(%i1) batch("diffeq.max")
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load("stringproc")
(%o2) /usr/share/maxima/5.31.3/share/stringproc/stringproc.mac
(%i3) alias(convfloat,float)
(%o3) [convfloat]
(%i4) alias(int_trunc,truncate)
(%o4) [truncate]
(%i5) alias(elapsed_time_seconds,elapsed_real_time)
(%o5) [elapsed_time_seconds]
(%i6) alias(ln,log)
(%o6) [log]
(%i7) alias(arcsin,asin)
(%o7) [asin]
(%i8) alias(arccos,acos)
(%o8) [acos]
(%i9) alias(arctan,atan)
(%o9) [atan]
(%i10) alias(float_abs,abs)
(%o10) [mabs]
(%i11) keepfloat:true
(%o11) true
(%i12) mode_declare(display_poles(),fixnum)
(%o12) [display_poles()]
(%i13) mode_declare(est_size_answer(),convfloat)
(%o13) [est_size_answer()]
(%i14) mode_declare(test_suggested_h(),convfloat)
(%o14) [test_suggested_h()]
(%i15) mode_declare(reached_interval(),boolean)
(%o15) [reached_interval()]
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%o16) [display_alot([iter], fixnum)]
(%i17) mode_declare(adjust_for_pole([h_param],convfloat),convfloat)
(%o17) [adjust_for_pole([h_param], convfloat)]
(%i18) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%o18) [prog_report([x_start], convfloat, [x_end], convfloat)]
(%i19) mode_declare(check_for_pole(),fixnum)
(%o19) [check_for_pole()]
(%i20) mode_declare(atomall(),fixnum)
(%o20) [atomall()]
(%i21) mode_declare(log10([x],convfloat),convfloat)
(%o21) [log10([x], convfloat)]
(%i22) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%o22) [logitem_timestr([fd], fixnum, [secs_in], number)]
(%i23) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%o23) [omniout_timestr(secs_in, number)]
(%i24) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum)
(%o24) [zero_ats_ar(ar, array([MAX_TERMS], convfloat))]
(%i25) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_ats],
fixnum),convfloat)
(%o25) [ats([mmm_ats], fixnum, [arr_a], completearray([MAX_TERMS], convfloat),
[arr_b], completearray([MAX_TERMS], convfloat), [jjj_ats], fixnum)]
(%i26) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_att],
fixnum),convfloat)
(%o26) [att([mmm_att], fixnum, [arr_a], completearray([MAX_TERMS], convfloat),
[arr_b], completearray([MAX_TERMS], convfloat), [jjj_att], fixnum)]
(%i27) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%o27) [logitem_ditto([file], fixnum)]
(%i28) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%o28) [logitem_integer([file], fixnum, [n], fixnum)]
(%i29) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%o29) [logitem_good_digits([file], fixnum, [relerror], convfloat)]
(%i30) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%o30) [logitem_number([file], fixnum, [x], number)]
(%i31) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%o31) [logitem_pole([file], fixnum, [pole], fixnum)]
(%i32) mode_declare(logstart([file],fixnum),fixnum)
(%o32) [logstart([file], fixnum)]
(%i33) mode_declare(logend([file],fixnum),fixnum)
(%o33) [logend([file], fixnum)]
(%i34) mode_declare(chk_data(),fixnum)
(%o34) [chk_data()]
(%i35) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%o35) [comp_expect_sec([t_end2], convfloat, [t_start2], convfloat, [t2],
convfloat, [clock_sec2], convfloat)]
(%i36) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%o36) [comp_percent([t_end2], convfloat, [start2], convfloat, [t2],
convfloat)]
(%i37) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%o37) [comp_rad_from_ratio([term1], convfloat, [term2], convfloat, [last_no],
fixnum)]
(%i38) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%o38) [comp_ord_from_ratio([term1], convfloat, [term2], convfloat, [last_no],
fixnum)]
(%i39) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%o39) [comp_rad_from_three_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [last_no], fixnum)]
(%i40) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%o40) [comp_ord_from_three_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [last_no], fixnum)]
(%i41) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%o41) [comp_rad_from_six_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [term4], convfloat, [term5], convfloat, [term6],
convfloat, [last_no], fixnum)]
(%i42) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%o42) [comp_ord_from_six_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [term4], convfloat, [term5], convfloat, [term6],
convfloat, [last_no], fixnum)]
(%i43) mode_declare(factorial_2([nnn],fixnum),fixnum)
(%o43) [factorial_2([nnn], fixnum)]
(%i44) mode_declare(factorial_1([nnn],fixnum),fixnum)
(%o44) [factorial_1([nnn], fixnum)]
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum)
(%o45) [factorial_3([mmm], fixnum, [nnn], fixnum)]
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%o46) [convfloat([mmm], fixnum)]
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%o47) [elaped_time_seconds()]
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%o48) [Si([x], convfloat)]
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%o49) [Ci([x], convfloat)]
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%o50) [estimated_needed_step_error([x_start], convfloat, [x_end], convfloat,
[estimated_h], convfloat, [estimated_answer], convfloat)]
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%o51) [my_check_sign([x0], convfloat, [xf], convfloat)]
(%i52) mode_declare(main_prog(),fixnum)
(%o52) [main_prog()]
(%i53) define_variable(MAX_TERMS,30,fixnum)
(%o53) 30
(%i54) define_variable(glob_iolevel,5,fixnum)
(%o54) 5
(%i55) define_variable(glob_yes_pole,4,fixnum)
(%o55) 4
(%i56) define_variable(glob_no_pole,3,fixnum)
(%o56) 3
(%i57) define_variable(glob_not_given,0,fixnum)
(%o57) 0
(%i58) define_variable(glob_no_sing_tests,4,fixnum)
(%o58) 4
(%i59) define_variable(glob_ratio_test,1,fixnum)
(%o59) 1
(%i60) define_variable(glob_three_term_test,2,fixnum)
(%o60) 2
(%i61) define_variable(glob_six_term_test,3,fixnum)
(%o61) 3
(%i62) define_variable(glob_log_10,log(10.0),convfloat)
(%o62) 2.302585092994046
(%i63) define_variable(ALWAYS,1,fixnum)
(%o63) 1
(%i64) define_variable(INFO,2,fixnum)
(%o64) 2
(%i65) define_variable(DEBUGL,3,fixnum)
(%o65) 3
(%i66) define_variable(DEBUGMASSIVE,4,fixnum)
(%o66) 4
(%i67) define_variable(MAX_UNCHANGED,10,fixnum)
(%o67) 10
(%i68) define_variable(glob_check_sign,1.0,convfloat)
(%o68) 1.0
(%i69) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%o69) 8.0
(%i70) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%o70) 0.0
(%i71) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%o71) 0.1
(%i72) define_variable(glob_percent_done,0.0,convfloat)
(%o72) 0.0
(%i73) define_variable(glob_subiter_method,3,fixnum)
(%o73) 3
(%i74) define_variable(glob_total_exp_sec,0.1,convfloat)
(%o74) 0.1
(%i75) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%o75) 0.1
(%i76) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%o76) 100.0
(%i77) define_variable(glob_html_log,true,boolean)
(%o77) true
(%i78) define_variable(glob_good_digits,0,fixnum)
(%o78) 0
(%i79) define_variable(glob_max_opt_iter,10,fixnum)
(%o79) 10
(%i80) define_variable(glob_dump,false,boolean)
(%o80) false
(%i81) define_variable(glob_djd_debug,true,boolean)
(%o81) true
(%i82) define_variable(glob_display_flag,true,boolean)
(%o82) true
(%i83) define_variable(glob_djd_debug2,true,boolean)
(%o83) true
(%i84) define_variable(glob_sec_in_minute,60,fixnum)
(%o84) 60
(%i85) define_variable(glob_min_in_hour,60.0,convfloat)
(%o85) 60.0
(%i86) define_variable(glob_hours_in_day,24.0,convfloat)
(%o86) 24.0
(%i87) define_variable(glob_days_in_year,365,fixnum)
(%o87) 365
(%i88) define_variable(glob_sec_in_hour,3600,fixnum)
(%o88) 3600
(%i89) define_variable(glob_sec_in_day,86400,fixnum)
(%o89) 86400
(%i90) define_variable(glob_sec_in_year,31536000,fixnum)
(%o90) 31536000
(%i91) define_variable(glob_almost_1,0.999,convfloat)
(%o91) 0.999
(%i92) define_variable(glob_clock_sec,0.0,convfloat)
(%o92) 0.0
(%i93) define_variable(glob_clock_start_sec,0.0,convfloat)
(%o93) 0.0
(%i94) define_variable(glob_not_yet_finished,true,boolean)
(%o94) true
(%i95) define_variable(glob_initial_pass,true,boolean)
(%o95) true
(%i96) define_variable(glob_not_yet_start_msg,true,boolean)
(%o96) true
(%i97) define_variable(glob_reached_optimal_h,false,boolean)
(%o97) false
(%i98) define_variable(glob_optimal_done,false,boolean)
(%o98) false
(%i99) define_variable(glob_disp_incr,0.1,convfloat)
(%o99) 0.1
(%i100) define_variable(glob_h,0.1,convfloat)
(%o100) 0.1
(%i101) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%o101) 0.1
(%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%o102) 0.1
(%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%o103) 0.1
(%i104) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%o104) 0.1
(%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%o105) 0.1
(%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%o106) 0.1
(%i107) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%o107) 0.1
(%i108) define_variable(glob_guess_error_rc,0.1,convfloat)
(%o108) 0.1
(%i109) define_variable(glob_guess_error_ord,0.1,convfloat)
(%o109) 0.1
(%i110) define_variable(glob_max_h,0.1,convfloat)
(%o110) 0.1
(%i111) define_variable(glob_min_h,1.0E-6,convfloat)
(%o111) 1.0E-6
(%i112) define_variable(glob_type_given_pole,0,fixnum)
(%o112) 0
(%i113) define_variable(glob_large_float,1.0E+100,convfloat)
(%o113) 1.0E+100
(%i114) define_variable(glob_larger_float,1.1E+100,convfloat)
(%o114) 1.1E+100
(%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat)
(%o115) 9.9E+100
(%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat)
(%o116) 9.9E+100
(%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%o117) 9.9E+100
(%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%o118) 9.9E+100
(%i119) define_variable(glob_last_good_h,0.1,convfloat)
(%o119) 0.1
(%i120) define_variable(glob_look_poles,false,boolean)
(%o120) false
(%i121) define_variable(glob_neg_h,false,boolean)
(%o121) false
(%i122) define_variable(glob_display_interval,0.0,convfloat)
(%o122) 0.0
(%i123) define_variable(glob_next_display,0.0,convfloat)
(%o123) 0.0
(%i124) define_variable(glob_dump_analytic,false,boolean)
(%o124) false
(%i125) define_variable(glob_abserr,1.0E-11,convfloat)
(%o125) 1.0E-11
(%i126) define_variable(glob_relerr,1.0E-11,convfloat)
(%o126) 1.0E-11
(%i127) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%o127) 1.0E+9
(%i128) define_variable(glob_max_hours,0.0,convfloat)
(%o128) 0.0
(%i129) define_variable(glob_max_iter,1000,fixnum)
(%o129) 1000
(%i130) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%o130) 1.0E-11
(%i131) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%o131) 1.0E-11
(%i132) define_variable(glob_no_eqs,0,fixnum)
(%o132) 0
(%i133) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%o133) 0.0
(%i134) define_variable(glob_optimal_start,0.0,convfloat)
(%o134) 0.0
(%i135) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%o135) 1.0001
(%i136) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%o136) 0.9999
(%i137) define_variable(glob_small_float,0.0,convfloat)
(%o137) 0.0
(%i138) define_variable(glob_smallish_float,0.0,convfloat)
(%o138) 0.0
(%i139) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%o139) 0
(%i140) define_variable(glob_warned,false,boolean)
(%o140) false
(%i141) define_variable(glob_warned2,false,boolean)
(%o141) false
(%i142) define_variable(glob_max_sec,10000.0,convfloat)
(%o142) 10000.0
(%i143) define_variable(glob_orig_start_sec,0.0,convfloat)
(%o143) 0.0
(%i144) define_variable(glob_start,0,fixnum)
(%o144) 0
(%i145) define_variable(glob_curr_iter_when_opt,0,fixnum)
(%o145) 0
(%i146) define_variable(glob_current_iter,0,fixnum)
(%o146) 0
(%i147) define_variable(glob_iter,0,fixnum)
(%o147) 0
(%i148) define_variable(glob_normmax,0.0,convfloat)
(%o148) 0.0
(%i149) define_variable(glob_max_minutes,0.0,convfloat)
(%o149) 0.0
(%i150) array(array_y_init,MAX_TERMS)
(%o150) array_y_init
(%i151) array(array_norms,MAX_TERMS)
(%o151) array_norms
(%i152) array(array_fact_1,MAX_TERMS)
(%o152) array_fact_1
(%i153) array(array_1st_rel_error,2)
(%o153) array_1st_rel_error
(%i154) array(array_last_rel_error,2)
(%o154) array_last_rel_error
(%i155) array(array_type_pole,2)
(%o155) array_type_pole
(%i156) array(array_type_real_pole,2)
(%o156) array_type_real_pole
(%i157) array(array_type_complex_pole,2)
(%o157) array_type_complex_pole
(%i158) array(array_y,MAX_TERMS)
(%o158) array_y
(%i159) array(array_x,MAX_TERMS)
(%o159) array_x
(%i160) array(array_tmp0,MAX_TERMS)
(%o160) array_tmp0
(%i161) array(array_tmp1_g,MAX_TERMS)
(%o161) array_tmp1_g
(%i162) array(array_tmp1,MAX_TERMS)
(%o162) array_tmp1
(%i163) array(array_tmp2,MAX_TERMS)
(%o163) array_tmp2
(%i164) array(array_m1,MAX_TERMS)
(%o164) array_m1
(%i165) array(array_y_higher,3,MAX_TERMS)
(%o165) array_y_higher
(%i166) array(array_y_higher_work,3,MAX_TERMS)
(%o166) array_y_higher_work
(%i167) array(array_y_higher_work2,3,MAX_TERMS)
(%o167) array_y_higher_work2
(%i168) array(array_y_set_initial,2,MAX_TERMS)
(%o168) array_y_set_initial
(%i169) array(array_given_rad_poles,2,3)
(%o169) array_given_rad_poles
(%i170) array(array_given_ord_poles,2,3)
(%o170) array_given_ord_poles
(%i171) array(array_rad_test_poles,2,3)
(%o171) array_rad_test_poles
(%i172) array(array_ord_test_poles,2,3)
(%o172) array_ord_test_poles
(%i173) array(array_fact_2,MAX_TERMS,MAX_TERMS)
(%o173) array_fact_2
(%i174) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%o174) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i175) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%o175) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i176) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%o176) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i177) 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))
(%o177) 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))
(%i178) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%o178) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i179) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%o179) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i180) 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)
(%o180) 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)
(%i181) 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)
(%o181) 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)
(%i182) 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)
(%o182) 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
(%i183) 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)
(%o183) 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)
(%i184) 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)
(%o184) 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
(%i185) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%o185) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "), 0)
(%i186) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%o186) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "), 0)
(%i187) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%o187) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "), 0)
(%i188) 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)
(%o188) 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)
(%i189) log_revs(file,revs):=printf(file,revs)
(%o189) log_revs(file, revs) := printf(file, revs)
(%i190) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%o190) logitem_float(file, x) := (printf(file, ""),
printf(file, "~g", x), printf(file, " | "), 0)
(%i191) 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)
(%o191) 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)
(%i192) logstart(file):=(printf(file,""),0)
(%o192) logstart(file) := (printf(file, "
"), 0)
(%i193) logend(file):=(printf(file,"
~%"),0)
(%o193) logend(file) := (printf(file, "~%"), 0)
(%i194) 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)
(%o194) 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)
(%i195) 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)
(%o195) 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
(%i196) 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)
(%o196) 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)
(%i197) 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)
(%o197) comp_rad_from_ratio(term1, term2, last_no) :=
!term1 glob_h!
(if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret)
! term2 !
(%i198) 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)
(%o198) 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)
(%i199) 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)
(%o199) 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 !
(%i200) 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)
(%o200) 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)
(%i201) 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)
(%o201) 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)
(%i202) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%o202) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6,
last_no) := glob_six_term_ord_save
(%i203) factorial_2(nnn):=nnn!
(%o203) factorial_2(nnn) := nnn!
(%i204) 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)
(%o204) 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
(%i205) 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)
(%o205) 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)
(%i206) log10(x):=log(x)/glob_log_10
log(x)
(%o206) log10(x) := -----------
glob_log_10
(%i207) expt(x,y):=(if x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y),x^y)
(%o207) expt(x, y) := (if (x <= 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i208) 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)
(%o208) 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)
(%i209) exact_soln_y(x):=block(2.0-sin(x))
(%o209) exact_soln_y(x) := block(2.0 - sin(x))
(%i210) exact_soln_yp(x):=block(-cos(x))
(%o210) exact_soln_yp(x) := block(- cos(x))
(%i211) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 4
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given,
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(ALWAYS,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "))
elseif glob_type_given_pole = 3
then omniout_str(ALWAYS,
"NO POLE (given) for Equation 1")
else omniout_str(ALWAYS,
"NO INFO (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(ALWAYS,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(ALWAYS,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > 0.0
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(ALWAYS,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > 0.0
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(ALWAYS,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%o211) display_poles() := (block(mode_declare([[rad_given], convfloat]),
if glob_type_given_pole = 4 then (rad_given :
sqrt(array_given_rad_poles array_given_rad_poles
1, 2 1, 2
+ (array_x - array_given_rad_poles )
1 1, 1
(array_x - array_given_rad_poles )),
1 1, 1
if rad_given < glob_least_given_sing then glob_least_given_sing : rad_given,
omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " "), omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles , 4, " ")) elseif glob_type_given_pole = 3
1, 1
then omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"),
if array_rad_test_poles < glob_large_float then (omniout_float(ALWAYS, "Ra\
1, 1
dius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles , 4, " "), if array_rad_test_poles <
1, 1 1, 1
glob_least_ratio_sing then glob_least_ratio_sing : array_rad_test_poles ,
1, 1
omniout_float(ALWAYS, "Order of pole (ratio test) ", 4,
array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS,
1, 1
"NO POLE (ratio test) for Equation 1"),
if (array_rad_test_poles > 0.0) and (array_rad_test_poles < glob_large_float)
1, 2 1, 2
then (omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles , 4, " "), if array_rad_test_poles <
1, 2 1, 2
glob_least_3_sing then glob_least_3_sing : array_rad_test_poles ,
1, 2
omniout_float(ALWAYS, "Order of pole (three term test) ", 4,
array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS,
1, 2
"NO REAL POLE (three term test) for Equation 1"),
if (array_rad_test_poles > 0.0) and (array_rad_test_poles <
1, 3 1, 3
glob_large_float)
then (omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles , 4, " "), if array_rad_test_poles <
1, 3 1, 3
glob_least_6_sing then glob_least_6_sing : array_rad_test_poles ,
1, 3
omniout_float(ALWAYS, "Order of pole (six term test) ", 4,
array_ord_test_poles , 4, " ")) else omniout_str(ALWAYS,
1, 3
"NO COMPLEX POLE (six term test) for Equation 1")), 0)
(%i212) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0
else ret:-1.0,ret)
(%o212) my_check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i213) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(ALWAYS,"min_size",32,min_size,
32,"")),
if min_size < 1.0
then (min_size:1.0,
omniout_float(ALWAYS,"min_size",32,min_size,
32,"")),min_size)
(%o213) est_size_answer() := block([min_size],
min_size : glob_estimated_size_answer,
if !array_y ! < min_size then (min_size : !array_y !,
! 1! ! 1!
