(%i1) batch("diffeq.max")
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load("stringproc")
(%o2) /usr/share/maxima/5.31.3/share/stringproc/stringproc.mac
(%i3) alias(convfloat,float)
(%o3) [convfloat]
(%i4) alias(int_trunc,truncate)
(%o4) [truncate]
(%i5) alias(elapsed_time_seconds,elapsed_real_time)
(%o5) [elapsed_time_seconds]
(%i6) alias(ln,log)
(%o6) [log]
(%i7) alias(arcsin,asin)
(%o7) [asin]
(%i8) alias(arccos,acos)
(%o8) [acos]
(%i9) alias(arctan,atan)
(%o9) [atan]
(%i10) alias(float_abs,abs)
(%o10) [mabs]
(%i11) keepfloat:true
(%o11) true
(%i12) mode_declare(display_poles(),fixnum)
(%o12) [display_poles()]
(%i13) mode_declare(est_size_answer(),convfloat)
(%o13) [est_size_answer()]
(%i14) mode_declare(test_suggested_h(),convfloat)
(%o14) [test_suggested_h()]
(%i15) mode_declare(reached_interval(),boolean)
(%o15) [reached_interval()]
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%o16) [display_alot([iter], fixnum)]
(%i17) mode_declare(adjust_for_pole([h_param],convfloat),convfloat)
(%o17) [adjust_for_pole([h_param], convfloat)]
(%i18) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%o18) [prog_report([x_start], convfloat, [x_end], convfloat)]
(%i19) mode_declare(check_for_pole(),fixnum)
(%o19) [check_for_pole()]
(%i20) mode_declare(atomall(),fixnum)
(%o20) [atomall()]
(%i21) mode_declare(log10([x],convfloat),convfloat)
(%o21) [log10([x], convfloat)]
(%i22) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%o22) [logitem_timestr([fd], fixnum, [secs_in], number)]
(%i23) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%o23) [omniout_timestr(secs_in, number)]
(%i24) mode_declare(zero_ats_ar(ar,array([MAX_TERMS],convfloat)),fixnum)
(%o24) [zero_ats_ar(ar, array([MAX_TERMS], convfloat))]
(%i25) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_ats],
fixnum),convfloat)
(%o25) [ats([mmm_ats], fixnum, [arr_a], completearray([MAX_TERMS], convfloat),
[arr_b], completearray([MAX_TERMS], convfloat), [jjj_ats], fixnum)]
(%i26) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([MAX_TERMS],convfloat),[arr_b],
completearray([MAX_TERMS],convfloat),[jjj_att],
fixnum),convfloat)
(%o26) [att([mmm_att], fixnum, [arr_a], completearray([MAX_TERMS], convfloat),
[arr_b], completearray([MAX_TERMS], convfloat), [jjj_att], fixnum)]
(%i27) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%o27) [logitem_ditto([file], fixnum)]
(%i28) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%o28) [logitem_integer([file], fixnum, [n], fixnum)]
(%i29) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%o29) [logitem_good_digits([file], fixnum, [relerror], convfloat)]
(%i30) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%o30) [logitem_number([file], fixnum, [x], number)]
(%i31) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%o31) [logitem_pole([file], fixnum, [pole], fixnum)]
(%i32) mode_declare(logstart([file],fixnum),fixnum)
(%o32) [logstart([file], fixnum)]
(%i33) mode_declare(logend([file],fixnum),fixnum)
(%o33) [logend([file], fixnum)]
(%i34) mode_declare(chk_data(),fixnum)
(%o34) [chk_data()]
(%i35) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%o35) [comp_expect_sec([t_end2], convfloat, [t_start2], convfloat, [t2],
convfloat, [clock_sec2], convfloat)]
(%i36) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%o36) [comp_percent([t_end2], convfloat, [start2], convfloat, [t2],
convfloat)]
(%i37) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%o37) [comp_rad_from_ratio([term1], convfloat, [term2], convfloat, [last_no],
fixnum)]
(%i38) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%o38) [comp_ord_from_ratio([term1], convfloat, [term2], convfloat, [last_no],
fixnum)]
(%i39) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%o39) [comp_rad_from_three_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [last_no], fixnum)]
(%i40) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%o40) [comp_ord_from_three_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [last_no], fixnum)]
(%i41) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%o41) [comp_rad_from_six_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [term4], convfloat, [term5], convfloat, [term6],
convfloat, [last_no], fixnum)]
(%i42) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%o42) [comp_ord_from_six_terms([term1], convfloat, [term2], convfloat,
[term3], convfloat, [term4], convfloat, [term5], convfloat, [term6],
convfloat, [last_no], fixnum)]
(%i43) mode_declare(factorial_2([nnn],fixnum),fixnum)
(%o43) [factorial_2([nnn], fixnum)]
(%i44) mode_declare(factorial_1([nnn],fixnum),fixnum)
(%o44) [factorial_1([nnn], fixnum)]
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),fixnum)
(%o45) [factorial_3([mmm], fixnum, [nnn], fixnum)]
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%o46) [convfloat([mmm], fixnum)]
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%o47) [elaped_time_seconds()]
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%o48) [Si([x], convfloat)]
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%o49) [Ci([x], convfloat)]
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%o50) [estimated_needed_step_error([x_start], convfloat, [x_end], convfloat,
[estimated_h], convfloat, [estimated_answer], convfloat)]
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%o51) [my_check_sign([x0], convfloat, [xf], convfloat)]
(%i52) mode_declare(main_prog(),fixnum)
(%o52) [main_prog()]
(%i53) define_variable(MAX_TERMS,30,fixnum)
(%o53) 30
(%i54) define_variable(glob_iolevel,5,fixnum)
(%o54) 5
(%i55) define_variable(glob_yes_pole,4,fixnum)
(%o55) 4
(%i56) define_variable(glob_no_pole,3,fixnum)
(%o56) 3
(%i57) define_variable(glob_not_given,0,fixnum)
(%o57) 0
(%i58) define_variable(glob_no_sing_tests,4,fixnum)
(%o58) 4
(%i59) define_variable(glob_ratio_test,1,fixnum)
