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.419999999999971 " " y[1] (analytic) = 1.577878815014265 " " y[1] (numeric) = 1.5778788150142733 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2067689255032450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22432665774966415 " " Order of pole (three term test) = 22.720703879647502 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.429999999999971 " " y[1] (analytic) = 1.5786608073399222 " " y[1] (numeric) = 1.5786608073399304 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.204189743628150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22856012095012038 " " Order of pole (three term test) = 22.702585992716834 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999999706 " " y[1] (analytic) = 1.5794973335248117 " " y[1] (numeric) = 1.57949733352482 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.2014335243555520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23242793671394843 " " Order of pole (three term test) = 22.684144011413856 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4499999999999704 " " y[1] (analytic) = 1.5803900589029474 " " y[1] (numeric) = 1.5803900589029556 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.1984953562218560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2359239173610164 " " Order of pole (three term test) = 22.66540743897458 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999997 " " y[1] (analytic) = 1.581340626329415 " " y[1] (numeric) = 1.5813406263294232 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.1953704631596090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23904247006805798 " " Order of pole (three term test) = 22.646406249917977 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.46999999999997 " " y[1] (analytic) = 1.5823506555232523 " " y[1] (numeric) = 1.5823506555232605 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.1920542096969050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24177860581599828 " " Order of pole (three term test) = 22.627170842093186 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.47999999999997 " " y[1] (analytic) = 1.5834217424195827 " " y[1] (numeric) = 1.583421742419591 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.3287729738116290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24412794737131788 " " Order of pole (three term test) = 22.607731988049363 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999999696 " " y[1] (analytic) = 1.5845554585312631 " " y[1] (numeric) = 1.5845554585312716 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.3249603487984920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24608673628869462 " " Order of pole (three term test) = 22.588120785806264 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999999694 " " y[1] (analytic) = 1.585753350320299 " " y[1] (numeric) = 1.5857533503203074 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.3209378277188560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2476518389237134 " " Order of pole (three term test) = 22.568368609103977 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.509999999999969 " " y[1] (analytic) = 1.5870169385792805 " " y[1] (numeric) = 1.587016938579289 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.3167012790076020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24882075144602886 " " Order of pole (three term test) = 22.54850705721164 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.519999999999969 " " y[1] (analytic) = 1.588347717823086 " " y[1] (numeric) = 1.5883477178230945 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.3122467407297280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2495916038449601 " " Order of pole (three term test) = 22.528567904375393 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999687 " " y[1] (analytic) = 1.589747155691096 " " y[1] (numeric) = 1.5897471556911043 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 5.167897519310010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24996316292110848 " " Order of pole (three term test) = 22.50858304898631 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999999685 " " y[1] (analytic) = 1.5912166923601558 " " y[1] (numeric) = 1.5912166923601643 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.3026687236645720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24993483425921395 " " Order of pole (three term test) = 22.4885844625498 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5499999999999683 " " y[1] (analytic) = 1.592757739968526 " " y[1] (numeric) = 1.5927577399685344 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2975382102477960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2495066631790924 " " Order of pole (three term test) = 22.468604138538023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999968 " " y[1] (analytic) = 1.5943716820510443 " " y[1] (numeric) = 1.5943716820510527 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2921756464569810000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24867933466313374 " " Order of pole (three term test) = 22.448674041207163 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999968 " " y[1] (analytic) = 1.596059872985731 " " y[1] (numeric) = 1.5960598729857394 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2865779849266490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24745417226047597 " " Order of pole (three term test) = 22.4288260544614 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999999677 " " y[1] (analytic) = 1.5978236374520551 " " y[1] (numeric) = 1.5978236374520636 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2807423731734440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2458331359696098 " " Order of pole (three term test) = 22.409091930845552 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999999674 " " y[1] (analytic) = 1.5996642699010812 " " y[1] (numeric) = 1.5996642699010897 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.274666157088670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24381881910279737 " " Order of pole (three term test) = 22.38950324074766 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999999672 " " y[1] (analytic) = 1.6015830340377053 " " y[1] (numeric) = 1.6015830340377137 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2683468841944190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24141444413732788 " " Order of pole (three term test) = 22.37009132189318 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.609999999999967 " " y[1] (analytic) = 1.6035811623151899 " " y[1] (numeric) = 1.6035811623151983 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2617823066524220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23862385756024015 " " Order of pole (three term test) = 22.350887229211306 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.619999999999967 " " y[1] (analytic) = 1.6056598554421997 " " y[1] (numeric) = 1.6056598554422081 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.254970384015389000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23545152371476405 " " Order of pole (three term test) = 22.331921685153663 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999999666 " " y[1] (analytic) = 1.6078202819025338 " " y[1] (numeric) = 1.6078202819025422 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2479092857112520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23190251765832384 " " Order of pole (three term test) = 22.31322503054498 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999999664 " " y[1] (analytic) = 1.6100635774877474 " " y[1] (numeric) = 1.6100635774877559 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 5.2405973932513240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22798251704352918 " " Order of pole (three term test) = 22.294827176044226 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999966 " " y[1] (analytic) = 1.6123908448428508 " " y[1] (numeric) = 1.6123908448428594 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 5.3707447048424730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22369779303514123 " " Order of pole (three term test) = 22.276757554293933 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999966 " " y[1] (analytic) = 1.6148031530252662 " " y[1] (numeric) = 1.6148031530252749 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 5.3627215031457920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21905520027754774 " " Order of pole (three term test) = 22.259045072834247 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999657 " " y[1] (analytic) = 1.6173015370772186 " " y[1] (numeric) = 1.6173015370772272 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 5.3544372484342480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21406216592879385 " " Order of pole (three term test) = 22.24171806785705 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999999655 " " y[1] (analytic) = 1.6198869976117325 " " y[1] (numeric) = 1.6198869976117412 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 5.3458911670034000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.208726677778714 " " Order of pole (three term test) = 22.224804258874073 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999999653 " " y[1] (analytic) = 1.6225605004124006 " " y[1] (numeric) = 1.6225605004124095 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.4739309842337470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20305727147017139 " " Order of pole (three term test) = 22.20833070437162 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.699999999999965 " " y[1] (analytic) = 1.6253229760470835 " " y[1] (numeric) = 1.6253229760470924 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.4646272327992720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1970630168438507 " " Order of pole (three term test) = 22.192323758522697 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.709999999999965 " " y[1] (analytic) = 1.6281753194956938 " " y[1] (numeric) = 1.6281753194957027 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 5.4550539433015540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19075350342844816 " " Order of pole (three term test) = 22.176809029026042 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999647 " " y[1] (analytic) = 1.631118389792217 " " y[1] (numeric) = 1.6311183897922261 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 5.5813415254830110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18413882509947033 " " Order of pole (three term test) = 22.161811336139206 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999999645 " " y[1] (analytic) = 1.6341530096811092 " " y[1] (numeric) = 1.6341530096811185 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 5.7068544693199690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17722956393118786 " " Order of pole (three term test) = 22.147354672971492 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999999642 " " y[1] (analytic) = 1.6372799652882102 " " y[1] (numeric) = 1.6372799652882195 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 5.695955245631850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17003677326757272 " " Order of pole (three term test) = 22.133462167100028 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999964 " " y[1] (analytic) = 1.6405000058063035 " " y[1] (numeric) = 1.6405000058063128 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 5.6847749916755790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16257196003930643 " " Order of pole (three term test) = 22.120156043570635 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999964 " " y[1] (analytic) = 1.6438138431954492 " " y[1] (numeric) = 1.6438138431954588 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 5.8083937249341560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1548470663551459 " " Order of pole (three term test) = 22.107457589342474 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7699999999999636 " " y[1] (analytic) = 1.6472221518982102 " " y[1] (numeric) = 1.6472221518982197 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 5.7963754316766610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14687445039709612 " " Order of pole (three term test) = 22.095387119233454 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999999634 " " y[1] (analytic) = 1.6507255685698827 " " y[1] (numeric) = 1.6507255685698923 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 5.7840734968734090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13866686664995617 " " Order of pole (three term test) = 22.083963943420848 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.789999999999963 " " y[1] (analytic) = 1.6543246918238441 " " y[1] (numeric) = 1.6543246918238537 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 5.7714897558894860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13023744549686328 " " Order of pole (three term test) = 22.07320633654914 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.799999999999963 " " y[1] (analytic) = 1.6580200819921145 " " y[1] (numeric) = 1.6580200819921243 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 5.8925478182162590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12159967221348206 " " Order of pole (three term test) = 22.063131508494493 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999627 " " y[1] (analytic) = 1.6618122609012322 " " y[1] (numeric) = 1.661812260901242 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 5.8791012959568270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1127673653944392 " " Order of pole (three term test) = 22.053755576832618 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999999625 " " y[1] (analytic) = 