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i214) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:0.0,no_terms:MAX_TERMS,
hn_div_ho:0.5,hn_div_ho_2:0.25,hn_div_ho_3:0.125,
omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(ALWAYS,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%o214) test_suggested_h() := block([max_estimated_step_error, hn_div_ho,
hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp], max_estimated_step_error : 0.0,
no_terms : MAX_TERMS, hn_div_ho : 0.5, hn_div_ho_2 : 0.25,
hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32,
""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
est_tmp : mabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if est_tmp >= max_estimated_step_error then max_estimated_step_error :
est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, ""), max_estimated_step_error)
(%i215) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
then ret:true else ret:false,return(ret))
(%o215) reached_interval() := block(mode_declare([[ret], boolean]),
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i216) display_alot(iter):=(
block(mode_declare(
[[abserr],convfloat,[analytic_val_y],convfloat,
[ind_var],convfloat,[numeric_val],convfloat,
[relerr],convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(ALWAYS,
"x[1] ",
33,ind_var,20,
" "),
analytic_val_y
:exact_soln_y(ind_var),
omniout_float(ALWAYS,
"y[1] (analytic) ",
33,
analytic_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val-analytic_val_y),
omniout_float(ALWAYS,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if abs(analytic_val_y) # 0.0
then (
relerr
:abserr*100.0
/abs(analytic_val_y),
if relerr > 1.0E-34
then glob_good_digits
:3-floor(log10(relerr))
else glob_good_digits
:16)
else (relerr:-1.0,
glob_good_digits:-1),
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
omniout_float(ALWAYS,
"absolute error ",
4,abserr,20," "),
omniout_float(ALWAYS,
"relative error ",
4,relerr,20,"%"),
omniout_int(INFO,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(ALWAYS,
"h ",
4,glob_h,20,
" ")))),0)
(%o216) display_alot(iter) := (block(mode_declare([[abserr], convfloat,
[analytic_val_y], convfloat, [ind_var], convfloat, [numeric_val], convfloat,
[relerr], convfloat, [term_no], fixnum]),
if reached_interval() then (if iter >= 0
then (ind_var : array_x , omniout_float(ALWAYS,
1
"x[1] ", 33, ind_var, 20, " "),
analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : mabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if mabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : --------------------, if relerr > 1.0E-34
mabs(analytic_val_y)
then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16)
else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " ")))), 0)
(%i217) adjust_for_pole(h_param):=(
block(mode_declare(
[[hnew],convfloat,[sz2],convfloat,[tmp],
convfloat]),hnew:h_param,
glob_normmax:glob_small_float,
if abs(array_y_higher[1,1]) > glob_small_float
then (tmp:abs(array_y_higher[1,1]),
if tmp < glob_normmax
then glob_normmax:tmp),
if glob_look_poles
and glob_min_pole_est > glob_small_float
and glob_min_pole_est < glob_large_float
then (sz2:glob_min_pole_est/10.0,
if sz2 < hnew
then (
omniout_float(INFO,
"glob_h adjusted to ",
20,h_param,12,
"due to singularity."),
omniout_str(INFO,
"Reached Optimal"),
return(hnew))),
if not glob_reached_optimal_h
then (glob_reached_optimal_h:true,
glob_curr_iter_when_opt
:glob_current_iter,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
glob_optimal_start:array_x[1]),
hnew:sz2),hnew)
(%o217) adjust_for_pole(h_param) := (block(mode_declare([[hnew], convfloat,
[sz2], convfloat, [tmp], convfloat]), hnew : h_param,
glob_normmax : glob_small_float, if !array_y_higher ! > glob_small_float
! 1, 1!
then (tmp : !array_y_higher !, if tmp < glob_normmax
! 1, 1!
then glob_normmax : tmp), if glob_look_poles
and (glob_min_pole_est > glob_small_float)
and (glob_min_pole_est < glob_large_float)
glob_min_pole_est
then (sz2 : -----------------, if sz2 < hnew
10.0
then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))),
if not glob_reached_optimal_h then (glob_reached_optimal_h : true,
glob_curr_iter_when_opt : glob_current_iter,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), hnew)
1
(%i218) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
clock_sec1:elapsed_time_seconds(),
total_clock_sec:clock_sec1-glob_orig_start_sec,
glob_clock_sec:clock_sec1-glob_clock_start_sec,
left_sec:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
clock_sec1
-glob_orig_start_sec),
opt_clock_sec:clock_sec1
-glob_optimal_clock_start_sec,
glob_optimal_expect_sec
:comp_expect_sec(x_end,x_start,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:total_clock_sec+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
glob_percent_done:percent_done,
omniout_str_noeol(INFO,
"Total Elapsed Time "),
omniout_timestr(total_clock_sec),
omniout_str_noeol(INFO,
"Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec),
if percent_done < 100.0
then (omniout_str_noeol(INFO,
"Expected Time Remaining "),
omniout_timestr(expect_sec),
omniout_str_noeol(INFO,
"Optimized Time Remaining "),
omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(INFO,
"Expected Total Time "),
omniout_timestr(glob_total_exp_sec)),
omniout_str_noeol(INFO,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(INFO,
"Percent Done ",33,
percent_done,4,"%")),0)
(%o218) prog_report(x_start, x_end) :=
(block(mode_declare([[clock_sec], convfloat, [opt_clock_sec], convfloat,
[clock_sec1], convfloat, [expect_sec], convfloat, [left_sec], convfloat,
[percent_done], convfloat, [total_clock_sec], convfloat]),
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
clock_sec1 - glob_orig_start_sec, glob_clock_sec :
clock_sec1 - glob_clock_start_sec, left_sec :
- clock_sec1 + glob_orig_start_sec + glob_max_sec,
expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x ,
1
clock_sec1 - glob_orig_start_sec), opt_clock_sec :
clock_sec1 - glob_optimal_clock_start_sec,
glob_optimal_expect_sec : comp_expect_sec(x_end, x_start, glob_h + array_x ,
1
opt_clock_sec), glob_total_exp_sec : total_clock_sec
+ glob_optimal_expect_sec, percent_done :
comp_percent(x_end, x_start, glob_h + array_x ),
1
glob_percent_done : percent_done, omniout_str_noeol(INFO,
"Total Elapsed Time "), omniout_timestr(total_clock_sec),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec), if percent_done < 100.0
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(expect_sec), omniout_str_noeol(INFO,
"Optimized Time Remaining "), omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(glob_total_exp_sec)), omniout_str_noeol(INFO,
"Time to Timeout "), omniout_timestr(left_sec),
omniout_float(INFO, "Percent Done ", 33, percent_done, 4,
"%")), 0)
(%i219) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),
glob_min_pole_est:glob_larger_float,
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-2+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:-10-2+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:-10-2+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-7 and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
term:1,ratio:1.0,
while term <= MAX_TERMS do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%o219) check_for_pole() := (block(mode_declare([cnt], fixnum,
[dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat,
[ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5,
part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c,
rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum,
[h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad],
convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float,
tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float,
tmp_ratio : glob_larger_float, rad_c : glob_larger_float,
array_rad_test_poles : glob_larger_float,
1, 1
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 1
last_no : - 10 - 2 + 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 - 2 + 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 - 2 + MAX_TERMS, cnt : 0,
while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad :
comp_rad_from_six_terms(array_y_higher ,
1, last_no - 5
array_y_higher , array_y_higher ,
1, last_no - 4 1, last_no - 3
array_y_higher , array_y_higher ,
1, last_no - 2 1, last_no - 1
tmp_rad
array_y_higher , last_no), tmp_ratio : ------------,
1, last_no prev_tmp_rad
if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit)
and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0
then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0,
prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no),
if found_sing = 1 then (if rad_c < array_rad_test_poles
1, 3
then (array_rad_test_poles : rad_c, last_no : last_no - 1,
1, 3
tmp_ord : comp_ord_from_six_terms(array_y_higher ,
1, last_no - 5
array_y_higher , array_y_higher ,
1, last_no - 4 1, last_no - 3
array_y_higher , array_y_higher ,
1, last_no - 2 1, last_no - 1
array_y_higher , last_no), array_rad_test_poles : rad_c,
1, last_no 1, 3
if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c,
array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est)
1, 3
glob_ratio_of_radius < mabs(glob_h) then (h_new :
glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0,
while term <= MAX_TERMS do (array_y : array_y ratio,
term term
array_y_higher : array_y_higher ratio,
1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ------------, term : 1 + term),
term term mabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles()), 0)
(%i220) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),array_tmp1[1]:sin(array_x[1]),
array_tmp1_g[1]:cos(array_x[1]),
array_tmp2[1]:array_tmp1[1]+array_const_0D0[1],
if not array_y_set_initial[1,3]
then (if 1 <= MAX_TERMS
then (
temporary
:array_tmp2[1]*expt(glob_h,2)
*factorial_3(0,2),
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,
temporary:temporary*1.0/glob_h,
array_y_higher[3,1]:temporary,0)),kkk:2,
array_tmp1[2]:array_tmp1_g[1]*array_x[2]/1,
array_tmp1_g[2]:(-array_tmp1[1]*array_x[2])/1,
array_tmp2[2]:array_tmp1[2],
if not array_y_set_initial[1,4]
then (if 2 <= MAX_TERMS
then (
temporary
:array_tmp2[2]*expt(glob_h,2)
*factorial_3(1,3),
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,
temporary:temporary*2.0/glob_h,
array_y_higher[3,2]:temporary,0)),kkk:3,
array_tmp1[3]:array_tmp1_g[2]*array_x[2]/2,
array_tmp1_g[3]:(-array_tmp1[2]*array_x[2])/2,
array_tmp2[3]:array_tmp1[3],
if not array_y_set_initial[1,5]
then (if 3 <= MAX_TERMS
then (
temporary
:array_tmp2[3]*expt(glob_h,2)
*factorial_3(2,4),
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,
temporary:temporary*3.0/glob_h,
array_y_higher[3,3]:temporary,0)),kkk:4,
array_tmp1[4]:array_tmp1_g[3]*array_x[2]/3,
array_tmp1_g[4]:(-array_tmp1[3]*array_x[2])/3,
array_tmp2[4]:array_tmp1[4],
if not array_y_set_initial[1,6]
then (if 4 <= MAX_TERMS
then (
temporary
:array_tmp2[4]*expt(glob_h,2)
*factorial_3(3,5),
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,
temporary:temporary*4.0/glob_h,
array_y_higher[3,4]:temporary,0)),kkk:5,
array_tmp1[5]:array_tmp1_g[4]*array_x[2]/4,
array_tmp1_g[5]:(-array_tmp1[4]*array_x[2])/4,
array_tmp2[5]:array_tmp1[5],
if not array_y_set_initial[1,7]
then (if 5 <= MAX_TERMS
then (
temporary
:array_tmp2[5]*expt(glob_h,2)
*factorial_3(4,6),
if 7 <= MAX_TERMS
then (array_y[7]:temporary,
array_y_higher[1,7]:temporary),
temporary:temporary*6.0/glob_h,
array_y_higher[2,6]:temporary,
temporary:temporary*5.0/glob_h,
array_y_higher[3,5]:temporary,0)),kkk:6,
while kkk <= MAX_TERMS do
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/(kkk-1),
array_tmp1_g[kkk]
:(-array_tmp1[kkk-1]*array_x[2])/(kkk-1),
array_tmp2[kkk]:array_tmp1[kkk],order_d:2,
if order_d+kkk <= MAX_TERMS
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:array_tmp2[kkk]*expt(glob_h,order_d)
*factorial_3(kkk-1,
-1+order_d
+kkk),
array_y[order_d+kkk]:temporary,
array_y_higher[1,order_d+kkk]:temporary,
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= MAX_TERMS
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:temporary*adj2/glob_h
else temporary:temporary,
array_y_higher[adj3,term]
:temporary),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%o220) atomall() := (block(mode_declare([[kkk, order_d], fixnum,
[adj2, adj3, temporary, term, temp, temp2], convfloat]),
array_tmp1 : sin(array_x ), array_tmp1_g : cos(array_x ),
1 1 1 1
array_tmp2 : array_tmp1 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= MAX_TERMS
1, 3
then (temporary : array_tmp2 expt(glob_h, 2) factorial_3(0, 2),
1
if 3 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 3, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : array_tmp1 , if not array_y_set_initial
2 2 1, 4
then (if 2 <= MAX_TERMS then (temporary :
array_tmp2 expt(glob_h, 2) factorial_3(1, 3),
2
if 4 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 3, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : array_tmp1 , if not array_y_set_initial
3 3 1, 5
then (if 3 <= MAX_TERMS then (temporary :
array_tmp2 expt(glob_h, 2) factorial_3(2, 4),
3
if 5 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 3, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : array_tmp1 , if not array_y_set_initial
4 4 1, 6
then (if 4 <= MAX_TERMS then (temporary :
array_tmp2 expt(glob_h, 2) factorial_3(3, 5),
4
if 6 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 3, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : array_tmp1 , if not array_y_set_initial
5 5 1, 7
then (if 5 <= MAX_TERMS then (temporary :
array_tmp2 expt(glob_h, 2) factorial_3(4, 6),
5
if 7 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
7 1, 7
temporary 6.0
temporary : -------------, array_y_higher : temporary,
glob_h 2, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 3, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= MAX_TERMS do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 ,
kkk kkk - 1 kkk kkk
order_d : 2, if order_d + kkk <= MAX_TERMS
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp2 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while (term >= 1)
and (term <= MAX_TERMS) and (adj3 < 1 + order_d) do (if adj3 <= 1 + order_d
temporary adj2
then (if adj2 > 0 then temporary : -------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk)), 0)
(%i221) exact_soln_y(x):=block(2.0-sin(x))
(%o221) exact_soln_y(x) := block(2.0 - sin(x))
(%i222) exact_soln_yp(x):=block(-cos(x))
(%o222) exact_soln_yp(x) := block(- cos(x))
(%i223) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,best_h,found_h],
convfloat,[repeat_it],fixnum]),Digits:32,
max_terms:30,glob_html_log:true,term:1,
while term <= MAX_TERMS do
(array_y_init[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_norms[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_fact_1[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_1st_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do
(array_tmp0[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp1_g[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp1[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp2[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term),
ord:1,
while ord <= 3 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 <= 3 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 <= 3 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work2[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_set_initial[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_rad_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_ord_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= MAX_TERMS do
(term:1,
while term <= MAX_TERMS do
(array_fact_2[ord,term]:0.0,term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1_g),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_m1),zero_ats_ar(array_const_2),
array_const_2[1]:2,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]:true,
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/h2sinpostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 2 ) = 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,
"array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:100,"),
omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"glob_desired_digits_correct:10,"),
omniout_str(ALWAYS,"glob_display_interval:0.01,"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:1000000000,"),
omniout_str(ALWAYS,"glob_max_minutes:10.0,"),
omniout_str(ALWAYS,"glob_subiter_method:3,"),
omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS,"exact_soln_y (x) := (block("),
omniout_str(ALWAYS," (2.0 - sin(x)) "),
omniout_str(ALWAYS,"));"),
omniout_str(ALWAYS,"exact_soln_yp (x) := (block("),
omniout_str(ALWAYS," (- cos(x)) "),
omniout_str(ALWAYS,"));"),
omniout_str(ALWAYS,"/* END USER DEF BLOCK */"),
omniout_str(ALWAYS,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:0.0,glob_smallish_float:0.0,
glob_large_float:1.0E+100,glob_larger_float:1.1E+100,
glob_almost_1:0.99,x_start:0.1,x_end:5.0,
array_y_init[1+0]:exact_soln_y(x_start),
array_y_init[1+1]:exact_soln_yp(x_start),
glob_look_poles:true,glob_max_iter:100,
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:2,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:2,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:3,ord:3,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[3,iii]
:array_y_higher[3,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:3,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_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:2,
calc_term:2,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: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: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:3,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:3,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 , 2 ) = 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,
"2014-01-08T22:00:58-06:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"h2sin"),
logitem_str(html_log_file,
"diff ( y , x , 2 ) = 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,
"h2sin diffeq.max"),
logitem_str(html_log_file,
"h2sin 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)))
(%o223) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2],
convfloat, [niii, done_once, term, ord, order_diff, term_no, html_log_file,
iiif, jjjf, rows, r_order, sub_iter, calc_term, iii], fixnum, [temp_sum],
convfloat, [current_iter], fixnum, [x_start, x_end], convfloat,
[it, opt_iter], fixnum, [tmp], convfloat, [subiter], fixnum,
[est_needed_step_err, estimated_step_error, min_value, est_answer, best_h,
found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 30,
glob_html_log : true, term : 1, while term <=
MAX_TERMS do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_complex_pole : 0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <=
MAX_TERMS do (array_tmp1_g : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 3 do (term : 1, while term <=
MAX_TERMS do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 3 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 <= 3 do (term : 1, while term <=
MAX_TERMS do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1,
while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), zero_ats_ar(array_y), zero_ats_ar(array_x),
zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1_g), zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2), zero_ats_ar(array_m1), zero_ats_ar(array_const_2),
array_const_2 : 2, 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 : true, 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/h2sinpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 2 ) = 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, "array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.01,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000000,"),
omniout_str(ALWAYS, "glob_max_minutes:10.0,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (2.0 - sin(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "exact_soln_yp (x) := (block("),
omniout_str(ALWAYS, " (- cos(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 0.0, glob_smallish_float : 0.0,
glob_large_float : 1.0E+100, glob_larger_float : 1.1E+100,
glob_almost_1 : 0.99, x_start : 0.1, x_end : 5.0,
array_y_init : exact_soln_y(x_start),
1 + 0
array_y_init : exact_soln_yp(x_start), glob_look_poles : true,
1 + 1
glob_max_iter : 100, 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 : 2, 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 : 2, 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 : 3, ord : 3, calc_term : 1, iii : MAX_TERMS,
2
while iii >= calc_term do (array_y_higher_work :
3, iii
array_y_higher
3, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 3, calc_term : 1, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_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 : 2, calc_term : 2, iii : MAX_TERMS,
factorial_1(calc_term - 1)
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 : 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 : 2, calc_term : 1, iii : MAX_TERMS,
factorial_1(calc_term - 1)
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 : 3, 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 : 3, 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 , 2 ) = 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,
"2014-01-08T22:00:58-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "h2sin"),
logitem_str(html_log_file, "diff ( y , x , 2 ) = 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, "h2sin diffeq.max"), logitem_str(html_log_file, "h2sin 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)))
(%i224) main():=(alias(convfloat,convfloat),compile(all),main_prog())
(%o224) main() := (alias(convfloat, convfloat), compile(all), main_prog())
(%i225) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable fixnum in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable good_digits in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable MAX_TERMS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable rad_given in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable ALWAYS in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable analytic_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: encountered undefined variable tmp in translation.