(%o59) 1
(%i60) define_variable(glob_three_term_test,2,fixnum)
(%o60) 2
(%i61) define_variable(glob_six_term_test,3,fixnum)
(%o61) 3
(%i62) define_variable(glob_log_10,log(10.0),convfloat)
(%o62) 2.302585092994046
(%i63) define_variable(ALWAYS,1,fixnum)
(%o63) 1
(%i64) define_variable(INFO,2,fixnum)
(%o64) 2
(%i65) define_variable(DEBUGL,3,fixnum)
(%o65) 3
(%i66) define_variable(DEBUGMASSIVE,4,fixnum)
(%o66) 4
(%i67) define_variable(MAX_UNCHANGED,10,fixnum)
(%o67) 10
(%i68) define_variable(glob_check_sign,1.0,convfloat)
(%o68) 1.0
(%i69) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%o69) 8.0
(%i70) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%o70) 0.0
(%i71) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%o71) 0.1
(%i72) define_variable(glob_percent_done,0.0,convfloat)
(%o72) 0.0
(%i73) define_variable(glob_subiter_method,3,fixnum)
(%o73) 3
(%i74) define_variable(glob_total_exp_sec,0.1,convfloat)
(%o74) 0.1
(%i75) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%o75) 0.1
(%i76) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%o76) 100.0
(%i77) define_variable(glob_html_log,true,boolean)
(%o77) true
(%i78) define_variable(glob_good_digits,0,fixnum)
(%o78) 0
(%i79) define_variable(glob_max_opt_iter,10,fixnum)
(%o79) 10
(%i80) define_variable(glob_dump,false,boolean)
(%o80) false
(%i81) define_variable(glob_djd_debug,true,boolean)
(%o81) true
(%i82) define_variable(glob_display_flag,true,boolean)
(%o82) true
(%i83) define_variable(glob_djd_debug2,true,boolean)
(%o83) true
(%i84) define_variable(glob_sec_in_minute,60,fixnum)
(%o84) 60
(%i85) define_variable(glob_min_in_hour,60.0,convfloat)
(%o85) 60.0
(%i86) define_variable(glob_hours_in_day,24.0,convfloat)
(%o86) 24.0
(%i87) define_variable(glob_days_in_year,365,fixnum)
(%o87) 365
(%i88) define_variable(glob_sec_in_hour,3600,fixnum)
(%o88) 3600
(%i89) define_variable(glob_sec_in_day,86400,fixnum)
(%o89) 86400
(%i90) define_variable(glob_sec_in_year,31536000,fixnum)
(%o90) 31536000
(%i91) define_variable(glob_almost_1,0.999,convfloat)
(%o91) 0.999
(%i92) define_variable(glob_clock_sec,0.0,convfloat)
(%o92) 0.0
(%i93) define_variable(glob_clock_start_sec,0.0,convfloat)
(%o93) 0.0
(%i94) define_variable(glob_not_yet_finished,true,boolean)
(%o94) true
(%i95) define_variable(glob_initial_pass,true,boolean)
(%o95) true
(%i96) define_variable(glob_not_yet_start_msg,true,boolean)
(%o96) true
(%i97) define_variable(glob_reached_optimal_h,false,boolean)
(%o97) false
(%i98) define_variable(glob_optimal_done,false,boolean)
(%o98) false
(%i99) define_variable(glob_disp_incr,0.1,convfloat)
(%o99) 0.1
(%i100) define_variable(glob_h,0.1,convfloat)
(%o100) 0.1
(%i101) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%o101) 0.1
(%i102) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%o102) 0.1
(%i103) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%o103) 0.1
(%i104) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%o104) 0.1
(%i105) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%o105) 0.1
(%i106) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%o106) 0.1
(%i107) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%o107) 0.1
(%i108) define_variable(glob_guess_error_rc,0.1,convfloat)
(%o108) 0.1
(%i109) define_variable(glob_guess_error_ord,0.1,convfloat)
(%o109) 0.1
(%i110) define_variable(glob_max_h,0.1,convfloat)
(%o110) 0.1
(%i111) define_variable(glob_min_h,1.0E-6,convfloat)
(%o111) 1.0E-6
(%i112) define_variable(glob_type_given_pole,0,fixnum)
(%o112) 0
(%i113) define_variable(glob_large_float,1.0E+100,convfloat)
(%o113) 1.0E+100
(%i114) define_variable(glob_larger_float,1.1E+100,convfloat)
(%o114) 1.1E+100
(%i115) define_variable(glob_least_given_sing,9.9E+100,convfloat)
(%o115) 9.9E+100
(%i116) define_variable(glob_least_ratio_sing,9.9E+100,convfloat)
(%o116) 9.9E+100
(%i117) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%o117) 9.9E+100
(%i118) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%o118) 9.9E+100
(%i119) define_variable(glob_last_good_h,0.1,convfloat)
(%o119) 0.1
(%i120) define_variable(glob_look_poles,false,boolean)
(%o120) false
(%i121) define_variable(glob_neg_h,false,boolean)
(%o121) false
(%i122) define_variable(glob_display_interval,0.0,convfloat)
(%o122) 0.0
(%i123) define_variable(glob_next_display,0.0,convfloat)
(%o123) 0.0
(%i124) define_variable(glob_dump_analytic,false,boolean)
(%o124) false
(%i125) define_variable(glob_abserr,1.0E-11,convfloat)
(%o125) 1.0E-11
(%i126) define_variable(glob_relerr,1.0E-11,convfloat)
(%o126) 1.0E-11
(%i127) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%o127) 1.0E+9
(%i128) define_variable(glob_max_hours,0.0,convfloat)
(%o128) 0.0
(%i129) define_variable(glob_max_iter,1000,fixnum)
(%o129) 1000
(%i130) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%o130) 1.0E-11
(%i131) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%o131) 1.0E-11
(%i132) define_variable(glob_no_eqs,0,fixnum)
(%o132) 0
(%i133) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%o133) 0.0
(%i134) define_variable(glob_optimal_start,0.0,convfloat)
(%o134) 0.0
(%i135) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%o135) 1.0001
(%i136) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%o136) 0.9999
(%i137) define_variable(glob_small_float,0.0,convfloat)
(%o137) 0.0
(%i138) define_variable(glob_smallish_float,0.0,convfloat)
(%o138) 0.0
(%i139) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%o139) 0
(%i140) define_variable(glob_warned,false,boolean)
(%o140) false
(%i141) define_variable(glob_warned2,false,boolean)
(%o141) false
(%i142) define_variable(glob_max_sec,10000.0,convfloat)
(%o142) 10000.0
(%i143) define_variable(glob_orig_start_sec,0.0,convfloat)
(%o143) 0.0
(%i144) define_variable(glob_start,0,fixnum)
(%o144) 0