1.6657017116635295 " " y[1] (numeric) = 1.6657017116635393 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 5.8653734629018030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10375465484652037 " " Order of pole (three term test) = 22.04509354105408 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999999623 " " y[1] (analytic) = 1.6696888784838944 " " y[1] (numeric) = 1.6696888784839041 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 5.8513671274930380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.45759589839929100E-2 " " Order of pole (three term test) = 22.03715925856831 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999962 " " y[1] (analytic) = 1.6737741664820942 " " y[1] (numeric) = 1.673774166482104 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 5.8370853203187460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.52459617622196100E-2 " " Order of pole (three term test) = 22.029965422534747 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999962 " " y[1] (analytic) = 1.6779579415307337 " " y[1] (numeric) = 1.6779579415307437 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.9548615458806440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.57795891864619900E-2 " " Order of pole (three term test) = 22.023523541556433 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999617 " " y[1] (analytic) = 1.682240530108911 " " y[1] (numeric) = 1.682240530108921 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.939701869493961000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.61919854334559700E-2 " " Order of pole (three term test) = 22.01784392126874 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8699999999999615 " " y[1] (analytic) = 1.686622219171629 " " y[1] (numeric) = 1.6866222191716391 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 6.0559215397790680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.649848862396111000E-2 " " Order of pole (three term test) = 22.012935647852526 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999999613 " " y[1] (analytic) = 1.6911032560350188 " " y[1] (numeric) = 1.691103256035029 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 6.0398747327229620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.67146062850353650E-2 " " Order of pole (three term test) = 22.008806573498244 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.889999999999961 " " y[1] (analytic) = 1.6956838482774155 " " y[1] (numeric) = 1.695683848277426 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 6.1545060077550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.68559905413045840E-2 " " Order of pole (three term test) = 22.00546330384402 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.899999999999961 " " y[1] (analytic) = 1.7003641636563303 " " y[1] (numeric) = 1.7003641636563407 " " absolute error = 1.043609643147647100000000000000E-14 " " relative error = 6.1375655018719670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.693841307489989000E-2 " " Order of pole (three term test) = 22.002911187408102 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999999606 " " y[1] (analytic) = 1.705144330041349 " " y[1] (numeric) = 1.7051443300413596 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2505799940953090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.697773989413032300E-2 " " Order of pole (three term test) = 22.001154307032373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999999604 " " y[1] (analytic) = 1.7100244353629868 " " y[1] (numeric) = 1.7100244353629974 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2327419515143360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.98990595125497000E-3 " " Order of pole (three term test) = 22.00019547335066 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.92999999999996 " " y[1] (analytic) = 1.715004527577516 " " y[1] (numeric) = 1.715004527577527 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 6.3441148209066530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.0091103500421224000E-3 " " Order of pole (three term test) = 22.0000362202923 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.93999999999996 " " y[1] (analytic) = 1.720084614647786 " " y[1] (numeric) = 1.7200846146477968 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 6.3253781521407430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.30033127166883600E-2 " " Order of pole (three term test) = 22.000676802628234 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999598 " " y[1] (analytic) = 1.725264664540036 " " y[1] (numeric) = 1.725264664540047 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 6.306386414183730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.29767125568800500E-2 " " Order of pole (three term test) = 22.00211619556335 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9599999999999596 " " y[1] (analytic) = 1.73054460523671 " " y[1] (numeric) = 1.7305446052367208 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 6.2871454502834420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.291335455841837000E-2 " " Order of pole (three term test) = 22.004352096376014 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9699999999999593 " " y[1] (analytic) = 1.7359243247652616 " " y[1] (numeric) = 1.7359243247652725 " " absolute error = 1.088018564132653400000000000000E-14 " " relative error = 6.2676612604053430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.2797342213803700E-2 " " Order of pole (three term test) = 22.007380928101906 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999959 " " y[1] (analytic) = 1.7414036712429422 " " y[1] (numeric) = 1.7414036712429535 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 6.5029579517848360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.261286325126033000E-2 " " Order of pole (three term test) = 22.011197845256373 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.989999999999959 " " y[1] (analytic) = 1.7469824529375524 " " y[1] (numeric) = 1.7469824529375637 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 6.4821915252410360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.234421493099336000E-2 " " Order of pole (three term test) = 22.015796741586186 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999587 " " y[1] (analytic) = 1.7526604383441309 " " y[1] (numeric) = 1.7526604383441424 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 6.5878816018750870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.19758291662268600E-2 " " Order of pole (three term test) = 22.021170259838282 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999959 " " y[1] (analytic) = 1.7584373562775553 " " y[1] (numeric) = 1.7584373562775666 " " absolute error = 1.132427485117659700000000000000E-14 " " relative error = 6.4399648988059540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.14922974288194600E-2 " " Order of pole (three term test) = 22.027309803529736 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999959 " " y[1] (analytic) = 1.7643128959810102 " " y[1] (numeric) = 1.7643128959810217 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 6.5443717395045910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.08783953996217300E-2 " " Order of pole (three term test) = 22.034205550700353 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999999585 " " y[1] (analytic) = 1.7702867072502881 " " y[1] (numeric) = 1.7702867072503 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 6.6477164477532370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10011910732414175 " " Order of pole (three term test) = 22.041846469625664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999958 " " y[1] (analytic) = 1.7763584005738657 " " y[1] (numeric) = 1.7763584005738775 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 6.62499417754030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10919965003454674 " " Order of pole (three term test) = 22.05022033646536 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999958 " " y[1] (analytic) = 1.7825275472887023 " " y[1] (numeric) = 1.7825275472887143 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 6.7266330240952490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11810549659957996 " " Order of pole (three term test) = 22.059313754818845 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999958 " " y[1] (analytic) = 1.7887936797517006 " " y[1] (numeric) = 1.7887936797517128 " " absolute error = 1.221245327087672200000000000000E-14 " " relative error = 6.8272005928441750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12682239956454888 " " Order of pole (three term test) = 22.06911217715656 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999958 " " y[1] (analytic) = 1.7951562915267567 " " y[1] (numeric) = 1.7951562915267691 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 6.9266937561332760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13533641374421693 " " Order of pole (three term test) = 22.079599928092993 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999957 " " y[1] (analytic) = 1.8016148375873287 " " y[1] (numeric) = 1.8016148375873413 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 7.0251100383232110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14363391853212257 " " Order of pole (three term test) = 22.09076022946391 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999957 " " y[1] (analytic) = 1.8081687345344393 " " y[1] (numeric) = 1.808168734534452 " " absolute error = 1.265654248072678500000000000000E-14 " " relative error = 6.9996467912523360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1517016396906457 " " Order of pole (three term test) = 22.102575227167865 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999957 " " y[1] (analytic) = 1.814817360830028 " " y[1] (numeric) = 1.8148173608300409 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 7.0963543569814890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15952667058695394 " " Order of pole (three term test) = 22.115026019728905 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999957 " " y[1] (analytic) = 1.821560057045558 " " y[1] (numeric) = 1.821560057045571 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 7.1919844969729670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16709649284086464 " " Order of pole (three term test) = 22.12809268853499 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999957 " " y[1] (analytic) = 1.8283961261257786 " " y[1] (numeric) = 1.8283961261257917 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 7.1650948628599480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17439899635158057 " " Order of pole (three term test) = 22.14175432970342 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999956 " " y[1] (analytic) = 1.8353248336675385 " " y[1] (numeric) = 1.8353248336675516 " " absolute error = 1.310063169057684700000000000000E-14 " " relative error = 7.1380452387808590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18142249867126906 " " Order of pole (three term test) = 22.15598908752266 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999956 " " y[1] (analytic) = 1.8423454082135364 " " y[1] (numeric) = 1.8423454082135498 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 7.2313672757056190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18815576369448567 " " Order of pole (three term test) = 22.170774189416782 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999956 " " y[1] (analytic) = 1.849457041560895 " " y[1] (numeric) = 1.8494570415609084 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 7.2035608268348180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1945880196335467 " " Order of pole (three term test) = 22.186085982376735 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999956 " " y[1] (analytic) = 1.85665888908443 " " y[1] (numeric) = 1.8566588890844433 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 7.175618727719910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20070897625109105 " " Order of pole (three term test) = 22.20189997080014 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.1699999999999555 " " y[1] (analytic) = 1.8639500700744893 " " y[1] (numeric) = 1.8639500700745029 " " absolute error = 1.35447209004269100000000000000E-14 " " relative error = 7.2666758181379940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20650884132226488 " " Order of pole (three term test) = 22.218190855678987 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999955 " " y[1] (analytic) = 1.8713296680892255 " " y[1] (numeric) = 1.8713296680892395 " " absolute error = 1.398881011027697200000000000000E-14 " " relative error = 7.4753317647983670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21197833630019317 " " Order of pole (three term test) = 22.234932575072666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999955 " " y[1] (analytic) = 1.8787967313211607 " " y[1] (numeric) = 1.8787967313211749 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.5638063864466070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21710871115967453 " " Order of pole (three term test) = 22.252098345801524 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999955 " " y[1] (analytic) = 1.8863502729778956 " " y[1] (numeric) = 1.8863502729779098 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.5335185192132810000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2218917583953553 " " Order of pole (three term test) = 22.269660706294236 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999955 " " y[1] (analytic) = 1.893989271676814 " " y[1] (numeric) = 1.8939892716768285 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 7.6203701551852450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22631982615198734 " " Order of pole (three term test) = 22.287591560520454 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.2199999999999545 " " y[1] (analytic) = 1.9017126718536232 " " y[1] (numeric) = 1.9017126718536377 " " absolute error = 1.443289932012703500000000000000E-14 " " relative error = 7.5894216480448160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23038583046576422 " " Order of pole (three term test) = 22.305862222938448 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999954 " " y[1] (analytic) = 1.9095193841845635 " " y[1] (numeric) = 1.9095193841845781 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 7.6746766995037750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23408326659715178 " " Order of pole (three term test) = 22.324443464385897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999954 " " y[1] (analytic) = 1.9174082860221247 " " y[1] (numeric) = 1.9174082860221398 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 7.8747094424144480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23740621943708437 " " Order of pole (three term test) = 22.343305558840257 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999954 " " y[1] (analytic) = 1.9253782218440905 " " y[1] (numeric) = 1.9253782218441056 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 7.8421127670388650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24034937296987646 " " Order of pole (three term test) = 22.36241833097411 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999954 " " y[1] (analytic) = 1.9334280037157303 " " y[1] (numeric) = 1.9334280037157456 " " absolute error = 1.53210777398271600000000000000E-14 " " relative error = 7.9243073496311070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2429080187777153 " " Order of pole (three term test) = 22.381751204429218 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999953 " " y[1] (analytic) = 1.9415564117649586 " " y[1] (numeric) = 1.9415564117649744 " " absolute error = 1.576516694967722300000000000000E-14 " " relative error = 8.1198603626180530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2450780635731234 " " Order of pole (three term test) = 22.40127325073217 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999953 " " y[1] (analytic) = 1.9497621946702677 " " y[1] (numeric) = 1.9497621946702837 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 8.1995699774586710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2468560357473464 " " Order of pole (three term test) = 22.420953238773375 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999953 " " y[1] (analytic) = 1.9580440701612385 " " y[1] (numeric) = 1.9580440701612545 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 8.1648885222924320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24823909092418595 " " Order of pole (three term test) = 22.44075968477012 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999953 " " y[1] (analytic) = 1.966400725531432 " " y[1] (numeric) = 1.9664007255314484 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 8.3560286319624180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24922501651039533 " " Order of pole (three term test) = 22.460660902633986 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3099999999999525 " " y[1] (analytic) = 1.9748308181634555 " " y[1] (numeric) = 1.974830818163472 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 8.3203586926666580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24981223523535603 " " Order of pole (three term test) = 22.480625054661736 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999952 " " y[1] (analytic) = 1.9833329760659897 " " y[1] (numeric) = 1.9833329760660063 " " absolute error = 1.665334536937734800000000000000E-14 " " relative error = 8.3966462365839560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24999980767437482 " " Order of pole (three term test) = 22.50062020246893 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999952 " " y[1] (analytic) = 1.9919057984225685 " " y[1] (numeric) = 1.9919057984225854 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 8.4719819519910790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2497874337515625 " " Order of pole (three term test) = 22.520614358084476 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999952 " " y[1] (analytic) = 2.000547856151887 " " y[1] (numeric) = 2.0005478561519037 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 8.4353842985604420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24917545321989173 " " Order of pole (three term test) = 22.540575535124585 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999952 " " y[1] (analytic) = 2.009257692479412 " " y[1] (numeric) = 2.009257692479429 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 8.619839679588490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2481648451176641 " " Order of pole (three term test) = 22.56047179996414 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3599999999999515 " " y[1] (analytic) = 2.018033823520078 " " y[1] (numeric) = 2.018033823520095 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 8.5823532699476210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2467572262022584 " " Order of pole (three term test) = 22.580271322823727 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999951 " " y[1] (analytic) = 2.026874738871815 " " y[1] (numeric) = 2.026874738871833 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 8.7640188381300450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24495484836366327 " " Order of pole (three term test) = 22.59994242869042 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999951 " " y[1] (analytic) = 2.035778902219695 " " y[1] (numeric) = 2.0357789022197132 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 8.9438286171450130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24276059502193348 " " Order of pole (three term test) = 22.619453647991115 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999950 " " y[1] (analytic) = 2.044744751950433 " " y[1] (numeric) = 2.044744751950452 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 9.121797131847960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.24017797651433367 " " Order of pole (three term test) = 22.638773766937128 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999950 " " y[1] (analytic) = 2.053770701777015 " " y[1] (numeric) = 2.0537707017770335 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 9.0817084874978020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2372111244795467 " " Order of pole (three term test) = 22.657871877459527 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.40999999999995 " " y[1] (analytic) = 2.0628551413731873 " " y[1] (numeric) = 2.0628551413732064 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 9.256993203527180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23386478524793342 " " Order of pole (three term test) = 22.67671742665553 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999995 " " y[1] (analytic) = 2.071996437017571 " " y[1] (numeric) = 2.0719964370175905 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 9.4304820627628570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.23014431224841683 " " Order of pole (three term test) = 22.695280265666582 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.42999999999995 " " y[1] (analytic) = 2.081192932247125 " " y[1] (numeric) = 2.0811929322471445 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 9.3888101053201840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22605565744413772 " " Order of pole (three term test) = 22.713530697910144 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.43999999999995 " " y[1] (analytic) = 2.0904429485197094 " " y[1] (numeric) = 2.0904429485197293 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 9.5597033429704260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2216053618105831 " " Order of pole (three term test) = 22.73143952658784 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4499999999999496 " " y[1] (analytic) = 2.099744785885482 " " y[1] (numeric) = 2.099744785885502 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 9.5173540030129770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21680054487142053 " " Order of pole (three term test) = 22.74897810139412 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999950 " " y[1] (analytic) = 2.1090967236668523 " " y[1] (numeric) = 2.1090967236668727 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 9.6857120983938570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21164889330878012 " " Order of pole (three term test) = 22.766118364350664 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999950 " " y[1] (analytic) = 2.118497021146734 " " y[1] (numeric) = 2.1184970211467546 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 9.6427341880543350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20615864866620146 " " Order of pole (three term test) = 22.782832894693147 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999949 " " y[1] (analytic) = 2.1279439182648052 " " y[1] (numeric) = 2.1279439182648257 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 9.599925767668080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.20033859416392313 " " Order of pole (three term test) = 22.799094952738578 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999949 " " y[1] (analytic) = 2.137435636321509 " " y[1] (numeric) = 2.1374356363215297 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 9.765062633125011000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1941980406476033 " " Order of pole (three term test) = 22.81487852266315 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999999485 " " y[1] (analytic) = 2.146970378689512 " " y[1] (numeric) = 2.1469703786895327 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 9.7216957765822130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18774681169295312 " " Order of pole (three term test) = 22.830158354121963 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999948 " " y[1] (analytic) = 2.1565463315323283 " " y[1] (numeric) = 2.1565463315323496 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 9.8844535640728740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18099522789011124 " " Order of pole (three term test) = 22.84491000264421 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999948 " " y[1] (analytic) = 2.1661616645298345 " " y[1] (numeric) = 2.166161664529856 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 9.8405776548675580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17395409033290135 " " Order of pole (three term test) = 22.859109868739093 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999948 " " y[1] (analytic) = 2.175814531610367 " " y[1] (numeric) = 2.175814531610389 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 1.0001023049766906000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16663466333938548 " " Order of pole (three term test) = 22.872735235650023 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999948 " " y[1] (analytic) = 2.185503071689132 " " y[1] (numeric) = 2.185503071689154 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 9.956687576666230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.159048656431359 " " Order of pole (three term test) = 22.88576430569652 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999947 " " y[1] (analytic) = 2.1952254094126107 " " y[1] (numeric) = 2.195225409412633 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 1.0114888611117392000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.15120820560161272 " " Order of pole (three term test) = 22.898176235145904 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999947 " " y[1] (analytic) = 2.2049796559086774 " " y[1] (numeric) = 2.2049796559086996 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 1.007014302059518000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14312585389893417 " " Order of pole (three term test) = 22.909951167558777 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999947 " " y[1] (analytic) = 2.2147639095421225 " " y[1] (numeric) = 2.2147639095421447 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 1.0025655735510723000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.13481453136190436 " " Order of pole (three term test) = 22.92107026555514 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999947 " " y[1] (analytic) = 2.224576256675282 " " y[1] (numeric) = 2.2245762566753045 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 1.0181062408803354000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12628753433359505 " " Order of pole (three term test) = 22.931515740950154 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999947 " " y[1] (analytic) = 2.2344147724334666 " " y[1] (numeric) = 2.2344147724334893 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 1.0136233425312978000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1175585041902558 " " Order of pole (three term test) = 22.941270883211434 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999946 " " y[1] (analytic) = 2.2442775214748854 " " y[1] (numeric) = 2.2442775214749084 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.028956476693993000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10864140551802211 " " Order of pole (three term test) = 22.950320086192335 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999946 " " y[1] (analytic) = 2.2541625587647576 " " y[1] (numeric) = 2.254162558764781 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 1.0441451097010075000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.95505037725568500E-2 " " Order of pole (three term test) = 