warning: variable glob_normmax (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_normmax in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable hnew in translation.
warning: encountered undefined variable sz2 in translation.
warning: encountered undefined variable glob_look_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_current_iter in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_optimal_start (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_reached_optimal_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable INFO in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable MAX_TERMS in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable h_new in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp1_g in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable 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_2 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/h2sinpostode.ode#################"
"diff ( y , x , 2 ) = 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),"
"array_y_init[1 + 1] : exact_soln_yp(x_start),"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.01,"
"glob_look_poles:true,"
"glob_max_iter:1000000000,"
"glob_max_minutes:10.0,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (2.0 - sin(x)) "
"));"
"exact_soln_yp (x) := (block("
" (- cos(x)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
glob_desired_digits_correct = 10. ""
estimated_h = 1.000000E-6 ""
estimated_answer = 1. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 4.9 ""
estimated_steps = 4900000. ""
step_error = 2.040816326530612300000000000000000E-17 ""
est_needed_step_err = 2.040816326530612300000000000000000E-17 ""
opt_iter = 1
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.4754661255148730000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 ""
estimated_step_error = 2.4754661255148730000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-184 ""
best_h = 2.000000E-6 ""
opt_iter = 2
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.66125750215185720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 ""
estimated_step_error = 1.66125750215185720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-176 ""
best_h = 4.000000E-6 ""
opt_iter = 3
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.1148514493392445000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 ""
estimated_step_error = 1.1148514493392445000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 ""
best_h = 8.000000E-6 ""
opt_iter = 4
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 7.48164695285792800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 ""
estimated_step_error = 7.48164695285792800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-161 ""
best_h = 1.600000E-5 ""
opt_iter = 5
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.020855692025193000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 ""
estimated_step_error = 5.020855692025193000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-153 ""
best_h = 3.200000E-5 ""
opt_iter = 6
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.3694491681901960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 ""
estimated_step_error = 3.3694491681901960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-145 ""
best_h = 6.400000E-5 ""
opt_iter = 7
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.261212414751383500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 ""
estimated_step_error = 2.261212414751383500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-137 ""
best_h = 1.280000E-4 ""
opt_iter = 8
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.5174918888357422000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 ""
estimated_step_error = 1.5174918888357422000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-129 ""
best_h = 2.560000E-4 ""
opt_iter = 9
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.01839562596517830000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 ""
estimated_step_error = 1.01839562596517830000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 ""
best_h = 5.120000E-4 ""
opt_iter = 10
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.834660257908615000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 ""
estimated_step_error = 6.834660257908615000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-114 ""
best_h = 1.024000E-3 ""
opt_iter = 11
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.5870962482042430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
estimated_step_error = 4.5870962482042430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-106 ""
best_h = 2.048000E-3 ""
opt_iter = 12
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.07892986852341400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 ""
estimated_step_error = 3.07892986852341400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-98 ""
best_h = 4.096000E-3 ""
opt_iter = 13
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.0670155792407374000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 ""
estimated_step_error = 2.0670155792407374000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 ""
best_h = 8.192000E-3 ""
opt_iter = 14
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.388198528514440000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 ""
estimated_step_error = 1.388198528514440000000000000000000000000000000000000000000000000000000000000000000000000000000000E-82 ""
best_h = 1.638400E-2 ""
opt_iter = 15
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 9.330106380476464000000000000000000000000000000000000000000000000000000000000000000000000000E-75 ""
estimated_step_error = 9.330106380476464000000000000000000000000000000000000000000000000000000000000000000000000000E-75 ""
best_h = 3.276800E-2 ""
opt_iter = 16
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 6.2802036149313070000000000000000000000000000000000000000000000000000000000000000000E-67 ""
estimated_step_error = 6.2802036149313070000000000000000000000000000000000000000000000000000000000000000000E-67 ""
best_h = 6.553600E-2 ""
opt_iter = 17
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.23990490971055700000000000000000000000000000000000000000000000000000000000E-59 ""
estimated_step_error = 4.23990490971055700000000000000000000000000000000000000000000000000000000000E-59 ""
best_h = 0.131072 ""
opt_iter = 18
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.879345301267189000000000000000000000000000000000000000000000000000E-51 ""
estimated_step_error = 2.879345301267189000000000000000000000000000000000000000000000000000E-51 ""
best_h = 0.1 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 1.9001665833531718 " "
y[1] (numeric) = 1.9001665833531718 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.9334665397530600E-2 " "
Order of pole (three term test) = 22.990033288920618 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11 " "
y[1] (analytic) = 1.8902216991628251 " "
y[1] (numeric) = 1.8902216991628251 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10911481154043474 " "
Order of pole (three term test) = 22.9879487246653 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12 " "
y[1] (analytic) = 1.8802877927110806 " "
y[1] (numeric) = 1.8802877927110806 " "
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 = 0.11885131321356732 " "
Order of pole (three term test) = 22.985668987426013 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13 " "
y[1] (analytic) = 1.870365857380305 " "
y[1] (numeric) = 1.870365857380305 " "
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 = 0.12854027594607753 " "
Order of pole (three term test) = 22.983194989067254 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14 " "
y[1] (analytic) = 1.8604568853557635 " "
y[1] (numeric) = 1.8604568853557635 " "
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 = 0.13817782428205688 " "
Order of pole (three term test) = 22.980527719155386 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000002 " "
y[1] (analytic) = 1.8505618675264008 " "
y[1] (numeric) = 1.8505618675264008 " "
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 = 0.14776010333066988 " "
Order of pole (three term test) = 22.9776682445628 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000003 " "
y[1] (analytic) = 1.840681793385754 " "
y[1] (numeric) = 1.840681793385754 " "
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 = 0.1572832803080589 " "
Order of pole (three term test) = 22.97461770904122 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000004 " "
y[1] (analytic) = 1.8308176509330039 " "
y[1] (numeric) = 1.8308176509330039 " "
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 = 0.1667435460704072 " "
Order of pole (three term test) = 22.971377332764167 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000005 " "
y[1] (analytic) = 1.8209704265741757 " "
y[1] (numeric) = 1.8209704265741757 " "
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 = 0.17613711663754503 " "
Order of pole (three term test) = 22.967948411838968 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000006 " "
y[1] (analytic) = 1.8111411050234993 " "
y[1] (numeric) = 1.8111411050234993 " "
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 = 0.1854602347064914 " "
Order of pole (three term test) = 22.96433231778826 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000007 " "
y[1] (analytic) = 1.8013306692049387 " "
y[1] (numeric) = 1.8013306692049387 " "
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 = 0.19470917115432534 " "
Order of pole (three term test) = 22.96053049700144 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000008 " "
y[1] (analytic) = 1.7915401001539004 " "
y[1] (numeric) = 1.7915401001539004 " "
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 = 0.20388022652978532 " "
Order of pole (three term test) = 22.956544470156157 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000008 " "
y[1] (analytic) = 1.7817703769191306 " "
y[1] (numeric) = 1.7817703769191306 " "
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 = 0.21296973253299994 " "
Order of pole (three term test) = 22.952375831609977 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2300000000000001 " "
y[1] (analytic) = 1.7720224764648116 " "
y[1] (numeric) = 1.7720224764648116 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22197405348275998 " "
Order of pole (three term test) = 22.948026248762762 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000001 " "
y[1] (analytic) = 1.7622973735728653 " "
y[1] (numeric) = 1.7622973735728653 " "
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 = 0.2308895877707415 " "
Order of pole (three term test) = 22.943497461389644 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 1.752596040745477 " "
y[1] (numeric) = 1.752596040745477 " "
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 = 0.23971276930210172 " "
Order of pole (three term test) = 22.93879128094519 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 1.7429194481078447 " "
y[1] (numeric) = 1.742919448107845 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.273980878267714800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24844006892186848 " "
Order of pole (three term test) = 22.933909589838827 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 1.7332685633111686 " "
y[1] (numeric) = 1.7332685633111689 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.281074437194233400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.25706799582655665 " "
Order of pole (three term test) = 22.928854340681916 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 1.7236443514358861 " "
y[1] (numeric) = 1.7236443514358863 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.288227497395599800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2655930989604419 " "
Order of pole (three term test) = 22.923627555506705 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 1.7140477748951644 " "
y[1] (numeric) = 1.7140477748951646 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.295439999848383200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.27401196839593706 " "
Order of pole (three term test) = 22.918231324957592 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 1.7044797933386602 " "
y[1] (numeric) = 1.7044797933386606 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.605423728609889700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28232123669751796 " "
Order of pole (three term test) = 22.912667807454838 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 1.6949413635565564 " "
y[1] (numeric) = 1.6949413635565567 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.310042988502606000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29051758026865254 " "
Order of pole (three term test) = 22.90693922833126 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 1.6854334393838821 " "
y[1] (numeric) = 1.6854334393838823 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.317433247356245300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.298597720681196 " "
Order of pole (three term test) = 22.90104787894214 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 1.6759569716051315 " "
y[1] (numeric) = 1.6759569716051317 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.324882492134450700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3065584259867172 " "
Order of pole (three term test) = 22.894996115748683 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 1.6665129078591854 " "
y[1] (numeric) = 1.6665129078591856 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.33239054961939300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.31439651200923424 " "
Order of pole (three term test) = 22.888786359375466 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 1.6571021925445484 " "
y[1] (numeric) = 1.6571021925445486 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.339957221250626000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32210884361884556 " "
Order of pole (three term test) = 22.88242109364224 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 1.64772576672491 " "
y[1] (numeric) = 1.64772576672491 " "
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 = 0.3296923359857367 " "
Order of pole (three term test) = 22.875902864570445 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 1.6383845680350377 " "
y[1] (numeric) = 1.638384568035038 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.355265480749344700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33714395581407275 " "
Order of pole (three term test) = 22.86923427936479 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 1.6290795305870172 " "
y[1] (numeric) = 1.6290795305870172 " "
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 = 0.3444607225552759 " "
Order of pole (three term test) = 22.862418005370447 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 1.6198115848768384 " "
y[1] (numeric) = 1.6198115848768384 " "
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 = 0.3516397096002052 " "
Order of pole (three term test) = 22.855456769006132 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 1.6105816576913492 " "
y[1] (numeric) = 1.6105816576913494 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.378660956832924400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3586780454497617 " "
Order of pole (three term test) = 22.848353354673584 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 1.6013906720155768 " "
y[1] (numeric) = 1.601390672015577 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.386573612581099600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36557291486344806 " "
Order of pole (three term test) = 22.841110603643806 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 1.5922395469404296 " "
y[1] (numeric) = 1.5922395469404298 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.394542707796081700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37232155998542993 " "
Order of pole (three term test) = 22.833731412920656 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 1.583129197570789 " "
y[1] (numeric) = 1.5831291975707893 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.402567808525953800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37892128144763865 " "
Order of pole (three term test) = 22.826218734082026 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 1.5740605349340002 " "
y[1] (numeric) = 1.5740605349340004 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.41064844710271300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3853694394494848 " "
Order of pole (three term test) = 22.818575572099288 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 1.5650344658887696 " "
y[1] (numeric) = 1.5650344658887698 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.41878412114671280000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3916634548137418 " "
Order of pole (three term test) = 22.81080498413533 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 1.55605189303448 " "
y[1] (numeric) = 1.5560518930344802 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.42697429256050580000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3978008100181832 " "
Order of pole (three term test) = 22.80291007832173 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 1.5471137146209315 " "
y[1] (numeric) = 1.5471137146209317 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.435218386512952200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40377905020255705 " "
Order of pole (three term test) = 22.794894012515545 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 1.538220824458517 " "
y[1] (numeric) = 1.5382208244585172 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.443515790414521500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4095957841504992 " "
Order of pole (three term test) = 22.786759993036227 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 1.5293741118288418 " "
y[1] (numeric) = 1.529374111828842 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.45186585288479890000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4152486852459855 " "
Order of pole (three term test) = 22.778511273383113 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 1.5205744613957968 " "
y[1] (numeric) = 1.520574461395797 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.460267882713271200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42073549240394825 " "
Order of pole (three term test) = 22.77015115293407 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = 1.5118227531170922 " "
y[1] (numeric) = 1.5118227531170925 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.46872114781456620000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4260540109746817 " "
Order of pole (three term test) = 22.761682975625828 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = 1.503119862156263 " "
y[1] (numeric) = 1.5031198621562631 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.477224874179380300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43120211362166944 " "
Order of pole (three term test) = 22.75311012861639 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (analytic) = 1.4944666587951527 " "
y[1] (numeric) = 1.494466658795153 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.485778244822436600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4361777411724933 " "
Order of pole (three term test) = 22.744436040930264 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (analytic) = 1.4858640083468866 " "
y[1] (numeric) = 1.4858640083468868 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.494380398728880600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44097890344247404 " "
Order of pole (three term test) = 22.73566418208687 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = 1.4773127710693406 " "
y[1] (numeric) = 1.4773127710693408 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.503030429800631700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4456036800307179 " "
Order of pole (three term test) = 22.72679806071279 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (analytic) = 1.4688138020791164 " "
y[1] (numeric) = 1.4688138020791166 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.511727385804283500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4500502210882526 " "
Order of pole (three term test) = 22.717841223138354 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = 1.4603679512660306 " "
y[1] (numeric) = 1.4603679512660308 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.520470267322253400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4543167480579418 " "
Order of pole (three term test) = 22.708797251979185 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (analytic) = 1.451976063208126 " "
y[1] (numeric) = 1.4519760632081264 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.05851605341793400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45840155438588365 " "
Order of pole (three term test) = 22.69966976470314 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (analytic) = 1.443638977087216 " "
y[1] (numeric) = 1.4436389770872162 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.538089567053970700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46230300620401044 " "
Order of pole (three term test) = 22.690462412183443 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = 1.4353575266049643 " "
y[1] (numeric) = 1.4353575266049647 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.09392748230792400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4660195429836134 " "
Order of pole (three term test) = 22.681178877238334 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (analytic) = 1.4271325398995183 " "
y[1] (numeric) = 1.4271325398995187 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.11175870099164100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4695496781595341 " "
Order of pole (three term test) = 22.671822873158025 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (analytic) = 1.4189648394626946 " "
y[1] (numeric) = 1.4189648394626948 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.564835144252839600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4728919997247698 " "
Order of pole (three term test) = 22.662398142219388 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (analytic) = 1.41085524205773 " "
y[1] (numeric) = 1.4108552420577303 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.573829818296451400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4760451707952581 " "
Order of pole (three term test) = 22.65290845418914 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (analytic) = 1.4028045586376074 " "
y[1] (numeric) = 1.4028045586376077 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.582862014225839600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4790079301446124 " "
Order of pole (three term test) = 22.643357604815975 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (analytic) = 1.3948135942639601 " "
y[1] (numeric) = 1.3948135942639601 " "
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 = 0.4817790927085967 " "
Order of pole (three term test) = 22.633749414312295 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (analytic) = 1.3868831480265658 " "
y[1] (numeric) = 1.386883148026566 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.601033261100509600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4843575500591327 " "
Order of pole (three term test) = 22.624087725826186 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (analytic) = 1.3790140129634398 " "
y[1] (numeric) = 1.37901401296344 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.61016931545073520000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48674227084765975 " "
Order of pole (three term test) = 22.614376403904227 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (analytic) = 1.371206975981531 " "
y[1] (numeric) = 1.3712069759815313 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.619336896722600000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4889323012176583 " "
Order of pole (three term test) = 22.60461933294571 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (analytic) = 1.3634628177780317 " "
y[1] (numeric) = 1.363462817778032 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.628534361405516400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4909267651861799 " "
Order of pole (three term test) = 22.59482041564892 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = 1.3557823127623085 " "
y[1] (numeric) = 1.3557823127623088 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.637760006417486600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49272486499423024 " "
Order of pole (three term test) = 22.584983571450124 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (analytic) = 1.3481662289784628 " "
y[1] (numeric) = 1.348166228978463 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.647012068335814200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49432588142585987 " "
Order of pole (three term test) = 22.57511273495584 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (analytic) = 1.3406153280285265 " "
y[1] (numeric) = 1.3406153280285267 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.656288722668599300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49572917409584344 " "
Order of pole (three term test) = 22.56521185436907 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (analytic) = 1.3331303649963018 " "
y[1] (numeric) = 1.333130364996302 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.665588083170300200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49693418170582254 " "
Order of pole (three term test) = 22.555284889910034 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (analytic) = 1.3257120883718545 " "
y[1] (numeric) = 1.3257120883718547 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.67490820120476300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49794042226882007 " "
Order of pole (three term test) = 22.545335812232157 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (analytic) = 1.3183612399766655 " "
y[1] (numeric) = 1.3183612399766655 " "
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 = 0.4987474933020274 " "
Order of pole (three term test) = 22.535368600833852 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (analytic) = 1.3110785548894484 " "
y[1] (numeric) = 1.3110785548894484 " "
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 = 0.4993550719877915 " "
Order of pole (three term test) = 22.52538724246679 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (analytic) = 1.3038647613726428 " "
y[1] (numeric) = 1.3038647613726428 " "
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 = 0.49976291530273964 " "
Order of pole (three term test) = 22.515395729541233 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (analytic) = 1.2967205807995894 " "
y[1] (numeric) = 1.2967205807995894 " "
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 = 0.4999708601149831 " "
Order of pole (three term test) = 22.505398058529135 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (analytic) = 1.2896467275823917 " "
y[1] (numeric) = 1.2896467275823917 " "
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 = 0.4999788232493701 " "
Order of pole (three term test) = 22.4953982283656 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = 1.2826439091004769 " "
y[1] (numeric) = 1.2826439091004769 " "
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 = 0.4997868015207526 " "
Order of pole (three term test) = 22.485400238849355 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (analytic) = 1.275712825629857 " "
y[1] (numeric) = 1.275712825629857 " "
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 = 0.499394871735262 " "
Order of pole (three term test) = 22.475408089042915 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (analytic) = 1.2688541702731038 " "
y[1] (numeric) = 1.2688541702731038 " "
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 = 0.4988031906595868 " "
Order of pole (three term test) = 22.465425775672966 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (analytic) = 1.262068628890037 " "
y[1] (numeric) = 1.262068628890037 " "
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 = 0.4980119949582683 " "
Order of pole (three term test) = 22.455457291531772 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (analytic) = 1.2553568800291401 " "