(%i145) define_variable(glob_curr_iter_when_opt,0,fixnum)
(%o145) 0
(%i146) define_variable(glob_current_iter,0,fixnum)
(%o146) 0
(%i147) define_variable(glob_iter,0,fixnum)
(%o147) 0
(%i148) define_variable(glob_normmax,0.0,convfloat)
(%o148) 0.0
(%i149) define_variable(glob_max_minutes,0.0,convfloat)
(%o149) 0.0
(%i150) array(array_y_init,MAX_TERMS)
(%o150) array_y_init
(%i151) array(array_norms,MAX_TERMS)
(%o151) array_norms
(%i152) array(array_fact_1,MAX_TERMS)
(%o152) array_fact_1
(%i153) array(array_1st_rel_error,2)
(%o153) array_1st_rel_error
(%i154) array(array_last_rel_error,2)
(%o154) array_last_rel_error
(%i155) array(array_type_pole,2)
(%o155) array_type_pole
(%i156) array(array_type_real_pole,2)
(%o156) array_type_real_pole
(%i157) array(array_type_complex_pole,2)
(%o157) array_type_complex_pole
(%i158) array(array_y,MAX_TERMS)
(%o158) array_y
(%i159) array(array_x,MAX_TERMS)
(%o159) array_x
(%i160) array(array_tmp0,MAX_TERMS)
(%o160) array_tmp0
(%i161) array(array_tmp1_g,MAX_TERMS)
(%o161) array_tmp1_g
(%i162) array(array_tmp1,MAX_TERMS)
(%o162) array_tmp1
(%i163) array(array_tmp2,MAX_TERMS)
(%o163) array_tmp2
(%i164) array(array_tmp3,MAX_TERMS)
(%o164) array_tmp3
(%i165) array(array_tmp4_g,MAX_TERMS)
(%o165) array_tmp4_g
(%i166) array(array_tmp4,MAX_TERMS)
(%o166) array_tmp4
(%i167) array(array_tmp5,MAX_TERMS)
(%o167) array_tmp5
(%i168) array(array_m1,MAX_TERMS)
(%o168) array_m1
(%i169) array(array_y_higher,2,MAX_TERMS)
(%o169) array_y_higher
(%i170) array(array_y_higher_work,2,MAX_TERMS)
(%o170) array_y_higher_work
(%i171) array(array_y_higher_work2,2,MAX_TERMS)
(%o171) array_y_higher_work2
(%i172) array(array_y_set_initial,2,MAX_TERMS)
(%o172) array_y_set_initial
(%i173) array(array_given_rad_poles,2,3)
(%o173) array_given_rad_poles
(%i174) array(array_given_ord_poles,2,3)
(%o174) array_given_ord_poles
(%i175) array(array_rad_test_poles,2,3)
(%o175) array_rad_test_poles
(%i176) array(array_ord_test_poles,2,3)
(%o176) array_ord_test_poles
(%i177) array(array_fact_2,MAX_TERMS,MAX_TERMS)
(%o177) array_fact_2
(%i178) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%o178) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i179) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%o179) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i180) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%o180) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i181) 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))
(%o181) 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))
(%i182) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%o182) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i183) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%o183) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i184) 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)
(%o184) 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)
(%i185) 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)
(%o185) 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)
(%i186) 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)
(%o186) 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
(%i187) 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)
(%o187) 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)
(%i188) 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)
(%o188) 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
(%i189) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%o189) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "), 0)
(%i190) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%o190) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "), 0)
(%i191) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%o191) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "), 0)
(%i192) 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)
(%o192) 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)
(%i193) log_revs(file,revs):=printf(file,revs)
(%o193) log_revs(file, revs) := printf(file, revs)
(%i194) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%o194) logitem_float(file, x) := (printf(file, ""),
printf(file, "~g", x), printf(file, " | "), 0)
(%i195) 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)
(%o195) 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)
(%i196) logstart(file):=(printf(file,""),0)
(%o196) logstart(file) := (printf(file, "
"), 0)
(%i197) logend(file):=(printf(file,"
~%"),0)
(%o197) logend(file) := (printf(file, "~%"), 0)
(%i198) 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)
(%o198) 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)
(%i199) 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)
(%o199) 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
(%i200) 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)
(%o200) 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)
(%i201) 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)
(%o201) comp_rad_from_ratio(term1, term2, last_no) :=
!term1 glob_h!
(if term2 > 0.0 then ret : !------------! else ret : glob_larger_float, ret)
! term2 !
(%i202) 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)
(%o202) 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)
(%i203) 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)
(%o203) 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 !
(%i204) 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)
(%o204) 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)
(%i205) 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)
(%o205) 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)
(%i206) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%o206) comp_ord_from_six_terms(term1, term2, term3, term4, term5, term6,
last_no) := glob_six_term_ord_save
(%i207) factorial_2(nnn):=nnn!
(%o207) factorial_2(nnn) := nnn!
