(%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