y[1] (numeric) = 1.2553568800291404 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.768776739566497200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.497021601099038 " "
Order of pole (three term test) = 22.445506623880064 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (analytic) = 1.2487195948597067 " "
y[1] (numeric) = 1.248719594859707 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.778178270278348300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4958324052262342 " "
Order of pole (three term test) = 22.435577752852232 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (analytic) = 1.2421574371047226 " "
y[1] (numeric) = 1.2421574371047226 " "
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 = 0.4944448830023507 " "
Order of pole (three term test) = 22.425674649864316 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (analytic) = 1.2356710629744945 " "
y[1] (numeric) = 1.2356710629744945 " "
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 = 0.4928595894177767 " "
Order of pole (three term test) = 22.41580127602546 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (analytic) = 1.2292611211010303 " "
y[1] (numeric) = 1.2292611211010303 " "
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 = 0.49107715856880896 " "
Order of pole (three term test) = 22.40596158055356 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (analytic) = 1.2229282524731757 " "
y[1] (numeric) = 1.2229282524731757 " "
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 = 0.4890983034040221 " "
Order of pole (three term test) = 22.396159499195605 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (analytic) = 1.2166730903725163 " "
y[1] (numeric) = 1.2166730903725163 " "
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 = 0.4869238154390975 " "
Order of pole (three term test) = 22.38639895265346 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (analytic) = 1.210496260310049 " "
y[1] (numeric) = 1.2104962603100493 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.834327062424448700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.484554564440228 " "
Order of pole (three term test) = 22.37668384501558 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (analytic) = 1.2043983799636335 " "
y[1] (numeric) = 1.2043983799636337 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.843614277625779400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4819914980762238 " "
Order of pole (three term test) = 22.367018062195502 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (analytic) = 1.1983800591162224 " "
y[1] (numeric) = 1.1983800591162226 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.852872994972764300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47923564153945675 " "
Order of pole (three term test) = 22.357405470377483 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (analytic) = 1.1924418995948853 " "
y[1] (numeric) = 1.1924418995948853 " "
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 = 0.47628809713579756 " "
Order of pole (three term test) = 22.34784991447008 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (analytic) = 1.1865844952106257 " "
y[1] (numeric) = 1.186584495210626 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.871291979806436700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47315004384370707 " "
Order of pole (three term test) = 22.33835521656825 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (analytic) = 1.1808084316990013 " "
y[1] (numeric) = 1.1808084316990013 " "
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 = 0.46982273684266207 " "
Order of pole (three term test) = 22.32892517442455 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (analytic) = 1.1751142866615494 " "
y[1] (numeric) = 1.1751142866615496 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.889557530236916600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4663075070110999 " "
Order of pole (three term test) = 22.319563559930113 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (analytic) = 1.169502629508029 " "
y[1] (numeric) = 1.169502629508029 " "
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 = 0.46260576039408363 " "
Order of pole (three term test) = 22.31027411760592 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (analytic) = 1.1639740213994791 " "
y[1] (numeric) = 1.163974021399479 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.90764227416399500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4587189776409045 " "
Order of pole (three term test) = 22.301060563105043 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = 1.1585290151921033 " "
y[1] (numeric) = 1.1585290151921028 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.833216121707796000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4546487134128403 " "
Order of pole (three term test) = 22.291926581726425 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000007 " "
y[1] (analytic) = 1.1531681553819846 " "
y[1] (numeric) = 1.1531681553819841 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.8510360156707500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4503965957613134 " "
Order of pole (three term test) = 22.28287582694085 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000007 " "
y[1] (analytic) = 1.1478919780506367 " "
y[1] (numeric) = 1.1478919780506365 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.934368469950543700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44596432547668935 " "
Order of pole (three term test) = 22.273911918929542 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000007 " "
y[1] (analytic) = 1.1427010108113964 " "
y[1] (numeric) = 1.142701010811396 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.886311516734624600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44135367540798665 " "
Order of pole (three term test) = 22.265038443136202 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000007 " "
y[1] (analytic) = 1.1375957727566612 " "
y[1] (numeric) = 1.137595772756661 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.95187614302543700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4365664897537579 " "
Order of pole (three term test) = 22.25625894883282 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0500000000000007 " "
y[1] (analytic) = 1.1325767744059827 " "
y[1] (numeric) = 1.1325767744059825 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.960525855225045700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4316046833244363 " "
Order of pole (three term test) = 22.24757694770007 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0600000000000007 " "
y[1] (analytic) = 1.1276445176550134 " "
y[1] (numeric) = 1.1276445176550132 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.9691010903576500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4264702407764377 " "
Order of pole (three term test) = 22.238995912422645 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0700000000000007 " "
y[1] (analytic) = 1.122799495725318 " "
y[1] (numeric) = 1.1227994957253178 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.977598010779231500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4211652158183222 " "
Order of pole (three term test) = 22.230519275300242 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0800000000000007 " "
y[1] (analytic) = 1.1180421931150522 " "
y[1] (numeric) = 1.118042193115052 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.986012748824603800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.415691730389341 " "
Order of pole (three term test) = 22.22215042687469 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0900000000000007 " "
y[1] (analytic) = 1.1133730855505124 " "
y[1] (numeric) = 1.1133730855505122 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.99434140996178600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41005197381068675 " "
Order of pole (three term test) = 22.213892714573777 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1000000000000008 " "
y[1] (analytic) = 1.1087926399385644 " "
y[1] (numeric) = 1.1087926399385641 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.00258007608468900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40424820190979477 " "
Order of pole (three term test) = 22.205749441372326 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1100000000000008 " "
y[1] (analytic) = 1.104301314319952 " "
y[1] (numeric) = 1.1043013143199518 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.01072480894193500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3982827361180429 " "
Order of pole (three term test) = 22.197723864471033 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1200000000000008 " "
y[1] (analytic) = 1.0998995578234947 " "
y[1] (numeric) = 1.0998995578234945 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.018771653699161800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3921579625422094 " "
Order of pole (three term test) = 22.189819193993653 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1300000000000008 " "
y[1] (analytic) = 1.0955878106211738 " "
y[1] (numeric) = 1.0955878106211736 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.02671664263165700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3858763310100625 " "
Order of pole (three term test) = 22.182038591703 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1400000000000008 " "
y[1] (analytic) = 1.0913665038841165 " "
y[1] (numeric) = 1.0913665038841163 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.034555798943674400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3794403540904604 " "
Order of pole (three term test) = 22.174385169736222 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1500000000000008 " "
y[1] (analytic) = 1.0872360597394786 " "
y[1] (numeric) = 1.0872360597394783 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.042285140710263200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3728526060883595 " "
Order of pole (three term test) = 22.16686198936009 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1600000000000008 " "
y[1] (analytic) = 1.0831968912282326 " "
y[1] (numeric) = 1.0831968912282324 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.049900684936935600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36611572201512516 " "
Order of pole (three term test) = 22.15947205974642 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1700000000000008 " "
y[1] (analytic) = 1.079249402263864 " "
y[1] (numeric) = 1.0792494022638637 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.057398451731956300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3592323965345627 " "
Order of pole (three term test) = 22.15221833676855 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1800000000000008 " "
y[1] (analytic) = 1.0753939875919794 " "
y[1] (numeric) = 1.075393987591979 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.12954893717107800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3522053828850874 " "
Order of pole (three term test) = 22.145103721818934 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1900000000000008 " "
y[1] (analytic) = 1.0716310327508332 " "
y[1] (numeric) = 1.0716310327508325 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.21607432424904300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3450374917784676 " "
Order of pole (three term test) = 22.138131060648718 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2000000000000008 " "
y[1] (analytic) = 1.0679609140327733 " "
y[1] (numeric) = 1.0679609140327728 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.15829085142374900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33773159027557503 " "
Order of pole (three term test) = 22.131303142229378 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2100000000000009 " "
y[1] (analytic) = 1.0643839984466137 " "
y[1] (numeric) = 1.0643839984466132 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.172264995510798000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33029060063959964 " "
Order of pole (three term test) = 22.124622697637253 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2200000000000009 " "
y[1] (analytic) = 1.0609006436809323 " "
y[1] (numeric) = 1.0609006436809316 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.27894627779521700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32271749916718456 " "
Order of pole (three term test) = 22.11809239896111 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2300000000000009 " "
y[1] (analytic) = 1.057511198068302 " "
y[1] (numeric) = 1.0575111980683016 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.199380684206995300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3150153149979452 " "
Order of pole (three term test) = 22.111714858233352 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2400000000000009 " "
y[1] (analytic) = 1.0542160005504608 " "
y[1] (numeric) = 1.0542160005504602 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.3187602391471100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.30718712890285527 " "
Order of pole (three term test) = 22.10549262638523 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2500000000000009 " "
y[1] (analytic) = 1.0510153806444134 " "
y[1] (numeric) = 1.051015380644413 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.22533502390589570000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2992360720519776 " "
Order of pole (three term test) = 22.099428192226533 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.260000000000001 " "
y[1] (analytic) = 1.047909658409484 " "
y[1] (numeric) = 1.0479096584094834 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.35678666981799800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29116532476204005 " "
Order of pole (three term test) = 22.093523981450055 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.270000000000001 " "
y[1] (analytic) = 1.0448991444153075 " "
y[1] (numeric) = 1.0448991444153068 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.3751015429134210000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2829781152243507 " "
Order of pole (three term test) = 22.08778235566139 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280000000000001 " "
y[1] (analytic) = 1.0419841397107747 " "
y[1] (numeric) = 1.041984139710774 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.39293622031515500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2746777182135627 " "
Order of pole (three term test) = 22.082205611434297 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290000000000001 " "
y[1] (analytic) = 1.0391649357939272 " "
y[1] (numeric) = 1.0391649357939263 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.54703992703095300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26626745377781 " "
Order of pole (three term test) = 22.076795979392116 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000001 " "
y[1] (analytic) = 1.036441814582807 " "
y[1] (numeric) = 1.036441814582806 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.56949620522246800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2577506859107313 " "
Order of pole (three term test) = 22.071555623315525 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.310000000000001 " "
y[1] (analytic) = 1.0338150483872657 " "
y[1] (numeric) = 1.033815048387265 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.44345249001986900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2491308212059186 " "
Order of pole (three term test) = 22.066486639277098 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.320000000000001 " "
y[1] (analytic) = 1.0312848998817346 " "
y[1] (numeric) = 1.0312848998817337 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.61234775959562200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24041130749432324 " "
Order of pole (three term test) = 22.061591054802857 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.330000000000001 " "
y[1] (analytic) = 1.0288516220789552 " "
y[1] (numeric) = 1.0288516220789543 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.63271632799122400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23159563246517179 " "
Order of pole (three term test) = 22.056870828061324 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.340000000000001 " "
y[1] (analytic) = 1.0265154583046803 " "
y[1] (numeric) = 1.0265154583046794 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.65236283111583400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2226873222709348 " "
Order of pole (three term test) = 22.05232784708025 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.350000000000001 " "
y[1] (analytic) = 1.0242766421733407 " "
y[1] (numeric) = 1.0242766421733396 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08390934530094550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2136899401169141 " "
Order of pole (three term test) = 22.04796392899147 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.360000000000001 " "
y[1] (analytic) = 1.0221353975646836 " "
y[1] (numeric) = 1.0221353975646825 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08617999853086830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2046070848360078 " "
Order of pole (three term test) = 22.04378081930402 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.370000000000001 " "
y[1] (analytic) = 1.0200919386013856 " "
y[1] (numeric) = 1.0200919386013845 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08835584579498460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1954423894492252 " "
Order of pole (three term test) = 22.03978019120601 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.380000000000001 " "
y[1] (analytic) = 1.01814646962764 " "
y[1] (numeric) = 1.018146469627639 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.09043547047920420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18619951971252688 " "
Order of pole (three term test) = 22.035963644895332 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.390000000000001 " "
y[1] (analytic) = 1.0162991851887233 " "
y[1] (numeric) = 1.0162991851887222 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.09241750933706780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17688217265057046 " "
Order of pole (three term test) = 22.032332706939627 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000001 " "
y[1] (analytic) = 1.0145502700115396 " "
y[1] (numeric) = 1.0145502700115385 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.09430065462653580000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16749407507795153 " "
Order of pole (three term test) = 22.028888829665664 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.410000000000001 " "
y[1] (analytic) = 1.0128998989861495 " "
y[1] (numeric) = 1.0128998989861484 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.09608365618006420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15803898210852585 " "
Order of pole (three term test) = 22.025633390578445 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.420000000000001 " "
y[1] (analytic) = 1.01134823714828 " "
y[1] (numeric) = 1.011348237148279 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0977653234020320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14852067565341512 " "
Order of pole (three term test) = 22.022567691810185 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.430000000000001 " "
y[1] (analytic) = 1.009895439662822 " "
y[1] (numeric) = 1.0098954396628208 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0993445271877170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13894296290829233 " "
Order of pole (three term test) = 22.019692959599517 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.440000000000001 " "
y[1] (analytic) = 1.0085416518083135 " "
y[1] (numeric) = 1.0085416518083121 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3209842421098170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12930967483055428 " "
Order of pole (three term test) = 22.017010343801008 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.450000000000001 " "
y[1] (analytic) = 1.0072870089624115 " "
y[1] (numeric) = 1.00728700896241 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54306788496784920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11962466460699013 " "
Order of pole (three term test) = 22.014520917425205 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.460000000000001 " "
y[1] (analytic) = 1.006131636588355 " "
y[1] (numeric) = 1.0061316365883537 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32414843257261240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10989180611255746 " "
Order of pole (three term test) = 22.01222567620946 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.470000000000001 " "
y[1] (analytic) = 1.005075650222419 " "
y[1] (numeric) = 1.0050756502224176 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32553965391098950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1001149923608842 " "
Order of pole (three term test) = 22.010125538219654 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.480000000000001 " "
y[1] (analytic) = 1.0041191554623599 " "
y[1] (numeric) = 1.0041191554623585 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32680232450772000000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.02981339471153300E-2 " "
Order of pole (three term test) = 22.008221343482994 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.490000000000001 " "
y[1] (analytic) = 1.0032622479568565 " "
y[1] (numeric) = 1.0032622479568551 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32793557443564830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.04451574837267600E-2 " "
Order of pole (three term test) = 22.00651385365198 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000001 " "
y[1] (analytic) = 1.0025050133959454 " "
y[1] (numeric) = 1.0025050133959441 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32893862050343730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.05600040299324800E-2 " "
Order of pole (three term test) = 22.005003751699775 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5100000000000011 " "
y[1] (analytic) = 1.0018475275024517 " "
y[1] (numeric) = 1.0018475275024503 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.329810767584020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.06466275153138100E-2 " "
Order of pole (three term test) = 22.003691641647027 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5200000000000011 " "
y[1] (analytic) = 1.001289856024417 " "
y[1] (numeric) = 1.0012898560244154 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.55230997809820660000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.07089931582998300E-2 " "
Order of pole (three term test) = 22.00257804832027 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5300000000000011 " "
y[1] (analytic) = 1.0008320547285239 " "
y[1] (numeric) = 1.0008320547285223 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.5530200368100988000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.07510758801334400E-2 " "
Order of pole (three term test) = 22.001663417141977 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5400000000000011 " "
y[1] (analytic) = 1.000474169394521 " "
y[1] (numeric) = 1.0004741693945192 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77551494455402830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.07768587149554600E-2 " "
Order of pole (three term test) = 22.000948113952425 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5500000000000012 " "
y[1] (analytic) = 1.000216235810643 " "
y[1] (numeric) = 1.0002162358106412 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77597281047989660000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.07903312166441400E-2 " "
Order of pole (three term test) = 22.00043242486336 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5600000000000012 " "
y[1] (analytic) = 1.0000582797700337 " "
y[1] (numeric) = 1.000058279770032 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.7762533197652530000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.079548786304687100E-2 " "
Order of pole (three term test) = 22.00011655614353 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5700000000000012 " "
y[1] (analytic) = 1.0000003170681655 " "
y[1] (numeric) = 1.0000003170681635 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9984008106960030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.9632645824230390000E-4 " "
Order of pole (three term test) = 22.000000634136228 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5800000000000012 " "
y[1] (analytic) = 1.00004235350126 " "
y[1] (numeric) = 1.0000423535012581 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77628160765494260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.203153466528016000E-3 " "
Order of pole (three term test) = 22.0000847052087 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5900000000000012 " "
y[1] (analytic) = 1.000184384865709 " "
y[1] (numeric) = 1.0001843848657073 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77602936646401980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.919895225261880300E-2 " "
Order of pole (three term test) = 22.000368735733634 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6000000000000012 " "
y[1] (analytic) = 1.000426396958495 " "
y[1] (numeric) = 1.000426396958493 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.99754969521080130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.918707171379116300E-2 " "
Order of pole (three term test) = 22.000852612102623 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6100000000000012 " "
y[1] (analytic) = 1.0007683655786095 " "
y[1] (numeric) = 1.0007683655786077 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77499299587994350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.916351673543377000E-2 " "
Order of pole (three term test) = 22.00153614077156 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6200000000000012 " "
y[1] (analytic) = 1.001210256529476 " "
y[1] (numeric) = 1.0012102565294743 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77420959065849700000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.91242968725554500E-2 " "
Order of pole (three term test) = 22.002419048338083 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6300000000000012 " "
y[1] (analytic) = 1.0017520256223675 " "
y[1] (numeric) = 1.0017520256223658 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.773250059860510000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.90654279459099900E-2 " "
Order of pole (three term test) = 22.003500981650948 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6400000000000012 " "
y[1] (analytic) = 1.0023936186808264 " "
y[1] (numeric) = 1.0023936186808244 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.99362945561766950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.89829336356147400E-2 " "
Order of pole (three term test) = 22.004781507951265 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6500000000000012 " "
y[1] (analytic) = 1.0031349715460811 " "
y[1] (numeric) = 1.0031349715460793 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.77080541481117130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.88728470716254500E-2 " "
Order of pole (three term test) = 22.006260115045567 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6600000000000013 " "
y[1] (analytic) = 1.0039760100834634 " "
y[1] (numeric) = 1.0039760100834614 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9904872469603620000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.87312124204313700E-2 " "
Order of pole (three term test) = 22.00793621151074 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6700000000000013 " "
y[1] (analytic) = 1.00491665018982 " "
y[1] (numeric) = 1.004916650189818 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98862407538754730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.8554086467336200E-2 " "
Order of pole (three term test) = 22.009809126930552 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6800000000000013 " "
y[1] (analytic) = 1.0059567978019242 " "
y[1] (numeric) = 1.0059567978019222 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9865678612559790000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10833754019369096 " "
Order of pole (three term test) = 22.011878112163792 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6900000000000013 " "