(%i208) 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)
(%o208) 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
(%i209) 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)
(%o209) 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)
(%i210) log10(x):=log(x)/glob_log_10
log(x)
(%o210) log10(x) := -----------
glob_log_10
(%i211) expt(x,y):=(if x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y),x^y)
(%o211) expt(x, y) := (if (x <= 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i212) 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)
(%o212) 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)
(%i213) exact_soln_y(x):=block(cos(x)-sin(x))
(%o213) exact_soln_y(x) := block(cos(x) - sin(x))
(%i214) 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)
(%o214) 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)
(%i215) my_check_sign(x0,xf):=block([ret],if xf > x0 then ret:1.0
else ret:-1.0,ret)
(%o215) my_check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i216) 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)
(%o216) 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)
(%i217) 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)
(%o217) 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)
(%i218) 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))
(%o218) 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))
(%i219) 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)
(%o219) 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)
(%i220) 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)
(%o220) 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
(%i221) 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)
(%o221) 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)
(%i222) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),
glob_min_pole_est:glob_larger_float,
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-3 and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
glob_min_pole_est:glob_larger_float,
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-4 and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
glob_min_pole_est:glob_larger_float,
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+MAX_TERMS,cnt:0,
while last_no < MAX_TERMS-7 and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
tmp_ratio:tmp_rad/prev_tmp_rad,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
term:1,ratio:1.0,
while term <= MAX_TERMS do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%o222) check_for_pole() := (block(mode_declare([cnt], fixnum,
[dr1, dr2, ds1, ds2, hdrc], convfloat, [m, n], fixnum, [nr1, nr2], convfloat,
[ord_no], fixnum, [term1, term2, term3, part1, part2, part3, part4, part5,
part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c,
rcs, rm0, rm1, rm2, rm3, rm4], convfloat, [found_sing], fixnum,
[h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad],
convfloat, [last_no], fixnum), glob_min_pole_est : glob_larger_float,
tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float,
tmp_ratio : glob_larger_float, rad_c : glob_larger_float,
array_rad_test_poles : glob_larger_float,
1, 1
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 1
last_no : - 10 - 1 + MAX_TERMS, cnt : 0,
while (last_no < MAX_TERMS - 3) and (found_sing = 1) do (tmp_rad :
comp_rad_from_ratio(array_y_higher , array_y_higher ,
1, last_no - 1 1, last_no
tmp_rad
last_no), tmp_ratio : ------------, if (cnt > 0)
prev_tmp_rad
and (tmp_ratio < glob_upper_ratio_limit)
and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0
then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0,
prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no),
if found_sing = 1 then (if rad_c < array_rad_test_poles
1, 1
then (array_rad_test_poles : rad_c, last_no : last_no - 1,
1, 1
tmp_ord : comp_ord_from_ratio(array_y_higher ,
1, last_no - 1
array_y_higher , last_no), array_rad_test_poles : rad_c,
1, last_no 1, 1
array_ord_test_poles : tmp_ord)), glob_min_pole_est : glob_larger_float,
1, 1
tmp_rad : glob_larger_float, prev_tmp_rad : glob_larger_float,
tmp_ratio : glob_larger_float, rad_c : glob_larger_float,
array_rad_test_poles : glob_larger_float,
1, 2
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 2
last_no : - 10 - 1 + MAX_TERMS, cnt : 0,
while (last_no < MAX_TERMS - 4) and (found_sing = 1) do (tmp_rad :
comp_rad_from_three_terms(array_y_higher ,
1, last_no - 2
array_y_higher , array_y_higher , last_no),
1, last_no - 1 1, last_no
tmp_rad
tmp_ratio : ------------, if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit)
prev_tmp_rad
and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0
then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0,
prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no),
if found_sing = 1 then (if rad_c < array_rad_test_poles
1, 2
then (array_rad_test_poles : rad_c, last_no : last_no - 1,
1, 2
tmp_ord : comp_ord_from_three_terms(array_y_higher ,
1, last_no - 2
array_y_higher , array_y_higher , last_no),
1, last_no - 1 1, last_no
array_rad_test_poles : rad_c, if rad_c < glob_min_pole_est
1, 2
then glob_min_pole_est : rad_c, array_ord_test_poles : tmp_ord)),
1, 2
glob_min_pole_est : glob_larger_float, tmp_rad : glob_larger_float,
prev_tmp_rad : glob_larger_float, tmp_ratio : glob_larger_float,
rad_c : glob_larger_float, array_rad_test_poles : glob_larger_float,
1, 3
array_ord_test_poles : glob_larger_float, found_sing : 1,
1, 3
last_no : - 10 - 1 + MAX_TERMS, cnt : 0,
while (last_no < MAX_TERMS - 7) and (found_sing = 1) do (tmp_rad :
comp_rad_from_six_terms(array_y_higher ,
1, last_no - 5
array_y_higher , array_y_higher ,
1, last_no - 4 1, last_no - 3
array_y_higher , array_y_higher ,
1, last_no - 2 1, last_no - 1
tmp_rad
array_y_higher , last_no), tmp_ratio : ------------,
1, last_no prev_tmp_rad
if (cnt > 0) and (tmp_ratio < glob_upper_ratio_limit)
and (tmp_ratio > glob_lower_ratio_limit) then rad_c : tmp_rad elseif cnt = 0
then rad_c : tmp_rad elseif cnt > 0 then found_sing : 0,
prev_tmp_rad : tmp_rad, cnt : 1 + cnt, last_no : 1 + last_no),
if found_sing = 1 then (if rad_c < array_rad_test_poles
1, 3
then (array_rad_test_poles : rad_c, last_no : last_no - 1,
1, 3
tmp_ord : comp_ord_from_six_terms(array_y_higher ,
1, last_no - 5
array_y_higher , array_y_higher ,
1, last_no - 4 1, last_no - 3
array_y_higher , array_y_higher ,
1, last_no - 2 1, last_no - 1
array_y_higher , last_no), array_rad_test_poles : rad_c,
1, last_no 1, 3
if rad_c < glob_min_pole_est then glob_min_pole_est : rad_c,
array_ord_test_poles : tmp_ord)), if mabs(glob_min_pole_est)
1, 3
glob_ratio_of_radius < mabs(glob_h) then (h_new :
glob_check_sign glob_min_pole_est glob_ratio_of_radius, term : 1, ratio : 1.0,
while term <= MAX_TERMS do (array_y : array_y ratio,
term term
array_y_higher : array_y_higher ratio,
1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ------------, term : 1 + term),
term term mabs(glob_h)
glob_h : h_new), if reached_interval() then display_poles()), 0)
(%i223) 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_m1[1]*array_tmp1[1],
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
array_tmp4[1]:cos(array_x[1]),
array_tmp4_g[1]:sin(array_x[1]),