22.958648873098497 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999946 " " y[1] (analytic) = 2.2640679303533005 " " y[1] (numeric) = 2.2640679303533244 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 1.0591915997927347000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.03003424573636100E-2 " " Order of pole (three term test) = 22.966243919647578 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999946 " " y[1] (analytic) = 2.2739916741572825 " " y[1] (numeric) = 2.273991674157307 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 1.0740983275941438000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.09057198572843300E-2 " " Order of pole (three term test) = 22.973093075385272 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.6399999999999455 " " y[1] (analytic) = 2.2839318207448316 " " y[1] (numeric) = 2.283931820744856 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 1.069423628144383100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.13816653643997600E-2 " " Order of pole (three term test) = 22.97918538312351 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999945 " " y[1] (analytic) = 2.29388639412318 " " y[1] (numeric) = 2.2938863941232044 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 1.0647827461869433000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.17434154342085400E-2 " " Order of pole (three term test) = 22.984511096469497 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999945 " " y[1] (analytic) = 2.3038534125290364 " " y[1] (numeric) = 2.303853412529061 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 1.0601762425041271000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.20063892105488300E-2 " " Order of pole (three term test) = 22.98906169541799 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999945 " " y[1] (analytic) = 2.3138308892212645 " " y[1] (numeric) = 2.3138308892212893 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.0747974654264097000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.218616385825691400E-2 " " Order of pole (three term test) = 22.992829899981423 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999945 " " y[1] (analytic) = 2.3238168332755533 " " y[1] (numeric) = 2.323816833275578 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.0701788280167171000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.229844964302674000E-2 " " Order of pole (three term test) = 22.99580968183631 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999944 " " y[1] (analytic) = 2.3338092503807593 " " y[1] (numeric) = 2.333809250380784 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.0655967597842946000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.235906479833619200E-2 " " Order of pole (three term test) = 22.99799627396736 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999944 " " y[1] (analytic) = 2.3438061436366047 " " y[1] (numeric) = 2.34380614363663 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 1.079999087389466000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.238391021964774000E-2 " " Order of pole (three term test) = 22.999386178293594 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999944 " " y[1] (analytic) = 2.3538055143524117 " " y[1] (numeric) = 2.3538055143524375 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 1.0942779262878076000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.3889440263678002000E-3 " " Order of pole (three term test) = 22.999977171264604 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999944 " " y[1] (analytic) = 2.363805362846552 " " y[1] (numeric) = 2.363805362846578 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 1.0896486900379232000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.609843967740115000E-3 " " Order of pole (three term test) = 22.999768307417693 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999944 " " y[1] (analytic) = 2.373803689246291 " " y[1] (numeric) = 2.373803689246317 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 1.1037670680119673000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.759645783484646600E-2 " " Order of pole (three term test) = 22.998759920890475 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999943 " " y[1] (analytic) = 2.3837984942877117 " " y[1] (numeric) = 2.3837984942877384 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 1.1177686643755302000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.755492112312784000E-2 " " Order of pole (three term test) = 22.996953624886256 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999943 " " y[1] (analytic) = 2.3937877801153955 " " y[1] (numeric) = 2.393787780115422 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 1.1131042113398744000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.746930241568189300E-2 " " Order of pole (three term test) = 22.994352309093358 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999943 " " y[1] (analytic) = 2.4037695510815333 " " y[1] (numeric) = 2.4037695510815604 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 1.126956691362755900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.7323740817395704E-2 " " Order of pole (three term test) = 22.990960135062103 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999943 " " y[1] (analytic) = 2.413741814544162 " " y[1] (numeric) = 2.413741814544189 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 1.1223007215446403000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.71024713289946600E-2 " " Order of pole (three term test) = 22.986782529547316 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.7799999999999425 " " y[1] (analytic) = 2.4237025816641915 " " y[1] (numeric) = 2.423702581664219 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 1.1360111269014898000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.67898500676781200E-2 " " Order of pole (three term test) = 22.98182617582666 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999942 " " y[1] (analytic) = 2.4336498682009173 " " y[1] (numeric) = 2.433649868200945 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 1.1313678015259493000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.63703792939947700E-2 " " Order of pole (three term test) = 22.97609900300879 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999942 " " y[1] (analytic) = 2.4435816953056877 " " y[1] (numeric) = 2.4435816953057152 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 1.1267694083483257000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.5828732204919600E-2 " " Order of pole (three term test) = 22.969610173348475 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999942 " " y[1] (analytic) = 2.453496090313417 " " y[1] (numeric) = 2.4534960903134446 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 1.1222162170711536000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.51497774534696600E-2 " " Order of pole (three term test) = 22.962370067588957 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999942 " " y[1] (analytic) = 2.463391087531627 " " y[1] (numeric) = 2.463391087531655 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 1.1357360332332836000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.10431860335563087 " " Order of pole (three term test) = 22.95439026835499 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.8299999999999415 " " y[1] (analytic) = 2.473264729026696 " " y[1] (numeric) = 2.4732647290267242 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.1491575930728938000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.11332054174587151 " " Order of pole (three term test) = 22.94568354162308 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999941 " " y[1] (analytic) = 2.4831150654070067 " " y[1] (numeric) = 2.4831150654070355 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.1624833275908898000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.12214119144307828 " " Order of pole (three term test) = 22.93626381629865 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999941 " " y[1] (analytic) = 2.492940156602678 " " y[1] (numeric) = 2.4929401566027067 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.1579017877264942000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1307664412893742 " " Order of pole (three term test) = 22.926146161932795 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999940 " " y[1] (analytic) = 2.5027380726415647 " " y[1] (numeric) = 2.5027380726415935 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.153368742650208000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1391824927249599 " " Order of pole (three term test) = 22.91534676461418 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999940 " " y[1] (analytic) = 2.5125068944212225 " " y[1] (numeric) = 2.512506894421252 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.1665594994061067000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.14737588186286735 " " Order of pole (three term test) = 22.903882901074763 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.87999999999994 " " y[1] (analytic) = 2.522244714476524 " " y[1] (numeric) = 2.522244714476553 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.1620556753228133000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1553335010283058 " " Order of pole (three term test) = 22.891772911050726 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.88999999999994 " " y[1] (analytic) = 2.531949637742616 " " y[1] (numeric) = 2.5319496377426454 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.1576015341377661000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.16304261972814502 " " Order of pole (three term test) = 22.87903616794276 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999994 " " y[1] (analytic) = 2.541619782312924 " " y[1] (numeric) = 2.541619782312954 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.1706698722999980000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17049090501698963 " " Order of pole (three term test) = 22.865693047822834 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90999999999994 " " y[1] (analytic) = 2.5512532801918875 " " y[1] (numeric) = 2.5512532801919177 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.183656146736358900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.17766644122726064 " " Order of pole (three term test) = 22.851764896836738 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9199999999999395 " " y[1] (analytic) = 2.5608482780421347 " " y[1] (numeric) = 2.560848278042165 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.179221218560118100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.18455774903172065 " " Order of pole (three term test) = 22.837273997054886 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999940 " " y[1] (analytic) = 2.5704029379257904 " " y[1] (numeric) = 2.5704029379258206 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.1748378366767996000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.19115380380795002 " " Order of pole (three term test) = 22.822243530825688 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999939 " " y[1] (analytic) = 2.5799154380396296 " " y[1] (numeric) = 2.5799154380396603 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.1877193735829582000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.1974440532753898 " " Order of pole (three term test) = 22.80669754368879 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999939 " " y[1] (analytic) = 2.5893839734437725 " " y[1] (numeric) = 2.5893839734438036 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.2005266506751787000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2034184343767406 " " Order of pole (three term test) = 22.790660905907313 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999939 " " y[1] (analytic) = 2.5988067567836373 " " y[1] (numeric) = 2.5988067567836683 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.1961737673784438000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.2090673893767072 " " Order of pole (three term test) = 22.774159272680745 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999385 " " y[1] (analytic) = 2.6081820190048575 " " y[1] (numeric) = 2.608182019004889 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.208900823240271000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21438188115233514 " " Order of pole (three term test) = 22.75721904310207 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999938 " " y[1] (analytic) = 2.617508010060881 " " y[1] (numeric) = 2.6175080100609125 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.2045935973514395000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.21935340765048186 " " Order of pole (three term test) = 22.739867317924897 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999938 " " y[1] (analytic) = 2.626782999612964 " " y[1] (numeric) = 2.626782999612996 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.217246461314684000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22397401548928556 " " Order of pole (three term test) = 22.72213185620802 " " "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999938 " " y[1] (analytic) = 2.636005277722285 " " y[1] (numeric) = 2.636005277722317 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.2129878259133423000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 0.22823631268188155 " " Order of pole (three term test) = 22.70404103090681 " " "NO COMPLEX POLE (six term test) for Equation 1" "Finished!" "diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; " Iterations = 491 "Total Elapsed Time "= 22 Seconds "Elapsed Time(since restart) "= 21 Seconds "Time to Timeout "= 9 Minutes 37 Seconds Percent Done = 100.40816326530484 "%" (%o226) true (%o226) diffeq.max