y[1] (analytic) = 1.0070963489058817 " "
y[1] (numeric) = 1.0070963489058795 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20480001904745760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11807766034844973 " "
Order of pole (three term test) = 22.014142339643964 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7000000000000013 " "
y[1] (analytic) = 1.0083351895475317 " "
y[1] (numeric) = 1.0083351895475294 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.20209120168333080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1277705510134168 " "
Order of pole (three term test) = 22.016600903710266 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7100000000000013 " "
y[1] (analytic) = 1.009673195843842 " "
y[1] (numeric) = 1.00967319584384 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9792557161578430000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1374123351615633 " "
Order of pole (three term test) = 22.019252820969857 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7200000000000013 " "
y[1] (analytic) = 1.0111102339952986 " "
y[1] (numeric) = 1.0111102339952966 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.97644270341207300000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14699915620778514 " "
Order of pole (three term test) = 22.022097030691167 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7300000000000013 " "
y[1] (analytic) = 1.0126461602992838 " "
y[1] (numeric) = 1.0126461602992816 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.19271660359040780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15652717955148637 " "
Order of pole (three term test) = 22.025132395228248 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7400000000000013 " "
y[1] (analytic) = 1.0142808211644467 " "
y[1] (numeric) = 1.0142808211644445 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.18918272229689430000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1659925941103682 " "
Order of pole (three term test) = 22.028357700475762 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7500000000000013 " "
y[1] (analytic) = 1.0160140531260633 " "
y[1] (numeric) = 1.016014053126061 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.18544816621233120000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17539161384481128 " "
Order of pole (three term test) = 22.031771656354604 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7600000000000013 " "
y[1] (analytic) = 1.0178456828623816 " "
y[1] (numeric) = 1.0178456828623794 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.18151541695985100000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18472047927223964 " "
Order of pole (three term test) = 22.035372897327935 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7700000000000014 " "
y[1] (analytic) = 1.0197755272119546 " "
y[1] (numeric) = 1.0197755272119524 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.17738707195785220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1939754589708663 " "
Order of pole (three term test) = 22.039159982947396 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7800000000000014 " "
y[1] (analytic) = 1.0218033931919557 " "
y[1] (numeric) = 1.0218033931919532 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.39037242433241650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20315285107220943 " "
Order of pole (three term test) = 22.04313139842923 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7900000000000014 " "
y[1] (analytic) = 1.0239290780174761 " "
y[1] (numeric) = 1.0239290780174737 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.38540999236438980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21224898474179243 " "
Order of pole (three term test) = 22.04728555526019 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8000000000000014 " "
y[1] (analytic) = 1.026152369121805 " "
y[1] (numeric) = 1.0261523691218026 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.38024169477449060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22126022164742723 " "
Order of pole (three term test) = 22.051620791832928 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8100000000000014 " "
y[1] (analytic) = 1.028473044177685 " "
y[1] (numeric) = 1.0284730441776824 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.59076820164091200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23018295741450034 " "
Order of pole (three term test) = 22.056135374110625 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8200000000000014 " "
y[1] (analytic) = 1.030890871119544 " "
y[1] (numeric) = 1.0308908711195413 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.5846918754908554000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23901362306767263 " "
Order of pole (three term test) = 22.060827496320563 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8300000000000014 " "
y[1] (analytic) = 1.033405608166703 " "
y[1] (numeric) = 1.0334056081667 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.79326901384471750000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2477486864584236 " "
Order of pole (three term test) = 22.065695281676415 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8400000000000014 " "
y[1] (analytic) = 1.0360170038475522 " "
y[1] (numeric) = 1.0360170038475494 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.7862282697149260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2563846536778632 " "
Order of pole (three term test) = 22.070736783128954 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8500000000000014 " "
y[1] (analytic) = 1.0387247970247004 " "
y[1] (numeric) = 1.0387247970246976 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.77896500814620030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26491807045424787 " "
Order of pole (three term test) = 22.0759499841448 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8600000000000014 " "
y[1] (analytic) = 1.041528716921086 " "
y[1] (numeric) = 1.0415287169210834 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.55829264792346630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2733455235346447 " "
Order of pole (three term test) = 22.08133279951306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8700000000000014 " "
y[1] (analytic) = 1.0444284831470565 " "
y[1] (numeric) = 1.0444284831470536 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.76378891480210050000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2816636420501861 " "
Order of pole (three term test) = 22.08688307617936 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8800000000000014 " "
y[1] (analytic) = 1.047423805728405 " "
y[1] (numeric) = 1.0474238057284022 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.75588529517715730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2898690988643725 " "
Order of pole (three term test) = 22.09259859410705 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8900000000000015 " "
y[1] (analytic) = 1.05051438513537 " "
y[1] (numeric) = 1.050514385135367 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.74777756960790260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2979586119038833 " "
Order of pole (three term test) = 22.098477067165135 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9000000000000015 " "
y[1] (analytic) = 1.0536999123125859 " "
y[1] (numeric) = 1.053699912312583 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.73947053643588730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.30592894547136057 " "
Order of pole (three term test) = 22.10451614404279 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9100000000000015 " "
y[1] (analytic) = 1.05698006870999 " "
y[1] (numeric) = 1.0569800687099868 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.94104360240625360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3137769115396477 " "
Order of pole (three term test) = 22.110713409189785 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9200000000000015 " "
y[1] (analytic) = 1.0603545263146756 " "
y[1] (numeric) = 1.0603545263146725 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.9316840658516780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32149937102695564 " "
Order of pole (three term test) = 22.11706638378268 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9300000000000015 " "
y[1] (analytic) = 1.0638229476836945 " "
y[1] (numeric) = 1.0638229476836913 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.92212578767827300000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32909323505245364 " "
Order of pole (three term test) = 22.123572526716355 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9400000000000015 " "
y[1] (analytic) = 1.0673849859778 " "
y[1] (numeric) = 1.0673849859777969 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.91237417594245000000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.336555466171782 " "
Order of pole (three term test) = 22.130229235620376 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9500000000000015 " "
y[1] (analytic) = 1.0710402849961311 " "
y[1] (numeric) = 1.071040284996128 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.90243468196125560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3438830795919879 " "
Order of pole (three term test) = 22.13703384789993 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9600000000000015 " "
y[1] (analytic) = 1.0747884792118323 " "
y[1] (numeric) = 1.074788479211829 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.09890656468324600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3510731443654038 " "
Order of pole (three term test) = 22.14398364180085 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9700000000000015 " "
y[1] (analytic) = 1.0786291938086052 " "
y[1] (numeric) = 1.078629193808602 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.0878721742316130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3581227845619863 " "
Order of pole (three term test) = 22.15107583749822 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9800000000000015 " "
y[1] (analytic) = 1.0825620447181907 " "
y[1] (numeric) = 1.0825620447181874 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.07665421129973140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3650291804196506 " "
Order of pole (three term test) = 22.15830759820833 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9900000000000015 " "
y[1] (analytic) = 1.0865866386587755 " "
y[1] (numeric) = 1.086586638658772 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.2696092077717620000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3717895694721383 " "
Order of pole (three term test) = 22.165676031323322 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0000000000000013 " "
y[1] (analytic) = 1.090702573174319 " "
y[1] (numeric) = 1.0907025731743154 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 3.25727083274488350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3784012476539651 " "
Order of pole (three term test) = 22.173178189568198 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.010000000000001 " "
y[1] (analytic) = 1.0949094366747996 " "
y[1] (numeric) = 1.0949094366747962 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.0419585057103820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38486157038201296 " "
Order of pole (three term test) = 22.18081107217967 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.020000000000001 " "
y[1] (analytic) = 1.0992068084773732 " "
y[1] (numeric) = 1.0992068084773698 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.03006590587728330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3911679536133269 " "
Order of pole (three term test) = 22.188571626106484 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0300000000000007 " "
y[1] (analytic) = 1.1035942588484404 " "
y[1] (numeric) = 1.1035942588484373 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.8168182681506265000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3973178748786991 " "
Order of pole (three term test) = 22.19645674723052 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0400000000000005 " "
y[1] (analytic) = 1.1080713490466207 " "
y[1] (numeric) = 1.1080713490466176 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.80543709719151550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4033088742916205 " "
Order of pole (three term test) = 22.204463281608486 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0500000000000003 " "
y[1] (analytic) = 1.1126376313666246 " "
y[1] (numeric) = 1.1126376313666217 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.594357572177290000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40913855553220535 " "
Order of pole (three term test) = 22.212588026733368 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.06 " "
y[1] (analytic) = 1.117292649184026 " "
y[1] (numeric) = 1.1172926491840232 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.58354860397006560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41480458680568544 " "
Order of pole (three term test) = 22.22082773281544 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.07 " "
y[1] (analytic) = 1.1220359370009219 " "
y[1] (numeric) = 1.1220359370009192 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.37473254753531730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4203047017750973 " "
Order of pole (three term test) = 22.229179104082153 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0799999999999996 " "
y[1] (analytic) = 1.1268670204924833 " "
y[1] (numeric) = 1.1268670204924807 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.3645516379881928000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4256367004677871 " "
Order of pole (three term test) = 22.23763880009632 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0899999999999994 " "
y[1] (analytic) = 1.1317854165543872 " "
y[1] (numeric) = 1.1317854165543846 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.3542760139217017000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43079845015537005 " "
Order of pole (three term test) = 22.246203437092362 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999999 " "
y[1] (analytic) = 1.1367906333511257 " "
y[1] (numeric) = 1.1367906333511233 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.14858442928507230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4357878862067935 " "
Order of pole (three term test) = 22.254869589329644 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.109999999999999 " "
y[1] (analytic) = 1.1418821703651907 " "
y[1] (numeric) = 1.1418821703651882 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.13900410879889670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4406030129141622 " "
Order of pole (three term test) = 22.26363379046284 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999999988 " "
y[1] (analytic) = 1.147059518447123 " "
y[1] (numeric) = 1.1470595184471208 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.93577230609299960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4452419042909938 " "
Order of pole (three term test) = 22.272492534928347 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999999986 " "
y[1] (analytic) = 1.1523221598664295 " "
y[1] (numeric) = 1.1523221598664273 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.92693165729598940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4497027048425882 " "
Order of pole (three term test) = 22.281442279346482 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999999983 " "
y[1] (analytic) = 1.1576695683633536 " "
y[1] (numeric) = 1.1576695683633513 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.91803093899190230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.453983630308202 " "
Order of pole (three term test) = 22.290479443938825 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.149999999999998 " "
y[1] (analytic) = 1.1631012092015012 " "
y[1] (numeric) = 1.1631012092014994 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.52725904276186350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45808296837472673 " "
Order of pole (three term test) = 22.29960041396001 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999998 " "
y[1] (analytic) = 1.1686165392213157 " "
y[1] (numeric) = 1.168616539221314 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.52005108586251080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46199907936159307 " "
Order of pole (three term test) = 22.308801541143655 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1699999999999977 " "
y[1] (analytic) = 1.1742150068943906 " "
y[1] (numeric) = 1.174215006894389 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.32370326162507880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4657303968766203 " "
Order of pole (three term test) = 22.31807914516157 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1799999999999975 " "
y[1] (analytic) = 1.1798960523786244 " "
y[1] (numeric) = 1.1798960523786228 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.31732980319900740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.469275428442553 " "
Order of pole (three term test) = 22.327429515095833 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1899999999999973 " "
y[1] (analytic) = 1.1856591075742025 " "
y[1] (numeric) = 1.1856591075742011 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.1236514956444260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4726327560940308 " "
Order of pole (three term test) = 22.336848910923155 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999997 " "
y[1] (analytic) = 1.1915035961804081 " "
y[1] (numeric) = 1.1915035961804068 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.11813983090023870000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47580103694475717 " "
Order of pole (three term test) = 22.34633356501078 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.209999999999997 " "
y[1] (analytic) = 1.1974289337532509 " "
y[1] (numeric) = 1.1974289337532498 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.2717237184610700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47877900372463467 " "
Order of pole (three term test) = 22.355879683623552 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999999966 " "
y[1] (analytic) = 1.2034345277639114 " "
y[1] (numeric) = 1.2034345277639105 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.38036344486841300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4815654652866574 " "
Order of pole (three term test) = 22.3654834484413 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999999964 " "
y[1] (analytic) = 1.209519777657993 " "
y[1] (numeric) = 1.2095197776579922 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.507423913852293000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48415930708335264 " "
Order of pole (three term test) = 22.37514101808613 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.239999999999996 " "
y[1] (analytic) = 1.2156840749155777 " "
y[1] (numeric) = 1.215684074915577 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.47949774550886700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48655949161258594 " "
Order of pole (three term test) = 22.384848529658964 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999996 " "
y[1] (analytic) = 1.2219268031120762 " "
y[1] (numeric) = 1.2219268031120758 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.63433561420397400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4887650588325476 " "
Order of pole (three term test) = 22.394602100284605 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999996 " "
y[1] (analytic) = 1.2282473379798715 " "
y[1] (numeric) = 1.228247337979871 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.61563339986933740000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49077512654575683 " "
Order of pole (three term test) = 22.404397828664845 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2699999999999956 " "
y[1] (analytic) = 1.2346450474707438 " "
y[1] (numeric) = 1.2346450474707433 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.596897835210291500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49258889075192897 " "
Order of pole (three term test) = 22.414231796638937 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2799999999999954 " "
y[1] (analytic) = 1.241119291819075 " "
y[1] (numeric) = 1.241119291819075 " "
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 = 0.49420562596956447 " "
Order of pole (three term test) = 22.424100070750818 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999995 " "
y[1] (analytic) = 1.2476694236058261 " "
y[1] (numeric) = 1.2476694236058261 " "
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 = 0.49562468552613287 " "
Order of pole (three term test) = 22.43399870382241 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999995 " "
y[1] (analytic) = 1.2542947878232764 " "
y[1] (numeric) = 1.2542947878232766 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.770274476786841400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49684550181673165 " "
Order of pole (three term test) = 22.44392373653247 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999999947 " "
y[1] (analytic) = 1.2609947219405255 " "
y[1] (numeric) = 1.260994721940526 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.521737261252454000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4978675865311223 " "
Order of pole (three term test) = 22.45387119900024 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999999945 " "
y[1] (analytic) = 1.267768555969745 " "
y[1] (numeric) = 1.2677685559697456 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.25438031759316700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4986905308490463 " "
Order of pole (three term test) = 22.463837112373366 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999999943 " "
y[1] (analytic) = 1.2746156125331765 " "
y[1] (numeric) = 1.2746156125331773 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.96820602985519500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4993140056037492 " "
Order of pole (three term test) = 22.473817490419382 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.339999999999994 " "
y[1] (analytic) = 1.2815352069308696 " "
y[1] (numeric) = 1.2815352069308708 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.66322687524140500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4997377614136418 " "
Order of pole (three term test) = 22.48380834112013 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999994 " "
y[1] (analytic) = 1.2885266472091512 " "
y[1] (numeric) = 1.2885266472091526 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.0339465097099670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49996162878205036 " "
Order of pole (three term test) = 22.493805668268546 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3599999999999937 " "
y[1] (analytic) = 1.2955892342298194 " "
y[1] (numeric) = 1.2955892342298208 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.02831020384494960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49998551816501235 " "
Order of pole (three term test) = 22.503805473067068 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3699999999999934 " "
y[1] (analytic) = 1.3027222617400573 " "
y[1] (numeric) = 1.3027222617400591 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.36357295148050620000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4998094200070929 " "
Order of pole (three term test) = 22.5138037557271 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3799999999999932 " "
y[1] (analytic) = 1.3099250164430587 " "
y[1] (numeric) = 1.3099250164430605 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.3560752082006422000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4994334047452075 " "
Order of pole (three term test) = 22.523796517068885 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999993 " "
y[1] (analytic) = 1.3171967780693552 " "
y[1] (numeric) = 1.317196778069357 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.34858881298198790000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4988576227804472 " "
Order of pole (three term test) = 22.533779760121128 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999993 " "
y[1] (analytic) = 1.3245368194488436 " "
y[1] (numeric) = 1.3245368194488458 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.67639435661310540000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4980823044179209 " "
Order of pole (three term test) = 22.543749491719716 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999999926 " "
y[1] (analytic) = 1.3319444065835033 " "
y[1] (numeric) = 1.3319444065835058 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.83377822835747440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49710775977463645 " "
Order of pole (three term test) = 22.553701724104933 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999999924 " "
y[1] (analytic) = 1.3394187987207937 " "
y[1] (numeric) = 1.3394187987207962 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.82354514996208420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49593437865545725 " "
Order of pole (three term test) = 22.56363247651652 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.429999999999992 " "
y[1] (analytic) = 1.346959248427729 " "
y[1] (numeric) = 1.346959248427732 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.14303429550287970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49456263039718606 " "
Order of pole (three term test) = 22.573537776785926 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.439999999999992 " "
y[1] (analytic) = 1.3545650016656232 " "
y[1] (numeric) = 1.354565001665626 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.13100136241225900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49299306368083634 " "
Order of pole (three term test) = 22.5834136629251 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999999917 " "
y[1] (analytic) = 1.36223529786549 " "
y[1] (numeric) = 1.362235297865493 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.28200258341667960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4912263063121679 " "
Order of pole (three term test) = 22.593256184711276 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4599999999999915 " "
y[1] (analytic) = 1.3699693700041013 " "
y[1] (numeric) = 1.3699693700041047 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.4311996653366771000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48926306497057087 " "
Order of pole (three term test) = 22.60306140526697 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4699999999999913 " "
y[1] (analytic) = 1.3777664446806885 " "
y[1] (numeric) = 1.377766444680692 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.578603719459780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48710412492640653 " "
Order of pole (three term test) = 22.61282540263469 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999991 " "
y[1] (analytic) = 1.3856257421942813 " "
y[1] (numeric) = 1.3856257421942852 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.8844750548017495000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4847503497269066 " "
Order of pole (three term test) = 22.62254427134567 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999991 " "
y[1] (analytic) = 1.3935464766216779 " "
y[1] (numeric) = 1.393546476621682 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.0274178610843230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4822026808507677 " "
Order of pole (three term test) = 22.632214123982013 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999999907 " "
y[1] (analytic) = 1.401527855896036 " "
y[1] (numeric) = 1.4015278558960405 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.16860780170611640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47946213733157195 " "
Order of pole (three term test) = 22.641831092731607 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999999905 " "
y[1] (analytic) = 1.4095690818860795 " "
y[1] (numeric) = 1.4095690818860842 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.30805830189350950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47652981535018685 " "
Order of pole (three term test) = 22.65139133093516 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999999902 " "
y[1] (analytic) = 1.4176693504759101 " "