array_tmp5[1]:array_tmp3[1]-array_tmp4[1],
if not array_y_set_initial[1,2]
then (if 1 <= MAX_TERMS
then (
temporary
:array_tmp5[1]*expt(glob_h,1)
*factorial_3(0,1),
if 2 <= MAX_TERMS
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:temporary*1.0/glob_h,
array_y_higher[2,1]:temporary,0)),kkk:2,
array_tmp1[2]:array_tmp1_g[1]*array_x[2]/1,
array_tmp1_g[2]:(-array_tmp1[1]*array_x[2])/1,
array_tmp2[2]:ats(2,array_m1,array_tmp1,1),
array_tmp3[2]:array_tmp2[2],
array_tmp4[2]:(-array_tmp4_g[1]*array_x[2])/1,
array_tmp4_g[2]:array_tmp4[1]*array_x[2]/1,
array_tmp5[2]:array_tmp3[2]-array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= MAX_TERMS
then (
temporary
:array_tmp5[2]*expt(glob_h,1)
*factorial_3(1,2),
if 3 <= MAX_TERMS
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:temporary*2.0/glob_h,
array_y_higher[2,2]:temporary,0)),kkk:3,
array_tmp1[3]:array_tmp1_g[2]*array_x[2]/2,
array_tmp1_g[3]:(-array_tmp1[2]*array_x[2])/2,
array_tmp2[3]:ats(3,array_m1,array_tmp1,1),
array_tmp3[3]:array_tmp2[3],
array_tmp4[3]:(-array_tmp4_g[2]*array_x[2])/2,
array_tmp4_g[3]:array_tmp4[2]*array_x[2]/2,
array_tmp5[3]:array_tmp3[3]-array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= MAX_TERMS
then (
temporary
:array_tmp5[3]*expt(glob_h,1)
*factorial_3(2,3),
if 4 <= MAX_TERMS
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:temporary*3.0/glob_h,
array_y_higher[2,3]:temporary,0)),kkk:4,
array_tmp1[4]:array_tmp1_g[3]*array_x[2]/3,
array_tmp1_g[4]:(-array_tmp1[3]*array_x[2])/3,
array_tmp2[4]:ats(4,array_m1,array_tmp1,1),
array_tmp3[4]:array_tmp2[4],
array_tmp4[4]:(-array_tmp4_g[3]*array_x[2])/3,
array_tmp4_g[4]:array_tmp4[3]*array_x[2]/3,
array_tmp5[4]:array_tmp3[4]-array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= MAX_TERMS
then (
temporary
:array_tmp5[4]*expt(glob_h,1)
*factorial_3(3,4),
if 5 <= MAX_TERMS
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:temporary*4.0/glob_h,
array_y_higher[2,4]:temporary,0)),kkk:5,
array_tmp1[5]:array_tmp1_g[4]*array_x[2]/4,
array_tmp1_g[5]:(-array_tmp1[4]*array_x[2])/4,
array_tmp2[5]:ats(5,array_m1,array_tmp1,1),
array_tmp3[5]:array_tmp2[5],
array_tmp4[5]:(-array_tmp4_g[4]*array_x[2])/4,
array_tmp4_g[5]:array_tmp4[4]*array_x[2]/4,
array_tmp5[5]:array_tmp3[5]-array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= MAX_TERMS
then (
temporary
:array_tmp5[5]*expt(glob_h,1)
*factorial_3(4,5),
if 6 <= MAX_TERMS
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:temporary*5.0/glob_h,
array_y_higher[2,5]:temporary,0)),kkk:6,
while kkk <= MAX_TERMS do
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/(kkk-1),
array_tmp1_g[kkk]
:(-array_tmp1[kkk-1]*array_x[2])/(kkk-1),
array_tmp2[kkk]:ats(kkk,array_m1,array_tmp1,1),
array_tmp3[kkk]:array_tmp2[kkk],
array_tmp4[kkk]
:(-array_tmp4_g[kkk-1]*array_x[2])/(kkk-1),
array_tmp4_g[kkk]
:array_tmp4[kkk-1]*array_x[2]/(kkk-1),
array_tmp5[kkk]:array_tmp3[kkk]-array_tmp4[kkk],
order_d:1,
if order_d+kkk <= MAX_TERMS
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:array_tmp5[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)
(%o223) 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_m1 array_tmp1 , array_tmp3 :
1 1 1 1
array_tmp2 + array_const_0D0 , array_tmp4 : cos(array_x ),
1 1 1 1
array_tmp4_g : sin(array_x ), array_tmp5 : array_tmp3 - array_tmp4 ,
1 1 1 1 1
if not array_y_set_initial then (if 1 <= MAX_TERMS
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
if 2 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1_g array_x - array_tmp1 array_x
1 2 1 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
2 1 2 1
array_tmp2 : ats(2, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 ,
2 2 2
- array_tmp4_g array_x array_tmp4 array_x
1 2 1 2
array_tmp4 : ------------------------, array_tmp4_g : --------------------,
2 1 2 1
array_tmp5 : array_tmp3 - array_tmp4 ,
2 2 2
if not array_y_set_initial then (if 2 <= MAX_TERMS
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
if 3 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1_g array_x - array_tmp1 array_x
2 2 2 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
3 2 3 2
array_tmp2 : ats(3, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 ,
3 3 3
- array_tmp4_g array_x array_tmp4 array_x
2 2 2 2
array_tmp4 : ------------------------, array_tmp4_g : --------------------,
3 2 3 2
array_tmp5 : array_tmp3 - array_tmp4 ,
3 3 3
if not array_y_set_initial then (if 3 <= MAX_TERMS
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
if 4 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1_g array_x - array_tmp1 array_x
3 2 3 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
4 3 4 3
array_tmp2 : ats(4, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 ,
4 4 4
- array_tmp4_g array_x array_tmp4 array_x
3 2 3 2
array_tmp4 : ------------------------, array_tmp4_g : --------------------,
4 3 4 3
array_tmp5 : array_tmp3 - array_tmp4 ,
4 4 4
if not array_y_set_initial then (if 4 <= MAX_TERMS
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
if 5 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1_g array_x - array_tmp1 array_x
4 2 4 2
array_tmp1 : ----------------------, array_tmp1_g : ----------------------,
5 4 5 4
array_tmp2 : ats(5, array_m1, array_tmp1, 1), array_tmp3 : array_tmp2 ,
5 5 5
- array_tmp4_g array_x array_tmp4 array_x
4 2 4 2
array_tmp4 : ------------------------, array_tmp4_g : --------------------,
5 4 5 4
array_tmp5 : array_tmp3 - array_tmp4 ,
5 5 5
if not array_y_set_initial then (if 5 <= MAX_TERMS
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
if 6 <= MAX_TERMS then (array_y : temporary, array_y_higher : temporary),
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
array_tmp1_g array_x
kkk - 1 2
while kkk <= MAX_TERMS do (array_tmp1 : ----------------------------,
kkk kkk - 1
- array_tmp1 array_x
kkk - 1 2
array_tmp1_g : ----------------------------,
kkk kkk - 1
array_tmp2 : ats(kkk, array_m1, array_tmp1, 1),
kkk
- array_tmp4_g array_x
kkk - 1 2
array_tmp3 : array_tmp2 , array_tmp4 : ------------------------------,
kkk kkk kkk kkk - 1
array_tmp4 array_x
kkk - 1 2
array_tmp4_g : --------------------------,
kkk kkk - 1
array_tmp5 : array_tmp3 - array_tmp4 , order_d : 1,
kkk kkk kkk
if order_d + kkk <= MAX_TERMS then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp5 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)
(%i224) exact_soln_y(x):=block(cos(x)-sin(x))
(%o224) exact_soln_y(x) := block(cos(x) - sin(x))
(%i225) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,best_h,found_h],
convfloat,[repeat_it],fixnum]),Digits:32,
max_terms:30,glob_html_log:true,term:1,
while term <= MAX_TERMS do
(array_y_init[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_norms[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_fact_1[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_1st_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:0.0,term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= MAX_TERMS do (array_y[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do (array_x[term]:0.0,term:1+term),
term:1,
while term <= MAX_TERMS do
(array_tmp0[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp1_g[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp1[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp2[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp3[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp4_g[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp4[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do
(array_tmp5[term]:0.0,term:1+term),term:1,
while term <= MAX_TERMS do (array_m1[term]:0.0,term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher[ord,term]:0.0,term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_higher_work2[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= MAX_TERMS do
(array_y_set_initial[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_rad_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_ord_test_poles[ord,term]:0.0,
term:1+term),ord:1+ord),ord:1,
while ord <= MAX_TERMS do
(term:1,
while term <= MAX_TERMS do
(array_fact_2[ord,term]:0.0,term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_m1),zero_ats_ar(array_tmp0),
zero_ats_ar(array_tmp1_g),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3),
zero_ats_ar(array_tmp4_g),zero_ats_ar(array_tmp4),
zero_ats_ar(array_tmp5),zero_ats_ar(array_const_1),
array_const_1[1]:1,zero_ats_ar(array_const_0D0),
array_const_0D0[1]:0.0,zero_ats_ar(array_m1),
array_m1[1]:-1.0,iiif:0,
while iiif <= MAX_TERMS do
(jjjf:0,
while jjjf <= MAX_TERMS do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,ALWAYS:1,INFO:2,DEBUGL:3,
DEBUGMASSIVE:4,MAX_TERMS:30,glob_iolevel:INFO,
glob_orig_start_sec:elapsed_time_seconds(),
glob_curr_iter_when_opt:0,glob_display_flag:true,
glob_no_eqs:1,glob_iter:-1,opt_iter:-1,glob_max_iter:50000,
glob_max_hours:0.0,glob_max_minutes:15.0,
omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS,
"##############temp/sub_sin_cospostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; "),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"Digits:32,"),
omniout_str(ALWAYS,"max_terms:30,"),omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"x_start:0.1,"),
omniout_str(ALWAYS,"x_end:5.0,"),
omniout_str(ALWAYS,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:1000000,"),
omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"glob_desired_digits_correct:10,"),
omniout_str(ALWAYS,"glob_display_interval:0.01,"),
omniout_str(ALWAYS,"glob_look_poles:true,"),
omniout_str(ALWAYS,"glob_max_iter:1000000000,"),
omniout_str(ALWAYS,"glob_max_minutes:10.0,"),
omniout_str(ALWAYS,"glob_subiter_method:3,"),
omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"),
omniout_str(ALWAYS,"!"),
omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS,"exact_soln_y (x) := (block("),
omniout_str(ALWAYS," (cos(x) - sin(x)) "),
omniout_str(ALWAYS,"));"),
omniout_str(ALWAYS,"/* END USER DEF BLOCK */"),
omniout_str(ALWAYS,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:0.0,glob_smallish_float:0.0,
glob_large_float:1.0E+100,glob_larger_float:1.1E+100,
glob_almost_1:0.99,x_start:0.1,x_end:5.0,
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_max_iter:1000000,
glob_desired_digits_correct:10,glob_display_interval:0.01,
glob_look_poles:true,glob_max_iter:1000000000,
glob_max_minutes:10.0,glob_subiter_method:3,
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
omniout_str(ALWAYS,"START of Optimize"),
glob_check_sign:my_check_sign(x_start,x_end),found_h:false,
glob_h:glob_min_h*glob_check_sign,
if abs(glob_max_h) < abs(glob_h)
then glob_h:abs(glob_max_h)*glob_check_sign,
if abs(glob_display_interval) < abs(glob_h)
then glob_h:abs(glob_display_interval),
if glob_h > 0.0
then (glob_neg_h:false,
glob_display_interval:abs(glob_display_interval))
else (glob_neg_h:true,
glob_display_interval
:-abs(glob_display_interval)),chk_data(),
best_h:glob_h,min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(ALWAYS,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:0.0,
while opt_iter <= 100 and not found_h do
(omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""),
array_x[1]:x_start,array_x[2]:glob_h,
glob_next_display:x_start,order_diff:1,term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]*expt(glob_h,term_no-1)
/factorial_1(term_no-1),term_no:1+term_no),
rows:order_diff,r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < MAX_TERMS
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),r_order:1+r_order),
atomall(),estimated_step_error:test_suggested_h(),
omniout_float(ALWAYS,"estimated_step_error",32,
estimated_step_error,32,""),
if estimated_step_error > est_needed_step_err
and opt_iter = 1
or glob_check_sign*glob_h
>= glob_check_sign*glob_max_h
then (found_h:true,
glob_h:glob_check_sign*glob_max_h,
best_h:glob_h)
elseif estimated_step_error > est_needed_step_err
and not found_h
then (glob_h:glob_h/2.0,best_h:glob_h,
found_h:true)
else (glob_h:glob_h*2.0,best_h:glob_h),
omniout_float(ALWAYS,"best_h",32,best_h,32,""),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(ALWAYS,"Beginning glob_h too large."),
found_h:false),
if opt_iter > 100
then (glob_h:glob_check_sign*glob_max_h,found_h:false),
if glob_check_sign*glob_display_interval
< glob_check_sign*glob_h
then glob_h:glob_check_sign*glob_display_interval,
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(ALWAYS,"START of Soultion"),
array_x[1]:x_start,array_x[2]:glob_h,
glob_next_display:x_start,order_diff:1,term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < MAX_TERMS
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,term_no-1)
/factorial_1(term_no-1),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),
glob_current_iter:0,glob_iter:0,
omniout_str(DEBUGL," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_current_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(INFO," "),
omniout_str(INFO,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
glob_current_iter:1+glob_current_iter,
atomall(),display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:2,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),ord:1,
calc_term:2,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:1,
calc_term:2,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),ord:1,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,calc_term-1)
/factorial_3(iii-calc_term,iii-1),
iii:iii-1),temp_sum:0.0,ord:1,
calc_term:1,iii:MAX_TERMS,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,calc_term-1)
/factorial_1(calc_term-1),
term_no:MAX_TERMS,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(ALWAYS,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(INFO,
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; "),
omniout_int(INFO,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2014-01-09T00:55:55-06:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sub_sin_cos"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( 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,
"sub_sin_cos diffeq.max"),
logitem_str(html_log_file,
"sub_sin_cos 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)))
(%o225) main_prog() := block(mode_declare([[d1, d2, d3, d4, est_err_2],
convfloat, [niii, done_once, term, ord, order_diff, term_no, html_log_file,
iiif, jjjf, rows, r_order, sub_iter, calc_term, iii], fixnum, [temp_sum],