y[1] (numeric) = 1.4176693504759152 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.6024097661145720000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47340688779630763 " "
Order of pole (three term test) = 22.660891014624852 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.52999999999999 " "
y[1] (analytic) = 1.4258278516454195 " "
y[1] (numeric) = 1.4258278516454246 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.5817969942038670000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47009460379931745 " "
Order of pole (three term test) = 22.670326344053883 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.53999999999999 " "
y[1] (analytic) = 1.4340437695512889 " "
y[1] (numeric) = 1.4340437695512942 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.7161142716503087000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4665942882286525 " "
Order of pole (three term test) = 22.67969354521628 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999999896 " "
y[1] (analytic) = 1.4423162826085745 " "
y[1] (numeric) = 1.44231628260858 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.84875022910095070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46290734116387017 " "
Order of pole (three term test) = 22.688988871356482 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5599999999999894 " "
y[1] (analytic) = 1.4506445635728644 " "
y[1] (numeric) = 1.4506445635728702 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.9797203760456750000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45903523733463786 " "
Order of pole (three term test) = 22.698208604467954 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999989 " "
y[1] (analytic) = 1.4590277796230025 " "
y[1] (numeric) = 1.4590277796230084 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.10904056571489200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4549795255308598 " "
Order of pole (three term test) = 22.70734905678038 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999989 " "
y[1] (analytic) = 1.4674650924443695 " "
y[1] (numeric) = 1.4674650924443757 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.2367269721862690000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45074182798318213 " "
Order of pole (three term test) = 22.716406572234714 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999999888 " "
y[1] (analytic) = 1.4759556583127145 " "
y[1] (numeric) = 1.475955658312721 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.3627960681333683000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44632383971412243 " "
Order of pole (three term test) = 22.72537752794554 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999999885 " "
y[1] (analytic) = 1.484498628178526 " "
y[1] (numeric) = 1.4844986281785326 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.4872646032178390000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44172732786008206 " "
Order of pole (three term test) = 22.73425833565018 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999999883 " "
y[1] (analytic) = 1.4930931477519365 " "
y[1] (numeric) = 1.4930931477519436 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.7588640858068576000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4369541309645169 " "
Order of pole (three term test) = 22.743045443143956 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.619999999999988 " "
y[1] (analytic) = 1.501738357588151 " "
y[1] (numeric) = 1.5017383575881582 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.7314682492445537000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4320061582425432 " "
Order of pole (three term test) = 22.751735335701046 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.629999999999988 " "
y[1] (analytic) = 1.51043339317339 " "
y[1] (numeric) = 1.5104333931733975 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.9982452728946114000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4268853888172779 " "
Order of pole (three term test) = 22.76032453748028 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999999877 " "
y[1] (analytic) = 1.5191773850113408 " "
y[1] (numeric) = 1.5191773850113486 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 5.1156377451722530000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42159387092821515 " "
Order of pole (three term test) = 22.76880961291547 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999999875 " "
y[1] (analytic) = 1.5279694587101065 " "
y[1] (numeric) = 1.5279694587101145 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.2315219599017590000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4161337211119575 " "
Order of pole (three term test) = 22.77718716808958 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6599999999999873 " "
y[1] (analytic) = 1.5368087350696436 " "
y[1] (numeric) = 1.5368087350696518 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 5.345915984693990000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.410507123355631 " "
Order of pole (three term test) = 22.785453852092214 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999987 " "
y[1] (analytic) = 1.545694330169682 " "
y[1] (numeric) = 1.5456943301696906 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 5.6024916589592320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40471632822331727 " "
Order of pole (three term test) = 22.79360635836002 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999987 " "
y[1] (analytic) = 1.5546253554581169 " "
y[1] (numeric) = 1.5546253554581257 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 5.7131347857014530000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39876365195586017 " "
Order of pole (three term test) = 22.80164142599919 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999999866 " "
y[1] (analytic) = 1.5636009178398618 " "
y[1] (numeric) = 1.5636009178398709 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 5.8223480800352570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39265147554439855 " "
Order of pole (three term test) = 22.809555841089786 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999999864 " "
y[1] (analytic) = 1.5726201197661578 " "
y[1] (numeric) = 1.5726201197661673 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 6.0713441801800690000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3863822437780024 " "
Order of pole (three term test) = 22.817346437971306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.709999999999986 " "
y[1] (analytic) = 1.5816820593243286 " "
y[1] (numeric) = 1.5816820593243384 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 6.1769447020692400000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37995846426578933 " "
Order of pole (three term test) = 22.82501010050886 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.719999999999986 " "
y[1] (analytic) = 1.5907858303279698 " "
y[1] (numeric) = 1.5907858303279798 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 6.2811769071178940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3733827064339157 " "
Order of pole (three term test) = 22.83254376333963 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999999858 " "
y[1] (analytic) = 1.5999305224075675 " "
y[1] (numeric) = 1.599930522407578 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 6.5228435143372890000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36665760049783785 " "
Order of pole (three term test) = 22.83994441309892 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999999856 " "
y[1] (analytic) = 1.6091152211015343 " "
y[1] (numeric) = 1.6091152211015451 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 6.7615951292029950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3597858364102641 " "
Order of pole (three term test) = 22.847209089625498 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999999853 " "
y[1] (analytic) = 1.6183390079476547 " "
y[1] (numeric) = 1.6183390079476658 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 6.8602623997373660000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35277016278520645 " "
Order of pole (three term test) = 22.854334887145622 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999985 " "
y[1] (analytic) = 1.6276009605749306 " "
y[1] (numeric) = 1.627600960574942 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 6.9576481738966480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3456133857985741 " "
Order of pole (three term test) = 22.861318955435287 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999985 " "
y[1] (analytic) = 1.6369001527958176 " "
y[1] (numeric) = 1.6369001527958291 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 7.0537713839054680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33831836806573967 " "
Order of pole (three term test) = 22.868158500960302 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7799999999999847 " "
y[1] (analytic) = 1.6462356546988428 " "
y[1] (numeric) = 1.6462356546988546 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 7.1486509403658420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3308880274965303 " "
Order of pole (three term test) = 22.874850787993644 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999999845 " "
y[1] (analytic) = 1.6556065327415954 " "
y[1] (numeric) = 1.6556065327416074 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 7.2423057222999830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3233253361281034 " "
Order of pole (three term test) = 22.881393139709733 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999999843 " "
y[1] (analytic) = 1.6650118498440802 " "
y[1] (numeric) = 1.6650118498440927 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 7.4681137416326380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3156333189361729 " "
Order of pole (three term test) = 22.887782939255114 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.809999999999984 " "
y[1] (analytic) = 1.674450665482425 " "
y[1] (numeric) = 1.6744506654824376 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 7.5586236976891260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.30781505262505593 " "
Order of pole (three term test) = 22.89401763079516 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.819999999999984 " "
y[1] (analytic) = 1.683922035782931 " "
y[1] (numeric) = 1.683922035782944 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 7.7798326835753860000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29987366439703445 " "
Order of pole (three term test) = 22.900094720536387 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999999836 " "
y[1] (analytic) = 1.6934250136164615 " "
y[1] (numeric) = 1.6934250136164748 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 7.8672962713891310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2918123307015169 " "
Order of pole (three term test) = 22.906011777723936 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999999834 " "
y[1] (analytic) = 1.7029586486931518 " "
y[1] (numeric) = 1.7029586486931656 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 8.084028062523150000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2836342759644979 " "
Order of pole (three term test) = 22.911766435613806 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999983 " "
y[1] (analytic) = 1.7125219876574396 " "
y[1] (numeric) = 1.7125219876574533 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 8.0388839410952700000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.27534277129883283 " "
Order of pole (three term test) = 22.917356392419574 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999983 " "
y[1] (analytic) = 1.7221140741833971 " "
y[1] (numeric) = 1.7221140741834111 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 8.1230449945136630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26694113319583634 " "
Order of pole (three term test) = 22.922779412233048 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999983 " "
y[1] (analytic) = 1.7317339490703654 " "
y[1] (numeric) = 1.7317339490703798 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 8.3343629821861200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2584327221987291 " "
Order of pole (three term test) = 22.92803332591862 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8799999999999826 " "
y[1] (analytic) = 1.7413806503388725 " "
y[1] (numeric) = 1.7413806503388871 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 8.4157038969051460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24982094155846626 " "
Order of pole (three term test) = 22.933116031980852 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999999824 " "
y[1] (analytic) = 1.7510532133268302 " "
y[1] (numeric) = 1.7510532133268453 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 8.6228294034625250000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24110923587248126 " "
Order of pole (three term test) = 22.938025497405103 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.899999999999982 " "
y[1] (analytic) = 1.7607506707860003 " "
y[1] (numeric) = 1.7607506707860157 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 8.7014464875869220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2323010897068944 " "
Order of pole (three term test) = 22.942759758470654 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.909999999999982 " "
y[1] (analytic) = 1.7704720529787181 " "
y[1] (numeric) = 1.7704720529787337 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 8.779083701774211000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22340002620273142 " "
Order of pole (three term test) = 22.947316921536196 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999999817 " "
y[1] (analytic) = 1.7802163877748653 " "
y[1] (numeric) = 1.7802163877748811 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 8.8557588043453960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2144096056667146 " "
Order of pole (three term test) = 22.95169516379727 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999999815 " "
y[1] (analytic) = 1.7899827007490825 " "
y[1] (numeric) = 1.7899827007490987 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 9.0555378846644370000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20533342414718742 " "
Order of pole (three term test) = 22.955892734015347 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999999813 " "
y[1] (analytic) = 1.7997700152782112 " "
y[1] (numeric) = 1.7997700152782277 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 9.1296669157544220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19617511199574417 " "
Order of pole (three term test) = 22.959907953218313 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999981 " "
y[1] (analytic) = 1.8095773526389543 " "
y[1] (numeric) = 1.809577352638971 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 9.202892236185061000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18693833241513566 " "
Order of pole (three term test) = 22.96373921537201 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999981 " "
y[1] (analytic) = 1.8194037321057484 " "
y[1] (numeric) = 1.8194037321057652 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 9.2752310421893410000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1776267799940392 " "
Order of pole (three term test) = 22.96738498802266 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9699999999999807 " "
y[1] (analytic) = 1.8292481710488353 " "
y[1] (numeric) = 1.8292481710488526 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 9.4680861013090310000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16824417922927054 " "
Order of pole (three term test) = 22.970843812909834 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9799999999999804 " "
y[1] (analytic) = 1.839109685032525 " "
y[1] (numeric) = 1.8391096850325426 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 9.5380519888715880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15879428303603602 " "
Order of pole (three term test) = 22.97411430654967 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999999802 " "
y[1] (analytic) = 1.8489872879136364 " "
y[1] (numeric) = 1.8489872879136544 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 9.727277800391031000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.149280871246816 " "
Order of pole (three term test) = 22.977195160788316 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.99999999999998 " "
y[1] (analytic) = 1.858879991940113 " "
y[1] (numeric) = 1.8588799919401313 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 9.7949613115418150000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1397077490994821 " "
Order of pole (three term test) = 22.980085143325184 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00999999999998 " "
y[1] (analytic) = 1.868786807849796 " "
y[1] (numeric) = 1.8687868078498147 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 9.9806712758011760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13007874571525377 " "
Order of pole (three term test) = 22.98278309820575 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999999796 " "
y[1] (analytic) = 1.87870674496935 " "
y[1] (numeric) = 1.878706744969369 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.016435166088906000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12039771256709943 " "
Order of pole (three term test) = 22.985287946284064 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999999794 " "
y[1] (analytic) = 1.8886388113133297 " "
y[1] (numeric) = 1.8886388113133492 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.0346036053243553000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11066852193919968 " "
Order of pole (three term test) = 22.98759868565429 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999979 " "
y[1] (analytic) = 1.8985820136833773 " "
y[1] (numeric) = 1.8985820136833973 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.0525757801993751000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10089506537808487 " "
Order of pole (three term test) = 22.989714392051475 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999979 " "
y[1] (analytic) = 1.908535357767542 " "
y[1] (numeric) = 1.9085353577675623 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 1.0703550012821407000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.1081252136068500E-2 " "
Order of pole (three term test) = 22.991634219221293 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0599999999999787 " "
y[1] (analytic) = 1.9184978482397097 " "
y[1] (numeric) = 1.9184978482397304 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.0763706759939898000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.12310076075981200E-2 " "
Order of pole (three term test) = 22.993357399258446 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0699999999999785 " "
y[1] (analytic) = 1.928468488859135 " "
y[1] (numeric) = 1.9284684888591561 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.0938336607385864000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.13482717591504700E-2 " "
Order of pole (three term test) = 22.99488324291391 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0799999999999783 " "
y[1] (analytic) = 1.9384462825700652 " "
y[1] (numeric) = 1.9384462825700866 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.0996581264321173000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.143699755329667000E-2 " "
Order of pole (three term test) = 22.99621113987056 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.089999999999978 " "
y[1] (analytic) = 1.9484302316014437 " "
y[1] (numeric) = 1.9484302316014654 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.1168155230668893000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.15011493675705600E-2 " "
Order of pole (three term test) = 22.997340558987318 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.099999999999978 " "
y[1] (analytic) = 1.9584193375666874 " "
y[1] (numeric) = 1.9584193375667094 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.1224570481871868000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.15447014087703200E-2 " "
Order of pole (three term test) = 22.998271048511604 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999999777 " "
y[1] (analytic) = 1.968412601563524 " "
y[1] (numeric) = 1.9684126015635464 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 1.1393193215494878000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.15716361233285700E-2 " "
Order of pole (three term test) = 22.99900223626002 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999999775 " "
y[1] (analytic) = 1.9784090242738814 " "
y[1] (numeric) = 1.978409024273904 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 1.1447860085790752000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.15859426043869800E-2 " "
Order of pole (three term test) = 22.99953382976719 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999999772 " "
y[1] (analytic) = 1.9884076060638192 " "
y[1] (numeric) = 1.988407606063842 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 1.150196480718158000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.15916149962123700E-2 " "
Order of pole (three term test) = 22.99986561640283 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999977 " "
y[1] (analytic) = 1.99840734708349 " "
y[1] (numeric) = 1.9984073470835133 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 1.1666632206468885000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.5926508965920890000E-3 " "
Order of pole (three term test) = 22.999997463456683 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999977 " "
y[1] (analytic) = 2.0084072473671255 " "
y[1] (numeric) = 2.008407247367149 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 1.1719101368962019000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.406950242151765000E-3 " "
Order of pole (three term test) = 22.999929318191704 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1599999999999766 " "
y[1] (analytic) = 2.0184063069330302 " "
y[1] (numeric) = 2.0184063069330542 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 1.1881065397750488000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.84031887128899500E-2 " "
Order of pole (three term test) = 22.999661207865092 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1699999999999764 " "
y[1] (analytic) = 2.02840352588358 " "
y[1] (numeric) = 2.0284035258836046 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 1.2041443544185254000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.83920661535155400E-2 " "
Order of pole (three term test) = 22.999193239717382 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999976 " "
y[1] (analytic) = 2.0383979045052114 " "
y[1] (numeric) = 2.0383979045052363 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.22002655598491010000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.83695871462355700E-2 " "
Order of pole (three term test) = 22.99852560092961 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.189999999999976 " "
y[1] (analytic) = 2.04838844336839 " "
y[1] (numeric) = 2.0483884433684154 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 1.2357560912533017000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.8331760815684800E-2 " "
Order of pole (three term test) = 22.99765855854838 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999999758 " "
y[1] (analytic) = 2.0583741434275558 " "
y[1] (numeric) = 2.058374143427581 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 1.22976112201365000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.82746024252225800E-2 " "
Order of pole (three term test) = 22.996592459379098 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999999755 " "
y[1] (analytic) = 2.0683540061210235 " "
y[1] (numeric) = 2.0683540061210492 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 1.2452981498853019000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.8194134970774600E-2 " "
Order of pole (three term test) = 22.995327729847205 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999999753 " "
y[1] (analytic) = 2.0783270334708406 " "
y[1] (numeric) = 2.078327033470867 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 1.2606901108049945000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.80863907715813200E-2 " "
Order of pole (three term test) = 22.993864875827654 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.229999999999975 " "
y[1] (analytic) = 2.0882922281825826 " "
y[1] (numeric) = 2.0882922281826093 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.2759398436392644000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.79474130572175400E-2 " "
Order of pole (three term test) = 22.99220448244255 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999975 " "
y[1] (analytic) = 2.0982485937450837 " "
y[1] (numeric) = 2.0982485937451103 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.2698854020650377000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.77732575502473700E-2 " "
Order of pole (three term test) = 22.99034721382711 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2499999999999747 " "
y[1] (analytic) = 2.1081951345300833 " "
y[1] (numeric) = 2.1081951345301104 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 1.28495893748906000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10755999404388314 " "
Order of pole (three term test) = 22.988293812864008 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2599999999999745 " "
y[1] (analytic) = 2.1181308558917924 " "
y[1] (numeric) = 2.11813085589182 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 1.2998975457119008000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1173037079740154 " "
Order of pole (three term test) = 22.98604510088627 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2699999999999743 " "
y[1] (analytic) = 2.1280547642663543 " "
y[1] (numeric) = 2.1280547642663823 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.3147039582977657000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1270005019849868 " "
Order of pole (three term test) = 22.983601977348698 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999974 " "
y[1] (analytic) = 2.1379658672712014 " "
y[1] (numeric) = 2.13796586727123 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.3293808785956032000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1366464974884814 " "
Order of pole (three term test) = 22.980965419468106 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.289999999999974 " "
y[1] (analytic) = 2.147863173804293 " "
y[1] (numeric) = 2.1478631738043212 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.323255120579376000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14623783621490985 " "
Order of pole (three term test) = 22.97813648183252 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999999736 " "
y[1] (analytic) = 2.1577456941432223 " "
y[1] (numeric) = 2.157745694143251 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 1.3377757498765783000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15577068175666406 " "
Order of pole (three term test) = 22.97511629597927 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999999734 " "
y[1] (analytic) = 2.167612440044192 " "
y[1] (numeric) = 2.167612440044221 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.3521738161599858000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16524122110263045 " "
Order of pole (three term test) = 22.971906069942435 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.319999999999973 " "
y[1] (analytic) = 2.177462424840834 " "
y[1] (numeric) = 2.177462424840863 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.3460571128912407000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17464566616334257 " "
Order of pole (three term test) = 22.96850708776961 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.329999999999973 " "
y[1] (analytic) = 2.1872946635428767 " "
y[1] (numeric) = 2.187294663542906 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.3400063712782692000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18398025528616727 " "
Order of pole (three term test) = 22.964920709008357 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999999728 " "
y[1] (analytic) = 2.197108172934643 " "
y[1] (numeric) = 2.197108172934673 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.3542335978939204000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19324125475991474 " "
Order of pole (three term test) = 22.961148368162366 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3499999999999726 " "