convfloat, [current_iter], fixnum, [x_start, x_end], convfloat,
[it, opt_iter], fixnum, [tmp], convfloat, [subiter], fixnum,
[est_needed_step_err, estimated_step_error, min_value, est_answer, best_h,
found_h], convfloat, [repeat_it], fixnum]), Digits : 32, max_terms : 30,
glob_html_log : true, term : 1, while term <=
MAX_TERMS do (array_y_init : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_norms : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_fact_1 : 0.0,
term
term : 1 + term), term : 1, while term <=
2 do (array_1st_rel_error : 0.0, term : 1 + term), term : 1,
term
while term <= 2 do (array_last_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_pole : 0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_real_pole : 0, term : 1 + term),
term
term : 1, while term <= 2 do (array_type_complex_pole : 0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_y : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_x : 0.0,
term
term : 1 + term), term : 1, while term <= MAX_TERMS do (array_tmp0 : 0.0,
term
term : 1 + term), term : 1, while term <=
MAX_TERMS do (array_tmp1_g : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= MAX_TERMS do (array_tmp4_g : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_tmp5 : 0.0, term : 1 + term),
term
term : 1, while term <= MAX_TERMS do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
MAX_TERMS do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= MAX_TERMS do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_rad_test_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= 3 do (array_ord_test_poles : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= MAX_TERMS do (term : 1,
while term <= MAX_TERMS do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), zero_ats_ar(array_y), zero_ats_ar(array_x),
zero_ats_ar(array_m1), zero_ats_ar(array_tmp0), zero_ats_ar(array_tmp1_g),
zero_ats_ar(array_tmp1), zero_ats_ar(array_tmp2), zero_ats_ar(array_tmp3),
zero_ats_ar(array_tmp4_g), zero_ats_ar(array_tmp4), zero_ats_ar(array_tmp5),
zero_ats_ar(array_const_1), array_const_1 : 1, zero_ats_ar(array_const_0D0),
1
array_const_0D0 : 0.0, zero_ats_ar(array_m1), array_m1 : - 1.0, iiif : 0,
1 1
while iiif <= MAX_TERMS do (jjjf : 0,
while jjjf <= MAX_TERMS do (array_fact_1 : 0, array_fact_2 : 0,
iiif iiif, jjjf
jjjf : 1 + jjjf), iiif : 1 + iiif), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, ALWAYS : 1, INFO : 2, DEBUGL : 3,
1, 30
DEBUGMASSIVE : 4, MAX_TERMS : 30, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), glob_curr_iter_when_opt : 0,
glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1,
glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0,
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS,
"##############temp/sub_sin_cospostode.ode#################"),
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; "),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.01,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:1000000000,"),
omniout_str(ALWAYS, "glob_max_minutes:10.0,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (cos(x) - sin(x)) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 0.0, glob_smallish_float : 0.0,
glob_large_float : 1.0E+100, glob_larger_float : 1.1E+100,
glob_almost_1 : 0.99, x_start : 0.1, x_end : 5.0,
array_y_init : exact_soln_y(x_start), glob_look_poles : true,
1 + 0
glob_max_iter : 1000000, glob_desired_digits_correct : 10,
glob_display_interval : 0.01, glob_look_poles : true,
glob_max_iter : 1000000000, glob_max_minutes : 10.0, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_sec :
3600.0 glob_max_hours + 60.0 glob_max_minutes,
omniout_str(ALWAYS, "START of Optimize"),
glob_check_sign : my_check_sign(x_start, x_end), found_h : false,
glob_h : glob_min_h glob_check_sign, if mabs(glob_max_h) < mabs(glob_h)
then glob_h : mabs(glob_max_h) glob_check_sign,
if mabs(glob_display_interval) < mabs(glob_h)
then glob_h : mabs(glob_display_interval),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : mabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- mabs(glob_display_interval)), chk_data(), best_h : glob_h,
min_value : glob_larger_float, est_answer : est_size_answer(), opt_iter : 1,
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), estimated_step_error : 0.0,
while (opt_iter <= 100) and (not found_h) do (omniout_int(ALWAYS, "opt_iter",
32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
if term_no < MAX_TERMS then array_y_higher :
r_order, term_no
array_y_init expt(glob_h, term_no - 1)
it
----------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
r_order : 1 + r_order), atomall(), estimated_step_error : test_suggested_h(),
omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32,
""), if ((estimated_step_error > est_needed_step_err) and (opt_iter = 1))
or (glob_check_sign glob_h >= glob_check_sign glob_max_h)
then (found_h : true, glob_h : glob_check_sign glob_max_h, best_h : glob_h)
elseif (estimated_step_error > est_needed_step_err) and (not found_h)
glob_h
then (glob_h : ------, best_h : glob_h, found_h : true)
2.0
else (glob_h : glob_h 2.0, best_h : glob_h),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter),
if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS,
"Beginning glob_h too large."), found_h : false),
if opt_iter > 100 then (glob_h : glob_check_sign glob_max_h, found_h : false),
if glob_check_sign glob_display_interval < glob_check_sign glob_h
then glob_h : glob_check_sign glob_display_interval,
if glob_html_log then html_log_file : openw("entry.html"),
if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start,
1
array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1,
2
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
if term_no < MAX_TERMS then array_y_higher :
r_order, term_no
array_y_init expt(glob_h, term_no - 1)
it
----------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (glob_clock_sec - glob_orig_start_sec < glob_max_sec) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, iii : MAX_TERMS,
2
while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2, iii : MAX_TERMS,
factorial_1(calc_term - 1)
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1, iii : MAX_TERMS,
factorial_1(calc_term - 1)
while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : MAX_TERMS,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : MAX_TERMS,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - glob_orig_start_sec >= glob_max_sec
then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x \
, 1 ) = m1 * sin ( x ) - cos ( x ) ; "),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2014-01-09T00:55:55-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sub_sin_cos"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( 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, "sub_sin_cos diffeq.max"),
logitem_str(html_log_file,
"sub_sin_cos 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)))
(%i226) main():=(alias(convfloat,convfloat),compile(all),main_prog())
(%o226) main() := (alias(convfloat, convfloat), compile(all), main_prog())
(%i227) 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_m1 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp4_g in translation.