y[1] (analytic) = 2.2069019716733727 " "
y[1] (numeric) = 2.206901971673403 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 1.3683465173084566000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20242496030827398 " "
Order of pole (three term test) = 22.957191574117665 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3599999999999723 " "
y[1] (analytic) = 2.2166750803873527 " "
y[1] (numeric) = 2.216675080387383 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 1.3623136082049200000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21152769857147347 " "
Order of pole (three term test) = 22.953051909539134 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999972 " "
y[1] (analytic) = 2.2264265217738557 " "
y[1] (numeric) = 2.2264265217738863 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 1.3762931397008720000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2205458285755762 " "
Order of pole (three term test) = 22.948731030237397 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.379999999999972 " "
y[1] (analytic) = 2.2361553206968696 " "
y[1] (numeric) = 2.2361553206969007 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 1.3901648244996123000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2294757431888203 " "
Order of pole (three term test) = 22.944230664506563 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999999717 " "
y[1] (analytic) = 2.2458605042846096 " "
y[1] (numeric) = 2.2458605042846407 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 1.3841574145054264000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23831387056442477 " "
Order of pole (three term test) = 22.93955261243292 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999999715 " "
y[1] (analytic) = 2.255541102026804 " "
y[1] (numeric) = 2.2555411020268354 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 1.3979055345531785000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24705667556927938 " "
Order of pole (three term test) = 22.934698745174924 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999999713 " "
y[1] (analytic) = 2.2651961458717453 " "
y[1] (numeric) = 2.2651961458717778 " "
absolute error = 3.24185123190545700000000000000E-14 " "
relative error = 1.4311569608723015000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.25570066119795143 " "
Order of pole (three term test) = 22.929671004214768 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.419999999999971 " "
y[1] (analytic) = 2.2748246703230963 " "
y[1] (numeric) = 2.2748246703231287 " "
absolute error = 3.24185123190545700000000000000E-14 " "
relative error = 1.4250993820306215000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2642423699714409 " "
Order of pole (three term test) = 22.924471400581798 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.429999999999971 " "
y[1] (analytic) = 2.2844257125364344 " "
y[1] (numeric) = 2.2844257125364673 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 1.4385498004405126000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2726783853201265 " "
Order of pole (three term test) = 22.91910201404814 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999999706 " "
y[1] (analytic) = 2.2939983124155394 " "
y[1] (numeric) = 2.2939983124155727 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.4519056338661096000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2810053329503472 " "
Order of pole (three term test) = 22.913564992296813 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4499999999999704 " "
y[1] (analytic) = 2.303541512708401 " "
y[1] (numeric) = 2.3035415127084344 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.4458906234163837000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28921988219407574 " "
Order of pole (three term test) = 22.907862550062685 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999997 " "
y[1] (analytic) = 2.3130543591029418 " "
y[1] (numeric) = 2.3130543591029755 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 1.4591433969452464000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2973187473411404 " "
Order of pole (three term test) = 22.901996968246646 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.46999999999997 " "
y[1] (analytic) = 2.3225359003224506 " "
y[1] (numeric) = 2.3225359003224844 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 1.4531865769618008000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3052986889534657 " "
Order of pole (three term test) = 22.895970593003188 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.47999999999997 " "
y[1] (analytic) = 2.3319851882207057 " "
y[1] (numeric) = 2.33198518822074 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 1.4663416101945895000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3131565151608046 " "
Order of pole (three term test) = 22.889785834802066 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999999696 " "
y[1] (analytic) = 2.341401277876792 " "
y[1] (numeric) = 2.3414012778768267 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.4794114403027858000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3208890829374434 " "
Order of pole (three term test) = 22.88344516746409 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999999694 " "
y[1] (analytic) = 2.350783227689591 " "
y[1] (numeric) = 2.350783227689626 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.4923982426331778000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32849329935937155 " "
Order of pole (three term test) = 22.876951127171672 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.509999999999969 " "
y[1] (analytic) = 2.3601300994719394 " "
y[1] (numeric) = 2.360130099471975 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.5053041692893934000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33596612284140825 " "
Order of pole (three term test) = 22.870306311454332 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.519999999999969 " "
y[1] (analytic) = 2.3694409585444483 " "
y[1] (numeric) = 2.3694409585444838 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.4993889870895705000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3433045643537966 " "
Order of pole (three term test) = 22.863513378149754 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999999687 " "
y[1] (analytic) = 2.3787148738289687 " "
y[1] (numeric) = 2.3787148738290047 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.5122125982233810000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35050568861777687 " "
Order of pole (three term test) = 22.856575044340705 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999999685 " "
y[1] (analytic) = 2.3879509179417013 " "
y[1] (numeric) = 2.3879509179417373 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.5063637082147627000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35756661527965694 " "
Order of pole (three term test) = 22.84949408526819 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5499999999999683 " "
y[1] (analytic) = 2.397148167285931 " "
y[1] (numeric) = 2.3971481672859674 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 1.5191099033705050000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3644845200629164 " "
Order of pole (three term test) = 22.842273333221428 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999968 " "
y[1] (analytic) = 2.4063057021443877 " "
y[1] (numeric) = 2.4063057021444245 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.5317839451865078000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3712566358978797 " "
Order of pole (three term test) = 22.834915676404954 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999968 " "
y[1] (analytic) = 2.415422606771217 " "
y[1] (numeric) = 2.415422606771254 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 1.5443878649985060000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37788025402850595 " "
Order of pole (three term test) = 22.827424057783407 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999999677 " "
y[1] (analytic) = 2.424497969483553 " "
y[1] (numeric) = 2.424497969483591 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.5569236729571692000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3843527250958573 " "
Order of pole (three term test) = 22.81980147390434 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999999674 " "
y[1] (analytic) = 2.4335308827526885 " "
y[1] (numeric) = 2.433530882752726 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.5511445983605987000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39067146019780474 " "
Order of pole (three term test) = 22.812050973699673 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999999672 " "
y[1] (analytic) = 2.442520443294823 " "
y[1] (numeric) = 2.442520443294861 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.5454356970022307000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3968339319245565 " "
Order of pole (three term test) = 22.80417565726615 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.609999999999967 " "
y[1] (analytic) = 2.451465752161394 " "
y[1] (numeric) = 2.451465752161432 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 1.5579117111235505000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40283767536958737 " "
Order of pole (three term test) = 22.796178674625345 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.619999999999967 " "
y[1] (analytic) = 2.4603659148289685 " "
y[1] (numeric) = 2.460365914829007 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 1.5703258212159554000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40868028911556725 " "
Order of pole (three term test) = 22.788063224463688 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999999666 " "
y[1] (analytic) = 2.4692200412886978 " "
y[1] (numeric) = 2.4692200412887364 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 1.5646949486442390000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4143594361948992 " "
Order of pole (three term test) = 22.77983255285303 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999999664 " "
y[1] (analytic) = 2.478027246135313 " "
y[1] (numeric) = 2.478027246135352 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.5770549144588197000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4198728450244716 " "
Order of pole (three term test) = 22.77148995195229 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999966 " "
y[1] (analytic) = 2.48678664865567 " "
y[1] (numeric) = 2.486786648655709 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.571499930962379000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4252183103142643 " "
Order of pole (three term test) = 22.76303875869058 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999966 " "
y[1] (analytic) = 2.495497372916815 " "
y[1] (numeric) = 2.4954973729168546 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.5838101095838367000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43039369394943316 " "
Order of pole (three term test) = 22.754482353432532 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6699999999999657 " "
y[1] (analytic) = 2.504158547853582 " "
y[1] (numeric) = 2.5041585478536215 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.5783321591411686000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4353969258455288 " "
Order of pole (three term test) = 22.745824158626167 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999999655 " "
y[1] (analytic) = 2.5127693073556943 " "
y[1] (numeric) = 2.512769307355734 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.5729235294683092000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4402260047765006 " "
Order of pole (three term test) = 22.737067637433963 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999999653 " "
y[1] (analytic) = 2.521328790354377 " "
y[1] (numeric) = 2.521328790354417 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 1.585197021483583000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4448789991751639 " "
Order of pole (three term test) = 22.728216292347643 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.699999999999965 " "
y[1] (analytic) = 2.5298361409084635 " "
y[1] (numeric) = 2.529836140908504 " "
absolute error = 4.0412118096355700000000000000E-14 " "
relative error = 1.5974203800347211000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4493540479057982 " "
Order of pole (three term test) = 22.71927366378723 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.709999999999965 " "
y[1] (analytic) = 2.538290508289988 " "
y[1] (numeric) = 2.5382905082900287 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.6095954018175024000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4536493610085773 " "
Order of pole (three term test) = 22.71024332868491 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999999647 " "
y[1] (analytic) = 2.5466910470692574 " "
y[1] (numeric) = 2.5466910470692983 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.6042859754512923000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45776322041553064 " "
Order of pole (three term test) = 22.701128899054318 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999999645 " "
y[1] (analytic) = 2.555036917199394 " "
y[1] (numeric) = 2.5550369171994354 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 1.6164266057386584000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46169398063774575 " "
Order of pole (three term test) = 22.69193402054579 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7399999999999642 " "
y[1] (analytic) = 2.5633272841003403 " "
y[1] (numeric) = 2.5633272841003816 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 1.6111987248850718000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4654400694235438 " "
Order of pole (three term test) = 22.68266237098814 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999964 " "
y[1] (analytic) = 2.5715613187423143 " "
y[1] (numeric) = 2.5715613187423556 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 1.606039732167645000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4689999883873569 " "
Order of pole (three term test) = 22.673317658917544 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999964 " "
y[1] (analytic) = 2.5797381977287133 " "
y[1] (numeric) = 2.579738197728755 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.6181636478716724000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4723723136090651 " "
Order of pole (three term test) = 22.663903622094264 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7699999999999636 " "
y[1] (analytic) = 2.5878571033784534 " "
y[1] (numeric) = 2.587857103378495 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.6130869695783626000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47555569620354327 " "
Order of pole (three term test) = 22.654424026007497 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999999634 " "
y[1] (analytic) = 2.5959172238077346 " "
y[1] (numeric) = 2.595917223807777 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 1.6251856780653887000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4785488628601978 " "
Order of pole (three term test) = 22.64488266236928 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.789999999999963 " "
y[1] (analytic) = 2.603917753011231 " "
y[1] (numeric) = 2.603917753011274 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.6372469559111352000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48135061635227505 " "
Order of pole (three term test) = 22.635283347597866 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.799999999999963 " "
y[1] (analytic) = 2.61185789094269 " "
y[1] (numeric) = 2.6118578909427326 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.6322696687842678000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48395983601573395 " "
Order of pole (three term test) = 22.625629921291164 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999999627 " "
y[1] (analytic) = 2.619736843594934 " "
y[1] (numeric) = 2.619736843594977 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 1.6443122316188113000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48637547819749816 " "
Order of pole (three term test) = 22.61592624469099 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999999625 " "
y[1] (analytic) = 2.627553823079264 " "
y[1] (numeric) = 2.6275538230793076 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.6563216396573607000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48859657667290357 " "
Order of pole (three term test) = 22.606176199138606 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8299999999999623 " "
y[1] (analytic) = 2.6353080477042465 " "
y[1] (numeric) = 2.63530804770429 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.6514480196430664000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4906222430321739 " "
Order of pole (three term test) = 22.596383684522216 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999962 " "
y[1] (analytic) = 2.64299874205388 " "
y[1] (numeric) = 2.6429987420539236 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.6466425758298348000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4924516670357739 " "
Order of pole (three term test) = 22.586552617717125 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999962 " "
y[1] (analytic) = 2.6506251370651386 " "
y[1] (numeric) = 2.6506251370651825 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.6586589767210740000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49408411693849447 " "
Order of pole (three term test) = 22.57668693101897 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8599999999999617 " "
y[1] (analytic) = 2.658186470104876 " "
y[1] (numeric) = 2.6581864701049205 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.6706473185552762000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49551893978213996 " "
Order of pole (three term test) = 22.566790570570888 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8699999999999615 " "
y[1] (analytic) = 2.66568198504609 " "
y[1] (numeric) = 2.665681985046135 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.68260919518803000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4967555616567035 " "
Order of pole (three term test) = 22.556867494785095 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999999613 " "
y[1] (analytic) = 2.673110932343533 " "
y[1] (numeric) = 2.673110932343578 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 1.6945461879875723000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4977934879299238 " "
Order of pole (three term test) = 22.546921672759616 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.889999999999961 " "
y[1] (analytic) = 2.6804725691086655 " "
y[1] (numeric) = 2.680472569108711 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 1.6898922946176234000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49863230344513004 " "
Order of pole (three term test) = 22.53695708269065 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.899999999999961 " "
y[1] (analytic) = 2.6877661591839455 " "
y[1] (numeric) = 2.687766159183991 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.7018291735782662000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4992716726873003 " "
Order of pole (three term test) = 22.526977710281365 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999999606 " "
y[1] (analytic) = 2.6949909732164437 " "
y[1] (numeric) = 2.6949909732164894 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.697266858002304000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4997113399172627 " "
Order of pole (three term test) = 22.516987547147664 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999999604 " "
y[1] (analytic) = 2.7021462887307774 " "
y[1] (numeric) = 2.702146288730823 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.692772475173485200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49995112927398716 " "
Order of pole (three term test) = 22.506990589221598 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.92999999999996 " "
y[1] (analytic) = 2.709231390201358 " "
y[1] (numeric) = 2.709231390201404 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 1.7047372915967096000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.499990944844928 " "
Order of pole (three term test) = 22.49699083515305 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.93999999999996 " "
y[1] (analytic) = 2.7162455691239424 " "
y[1] (numeric) = 2.716245569123989 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.7166845135175210000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49983077070438825 " "
Order of pole (three term test) = 22.486992284710322 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9499999999999598 " "
y[1] (analytic) = 2.723188124086484 " "
y[1] (numeric) = 2.7231881240865308 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.7123079607252173000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4994706709198879 " "
Order of pole (three term test) = 22.476998937180277 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9599999999999596 " "
y[1] (analytic) = 2.730058360839272 " "
y[1] (numeric) = 2.7300583608393185 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.707998909588212000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4989107895265397 " "
Order of pole (three term test) = 22.467014789768676 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9699999999999593 " "
y[1] (analytic) = 2.7368555923643556 " "
y[1] (numeric) = 2.7368555923644027 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.719983194416192000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4981513504694364 " "
Order of pole (three term test) = 22.45704383600138 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.979999999999959 " "
y[1] (analytic) = 2.743579138944247 " "
y[1] (numeric) = 2.7435791389442943 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.715768121134676200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49719265751407454 " "
Order of pole (three term test) = 22.447090064126936 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.989999999999959 " "
y[1] (analytic) = 2.7502283282298916 " "
y[1] (numeric) = 2.7502283282299387 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.711619932095026000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4960350941248542 " "
Order of pole (three term test) = 22.43715745552138 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999999587 " "
y[1] (analytic) = 2.7568024953079013 " "
y[1] (numeric) = 2.7568024953079484 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.7075382195215658000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4946791233116969 " "
Order of pole (three term test) = 22.427249983095734 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999959 " "
y[1] (analytic) = 2.763300982767047 " "
y[1] (numeric) = 2.763300982767094 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.7035225817843905000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4931252874448485 " "
Order of pole (three term test) = 22.417371609706862 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999959 " "
y[1] (analytic) = 2.7697231407639977 " "
y[1] (numeric) = 2.769723140764045 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.6995726233894246000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49137420803793863 " "
Order of pole (three term test) = 22.407526286572413 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999999585 " "
y[1] (analytic) = 2.776068327088306 " "
y[1] (numeric) = 2.7760683270883533 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.6956879549675882000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48942658549938206 " "
Order of pole (three term test) = 22.397717951690353 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999958 " "
y[1] (analytic) = 2.782335907226627 " "
y[1] (numeric) = 2.7823359072266745 " "
absolute error = 4.7517545453956700000000000000E-14 " "
relative error = 1.7078292139542983000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48728319885222676 " "
Order of pole (three term test) = 22.387950528263886 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999958 " "
y[1] (analytic) = 2.7885252544261694 " "
y[1] (numeric) = 2.7885252544262173 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 1.7199641490669035000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4849449054225533 " "
Order of pole (three term test) = 22.378227923132147 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.059999999999958 " "
y[1] (analytic) = 2.7946357497573713 " "
y[1] (numeric) = 2.7946357497574197 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.7320942050447677000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4824126404965566 " "
Order of pole (three term test) = 22.368554025207544 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999958 " "
y[1] (analytic) = 2.8006667821757922 " "
y[1] (numeric) = 2.8006667821758406 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.7283642660285065000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47968741694644407 " "
Order of pole (three term test) = 22.358932703920257 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999957 " "
y[1] (analytic) = 2.806617748583215 " "
y[1] (numeric) = 2.806617748583264 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.7405224886134332000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4767703248252999 " "
Order of pole (three term test) = 22.349367807670543 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.089999999999957 " "
y[1] (analytic) = 2.8124880538879595 " "
y[1] (numeric) = 2.8124880538880084 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.736889620419092000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4736625309310787 " "
Order of pole (three term test) = 22.339863162289358 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999957 " "
y[1] (analytic) = 2.818277111064386 " "
y[1] (numeric) = 2.818277111064435 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.7490793257991583000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47036527833990116 " "
Order of pole (three term test) = 22.330422569508126 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999957 " "
y[1] (analytic) = 2.823984341211601 " "
y[1] (numeric) = 2.8239843412116508 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.7612700884122978000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46687988590884105 " "
Order of pole (three term test) = 22.321049805438083 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999957 " "
y[1] (analytic) = 2.8296091736113467 " "
y[1] (numeric) = 2.8296091736113964 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.7577689515237144000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46320774774839946 " "
Order of pole (three term test) = 22.3117486190599 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999956 " "
y[1] (analytic) = 2.8351510457850697 " "
y[1] (numeric) = 2.8351510457851195 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.7543330390509856000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4593503326648795 " "
Order of pole (three term test) = 22.302522730724103 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999956 " "
y[1] (analytic) = 2.8406094035501708 " "
y[1] (numeric) = 2.840609403550221 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.7665955991816376000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4553091835728832 " "
Order of pole (three term test) = 22.293375830663024 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999956 " "
y[1] (analytic) = 2.845983701075423 " "
y[1] (numeric) = 2.845983701075473 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.7632595961141512000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45108591687816574 " "
Order of pole (three term test) = 22.28431157751473 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999956 " "
y[1] (analytic) = 2.8512734009355514 " "
y[1] (numeric) = 2.8512734009356016 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.7599883861221963000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44668222183109585 " "
Order of pole (three term test) = 22.275333596859614 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.1699999999999555 " "
y[1] (analytic) = 2.856477974164978 " "
y[1] (numeric) = 2.8564779741650286 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.7723283841425900000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4420998598509774 " "
Order of pole (three term test) = 22.26644547977026 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999955 " "
y[1] (analytic) = 2.861596900310718 " "
y[1] (numeric) = 2.8615969003107686 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.7691579801966534000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4373406638215043 " "
Order of pole (three term test) = 22.257650781374966 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999955 " "
y[1] (analytic) = 2.8666296674844216 " "
y[1] (numeric) = 2.8666296674844727 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.7815436612561583000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4324065373576338 " "
Order of pole (three term test) = 22.24895301943584 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999955 " "
y[1] (analytic) = 2.871575772413566 " "
y[1] (numeric) = 2.871575772413617 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.7784750666646185000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42729945404416364 " "
Order of pole (three term test) = 22.2403556729417 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999955 " "
y[1] (analytic) = 2.8764347204917797 " "
y[1] (numeric) = 2.876434720491831 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.7754708204893938000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4220214566463264 " "
Order of pole (three term test) = 22.231862180716494 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2199999999999545 " "
y[1] (analytic) = 2.8812060258283037 " "
y[1] (numeric) = 2.881206025828355 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.787943933228366100000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.416574656292708 " "
Order of pole (three term test) = 22.223475940043883 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999954 " "
y[1] (analytic) = 2.8858892112965813 " "
y[1] (numeric) = 2.885889211296633 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.785042479834586000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4109612316308275 " "
Order of pole (three term test) = 22.215200305308322 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999954 " "
y[1] (analytic) = 2.8904838085819673 " "
y[1] (numeric) = 2.8904838085820193 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7975688844265642000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40518342795570444 " "
Order of pole (three term test) = 22.207038586653354 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999954 " "
y[1] (analytic) = 2.894989358228563 " "
y[1] (numeric) = 2.8949893582286146 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.7794313542530177000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3992435563117729 " "
Order of pole (three term test) = 22.198994048657628 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999954 " "
y[1] (analytic) = 2.8994054096851576 " "
y[1] (numeric) = 2.899405409685209 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.776721122562889000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39314399256849303 " "
Order of pole (three term test) = 22.191069909029075 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999953 " "
y[1] (analytic) = 2.9037315213502857 " "
y[1] (numeric) = 2.903731521350337 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.7740740823949244000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.386887176470036 " "
Order of pole (three term test) = 22.1832693373179 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999953 " "
y[1] (analytic) = 2.9079672606163856 " "
y[1] (numeric) = 2.9079672606164375 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7867614349084518000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3804756106594176 " "
Order of pole (three term test) = 22.17559545364878 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999953 " "
y[1] (analytic) = 2.912112203913061 " "
y[1] (numeric) = 2.912112203913113 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7842182551427713000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.373911859677476 " "
Order of pole (three term test) = 22.16805132747286 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999953 " "
y[1] (analytic) = 2.916165936749436 " "
y[1] (numeric) = 2.916165936749488 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7817380313540684000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3671985489370886 " "
Order of pole (three term test) = 22.160639976340025 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3099999999999525 " "
y[1] (analytic) = 2.9201280537556054 " "
y[1] (numeric) = 2.9201280537556573 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7793205159490547000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3603383636730415 " "
Order of pole (three term test) = 22.153364364691917 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999952 " "
y[1] (analytic) = 2.92399815872317 " "
y[1] (numeric) = 2.9239981587232218 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7769654675550875000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35333404786797273 " "
Order of pole (three term test) = 22.14622740267619 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999952 " "
y[1] (analytic) = 2.9277758646448575 " "
y[1] (numeric) = 2.92777586464491 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.789840793317144000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.34618840315481453 " "
Order of pole (three term test) = 22.13923194498249 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999952 " "
y[1] (analytic) = 2.9314607937532253 " "
y[1] (numeric) = 2.9314607937532773 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7724418372975610000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3389042876961786 " "
Order of pole (three term test) = 22.13238078970061 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999952 " "
y[1] (analytic) = 2.935052577558432 " "
y[1] (numeric) = 2.9350525775584844 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7854033404028224000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3314846150411275 " "
Order of pole (three term test) = 22.125676677201334 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3599999999999515 " "
y[1] (analytic) = 2.938550856885091 " "
y[1] (numeric) = 2.9385508568851435 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7832778575033706000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.323932352959796 " "
Order of pole (three term test) = 22.11912228904026 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999951 " "
y[1] (analytic) = 2.9419552819081844 " "
y[1] (numeric) = 2.9419552819082373 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7963092878108110000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.31625052225632116 " "
Order of pole (three term test) = 22.112720246885274 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999951 " "
y[1] (analytic) = 2.9452655121880476 " "
y[1] (numeric) = 2.9452655121881004 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.79429038752087000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3084421955605607 " "
Order of pole (three term test) = 22.106473111467867 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999950 " "
y[1] (analytic) = 2.94848121670441 " "
y[1] (numeric) = 2.948481216704463 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7923334791064200000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3005104960990842 " "
Order of pole (three term test) = 22.10038338155892 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999950 " "
y[1] (analytic) = 2.951602073889501 " "
y[1] (numeric) = 2.951602073889554 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7904383670024440000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2924585964459212 " "
Order of pole (three term test) = 22.0944534929692 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.40999999999995 " "
y[1] (analytic) = 2.9546277716602014 " "
y[1] (numeric) = 2.9546277716602547 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.8036351547614250000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28428971725357566 " "
Order of pole (three term test) = 22.08868581757508 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999995 " "
y[1] (analytic) = 2.957558007449257 " "
y[1] (numeric) = 2.95755800744931 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.801848181769663000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.27600712596480775 " "
Order of pole (three term test) = 22.083082662369804 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.42999999999995 " "
y[1] (analytic) = 2.9603924882355295 " "
y[1] (numeric) = 2.9603924882355828 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.80012296997045000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2676141355056999 " "
Order of pole (three term test) = 22.077646268540768 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.43999999999995 " "
y[1] (analytic) = 2.963130930573303 " "
y[1] (numeric) = 2.963130930573356 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7984593469076610000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.25911410296053106 " "
Order of pole (three term test) = 22.072378810573003 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4499999999999496 " "
y[1] (analytic) = 2.965773060620626 " "
y[1] (numeric) = 2.9657730606206787 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7818833367209366000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.250510428228986 " "
Order of pole (three term test) = 22.06728239537947 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999950 " "
y[1] (analytic) = 2.9683186141666944 " "
y[1] (numeric) = 2.9683186141667477 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7953162078919208000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24180655266624426 " "
Order of pole (three term test) = 22.06235906145829 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999950 " "
y[1] (analytic) = 2.970767336658276 " "
y[1] (numeric) = 2.970767336658329 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7938363777067973000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23300595770648033 " "
Order of pole (three term test) = 22.0576107780774 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999949 " "
y[1] (analytic) = 2.973118983225162 " "
y[1] (numeric) = 2.973118983225215 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7774806952001235000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22411216347033852 " "
Order of pole (three term test) = 22.05303944448683 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999949 " "
y[1] (analytic) = 2.975373318704655 " "
y[1] (numeric) = 2.9753733187047082 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7910594562032275000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21512872735693095 " "
Order of pole (three term test) = 22.04864688915907 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999999485 " "
y[1] (analytic) = 2.9775301176650864 " "
y[1] (numeric) = 2.977530117665139 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7748474031758446000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20605924262092526 " "
Order of pole (three term test) = 22.044434869057678 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999948 " "
y[1] (analytic) = 2.9795891644283565 " "
y[1] (numeric) = 2.9795891644284094 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7736208938824036000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1969073369352911 " "
Order of pole (three term test) = 22.04040506893455 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999948 " "
y[1] (analytic) = 2.9815502530915055 " "
y[1] (numeric) = 2.9815502530915583 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.772454310215362800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1876766709402792 " "
Order of pole (three term test) = 22.036559100656003 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999948 " "
y[1] (analytic) = 2.9834131875473013 " "
y[1] (numeric) = 2.983413187547354 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7713475355253516000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17837093677921334 " "
Order of pole (three term test) = 22.03289850255806 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999948 " "
y[1] (analytic) = 2.9851777815038503 " "
y[1] (numeric) = 2.9851777815039036 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7851769335882275000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16899385662168315 " "
Order of pole (three term test) = 22.02942473883115 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999947 " "
y[1] (analytic) = 2.986843858503228 " "
y[1] (numeric) = 2.9868438585032813 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7841811526335574000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1595491811747256 " "
Order of pole (three term test) = 22.02613919893446 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999947 " "
y[1] (analytic) = 2.9884112519391226 " "
y[1] (numeric) = 2.988411251939176 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.783245366494595000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15004068818259247 " "
Order of pole (three term test) = 22.02304319704014 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999947 " "
y[1] (analytic) = 2.9898798050734965 " "
y[1] (numeric) = 2.98987980507355 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7823694815951818000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.140472180915702 " "
Order of pole (three term test) = 22.02013797150766 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999947 " "
y[1] (analytic) = 2.99124937105226 " "
y[1] (numeric) = 2.991249371052313 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 1.7815534103484304000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13084748664938275 " "
Order of pole (three term test) = 22.017424684388494 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999947 " "
y[1] (analytic) = 2.992519812919957 " "
y[1] (numeric) = 2.9925198129200097 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.765957095555276000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12117045513301357 " "
Order of pole (three term test) = 22.014904420961333 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999946 " "
y[1] (analytic) = 2.9936910036334585 " "
y[1] (numeric) = 2.9936910036335114 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7652662184579918000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11144495705017574 " "
Order of pole (three term test) = 22.01257818929793 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999946 " "
y[1] (analytic) = 2.99476282607467 " "
y[1] (numeric) = 2.994762826074723 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.764634431549465000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10167488247043084 " "
Order of pole (three term test) = 22.010446919859934 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999946 " "
y[1] (analytic) = 2.9957351730622404 " "
y[1] (numeric) = 2.995735173062293 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7640616716509572000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.18641392933446800E-2 " "
Order of pole (three term test) = 22.008511465126706 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999946 " "
y[1] (analytic) = 2.996607947362281 " "
y[1] (numeric) = 2.996607947362334 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.7635478814862948000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.20166516853801900E-2 " "
Order of pole (three term test) = 22.006772599254337 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6399999999999455 " "
y[1] (analytic) = 2.997381061698089 " "
y[1] (numeric) = 2.997381061698142 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 1.763093009676206000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.21363585102822600E-2 " "
Order of pole (three term test) = 22.005231017765993 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999945 " "
y[1] (analytic) = 2.998054438758876 " "
y[1] (numeric) = 2.9980544387589285 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7478844308110963000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.22272117535854500E-2 " "
Order of pole (three term test) = 22.003887337273706 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999945 " "
y[1] (analytic) = 2.998628011207496 " "
y[1] (numeric) = 2.9986280112075483 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.747550098460055000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.229317494187233000E-2 " "
Order of pole (three term test) = 22.002742095231756 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999945 " "
y[1] (analytic) = 2.9991017216871825 " "
y[1] (numeric) = 2.999101721687235 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7472740715452520000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.23382215574155900E-2 " "
Order of pole (three term test) = 22.001795749721705 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999945 " "
y[1] (analytic) = 2.9994755228272822 " "
y[1] (numeric) = 2.9994755228273347 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7470563224637745000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.2366333448837903E-2 " "
Order of pole (three term test) = 22.001048679269136 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999944 " "
y[1] (analytic) = 2.999749377247993 " "
y[1] (numeric) = 2.9997493772480452 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7468968294405354000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.238149923842604500E-2 " "
Order of pole (three term test) = 22.00050118269225 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999944 " "
y[1] (analytic) = 2.9999232575641 " "
y[1] (numeric) = 2.9999232575641526 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.7467955765261003000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.238771272673481300E-2 " "
Order of pole (three term test) = 22.0001534789824 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999944 " "
y[1] (analytic) = 2.999997146387718 " "
y[1] (numeric) = 2.99999714638777 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.731949565852762000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.38897129512021020E-3 " "
Order of pole (three term test) = 22.00000570721642 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999944 " "
y[1] (analytic) = 2.9999710363300247 " "
y[1] (numeric) = 2.999971036330077 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.746767756345185800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.610725693159919000E-3 " "
Order of pole (three term test) = 22.000057926501054 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999944 " "
y[1] (analytic) = 2.9998449300020056 " "
y[1] (numeric) = 2.9998449300020575 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7320374474297437000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.760737849263778700E-2 " "
Order of pole (three term test) = 22.000310115949286 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999943 " "
y[1] (analytic) = 2.999618840014187 " "
y[1] (numeric) = 2.999618840014239 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7321679961248537000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.759698857548049000E-2 " "
Order of pole (three term test) = 22.000762174688692 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999943 " "
y[1] (analytic) = 2.99929278897538 " "
y[1] (numeric) = 2.999292788975432 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7323562989062963000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.75755602308479800E-2 " "
Order of pole (three term test) = 22.001413921901808 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999943 " "
y[1] (analytic) = 2.998866809490417 " "
y[1] (numeric) = 2.998866809490469 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.7326023746045052000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.75391021631238400E-2 " "
Order of pole (three term test) = 22.00226509689843 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999943 " "
y[1] (analytic) = 2.998340944156891 " "
y[1] (numeric) = 2.9983409441569426 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.7180950833159062000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.748362908838080000E-2 " "
Order of pole (three term test) = 22.003315359219926 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.7799999999999425 " "
y[1] (analytic) = 2.9977152455608973 " "
y[1] (numeric) = 2.997715245560949 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.7184536929880576000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.74051633284405500E-2 " "
Order of pole (three term test) = 22.004564288775356 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999942 " "
y[1] (analytic) = 2.996989776271774 " "
y[1] (numeric) = 2.9969897762718256 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.7188696721778815000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.72997364018924600E-2 " "
Order of pole (three term test) = 22.006011386009558 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999942 " "
y[1] (analytic) = 2.996164608835846 " "
y[1] (numeric) = 2.996164608835897 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.7045211395311305000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.7163390611432900E-2 " "
Order of pole (three term test) = 22.00765607210292 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999942 " "
y[1] (analytic) = 2.9952398257691684 " "
y[1] (numeric) = 2.9952398257692194 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.7050474120095713000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.69921806268919100E-2 " "
Order of pole (three term test) = 22.00949768920296 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999942 " "
y[1] (analytic) = 2.994215519549278 " "
y[1] (numeric) = 2.9942155195493285 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.6907991289327076000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10678217506331213 " "
Order of pole (three term test) = 22.011535500687362 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8299999999999415 " "
y[1] (analytic) = 2.9930917926059424 " "
y[1] (numeric) = 2.993091792605993 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.6914339228744246000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11652945805345026 " "
Order of pole (three term test) = 22.013768691458715 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999941 " "
y[1] (analytic) = 2.99186875731092 " "
y[1] (numeric) = 2.9918687573109706 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.6921253580792010000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12623013081407233 " "
Order of pole (three term test) = 22.01619636827049 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999941 " "
y[1] (analytic) = 2.9905465359667214 " "
y[1] (numeric) = 2.9905465359667716 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.6780237361140166000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13588031320541483 " "
Order of pole (three term test) = 22.018817560084333 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999940 " "
y[1] (analytic) = 2.9891252607943786 " "
y[1] (numeric) = 2.9891252607944288 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.6788216061484446000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14547614528318847 " "
Order of pole (three term test) = 22.021631218458456 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999940 " "
y[1] (analytic) = 2.987605073920225 " "
y[1] (numeric) = 2.9876050739202746 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.6648114550810647000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1550137888425049 " "
Order of pole (three term test) = 22.02463621796703 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.87999999999994 " "
y[1] (analytic) = 2.9859861273616803 " "
y[1] (numeric) = 2.98598612736173 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.6657140851204782000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16448942895310734 " "
Order of pole (three term test) = 22.027831356650314 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.88999999999994 " "
y[1] (analytic) = 2.984268583012052 " "
y[1] (numeric) = 2.984268583012102 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.666672758153891000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17389927548529174 " "
Order of pole (three term test) = 22.03121535649544 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999994 " "
y[1] (analytic) = 2.9824526126243436 " "
y[1] (numeric) = 2.9824526126243933 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.667687570044614000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18323956462590793 " "
Order of pole (three term test) = 22.034786863947595 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.90999999999994 " "
y[1] (analytic) = 2.9805383977940805 " "
y[1] (numeric) = 2.98053839779413 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.6687586222683287000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19250656038383568 " "
Order of pole (three term test) = 22.038544450451422 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9199999999999395 " "
y[1] (analytic) = 2.9785261299411507 " "
y[1] (numeric) = 2.9785261299412005 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 1.6698860219228537000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20169655608432943 " "
Order of pole (three term test) = 22.042486613022394 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999940 " "
y[1] (analytic) = 2.976416010290663 " "
y[1] (numeric) = 2.9764160102907122 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.6561496149371652000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21080587585164126 " "
Order of pole (three term test) = 22.04661177484806 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999939 " "
y[1] (analytic) = 2.974208249852823 " "
y[1] (numeric) = 2.974208249852872 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.657378977944676000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2198308760793199 " "
Order of pole (three term test) = 22.050918285918698 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999939 " "
y[1] (analytic) = 2.971903069401835 " "
y[1] (numeric) = 2.9719030694018844 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.6586645372414013000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22876794688760604 " "
Order of pole (three term test) = 22.055404423687293 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999939 " "
y[1] (analytic) = 2.9695006994538238 " "
y[1] (numeric) = 2.969500699453873 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.660006421363144000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23761351356733607 " "
Order of pole (three term test) = 22.060068393758545 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999385 " "
y[1] (analytic) = 2.9670013802437816 " "
y[1] (numeric) = 2.967001380243831 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.661404764473239000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2463640380097766 " "
Order of pole (three term test) = 22.06490833060662 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999938 " "
y[1] (analytic) = 2.964405361701547 " "
y[1] (numeric) = 2.964405361701596 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.647878988299611200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2550160201218237 " "
Order of pole (three term test) = 22.069922298321305 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.989999999999938 " "
y[1] (analytic) = 2.9617129034268106 " "
y[1] (numeric) = 2.9617129034268594 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.6493770556553897000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26356599922599033 " "
Order of pole (three term test) = 22.07510829138237 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.999999999999938 " "
y[1] (analytic) = 2.958924274663156 " "
y[1] (numeric) = 2.9589242746632047 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.6509315058111096000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2720105554446326 " "
Order of pole (three term test) = 22.080464235461744 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"diff ( y , x , 2 ) = 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 "%"
(%o225) true
(%o225) diffeq.max