warning: encountered undefined variable array_tmp5 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 ord in translation.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable jjjf in translation.
warning: encountered undefined variable INFO in translation.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable ALWAYS in translation.
warning: encountered undefined variable x_start in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable est_answer in translation.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: encountered undefined variable order_diff in translation.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: encountered undefined variable it in translation.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable best_h in translation.
warning: encountered undefined variable glob_html_log in translation.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable DEBUGL in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_current_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_look_poles in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable calc_term in translation.
warning: encountered undefined variable temp_sum in translation.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
WARNING: in $ADJUST_FOR_POLE : $GLOB_CURR_ITER_WHEN_OPT is neither declared
nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $ADJUST_FOR_POLE : $GLOB_OPTIMAL_START is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : |$debugmassive| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_CURR_ITER_WHEN_OPT is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NEG_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
Warning: modedcclare has a function or macro call which has not been translated properly.
The function was totaly undefined. Maybe you want to quote it."##############ECHO OF PROBLEM#################"
"##############temp/sub_sin_cospostode.ode#################"
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:0.1,"
"x_end:5.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:1000000,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.01,"
"glob_look_poles:true,"
"glob_max_iter:1000000000,"
"glob_max_minutes:10.0,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (cos(x) - sin(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 = 2.219661992980814000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 ""
estimated_step_error = 2.219661992980814000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-183 ""
best_h = 2.000000E-6 ""
opt_iter = 2
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.48958991439137960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 ""
estimated_step_error = 1.48958991439137960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-175 ""
best_h = 4.000000E-6 ""
opt_iter = 3
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 9.996468245245109000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-168 ""
estimated_step_error = 9.996468245245109000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 6.7085156717383930000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 ""
estimated_step_error = 6.7085156717383930000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-160 ""
best_h = 1.600000E-5 ""
opt_iter = 5
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.50200784283529700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 ""
estimated_step_error = 4.50200784283529700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 ""
best_h = 3.200000E-5 ""
opt_iter = 6
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.021245225662604000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 ""
estimated_step_error = 3.021245225662604000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 ""
best_h = 6.400000E-5 ""
opt_iter = 7
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.0275218801057812000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 ""
estimated_step_error = 2.0275218801057812000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 ""
best_h = 1.280000E-4 ""
opt_iter = 8
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.360644928770732300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 ""
estimated_step_error = 1.360644928770732300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 ""
best_h = 2.560000E-4 ""
opt_iter = 9
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 9.1311070756153740000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-121 ""
estimated_step_error = 9.1311070756153740000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-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 = 6.12774669861724700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 ""
estimated_step_error = 6.12774669861724700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-113 ""
best_h = 1.024000E-3 ""
opt_iter = 11
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 4.112213509539602300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
estimated_step_error = 4.112213509539602300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 ""
best_h = 2.048000E-3 ""
opt_iter = 12
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.7595957633816950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
estimated_step_error = 2.7595957633816950000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 ""
best_h = 4.096000E-3 ""
opt_iter = 13
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.85184745369409700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 ""
estimated_step_error = 1.85184745369409700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 ""
best_h = 8.192000E-3 ""
opt_iter = 14
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 1.2426384668892346000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 ""
estimated_step_error = 1.2426384668892346000000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 ""
best_h = 1.638400E-2 ""
opt_iter = 15
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 8.33765748040378200000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
estimated_step_error = 8.33765748040378200000000000000000000000000000000000000000000000000000000000000000000000000E-74 ""
best_h = 3.276800E-2 ""
opt_iter = 16
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 5.593228640648209000000000000000000000000000000000000000000000000000000000000000000E-66 ""
estimated_step_error = 5.593228640648209000000000000000000000000000000000000000000000000000000000000000000E-66 ""
best_h = 6.553600E-2 ""
opt_iter = 17
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 3.7507603847804890000000000000000000000000000000000000000000000000000000000E-58 ""
estimated_step_error = 3.7507603847804890000000000000000000000000000000000000000000000000000000000E-58 ""
best_h = 0.131072 ""
opt_iter = 18
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
max_estimated_step_error = 2.513340227882283000000000000000000000000000000000000000000000000000E-50 ""
estimated_step_error = 2.513340227882283000000000000000000000000000000000000000000000000000E-50 ""
best_h = 0.1 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (analytic) = 0.8951707486311977 " "
y[1] (numeric) = 0.8951707486311977 " "
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 = 0.49003328892062087 " "
Order of pole (three term test) = 22.59933466539753 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11 " "
y[1] (analytic) = 0.884177797119522 " "
y[1] (numeric) = 0.8841777971195222 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.255655851393289200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4879487246653028 " "
Order of pole (three term test) = 22.609114811540437 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12 " "
y[1] (analytic) = 0.8730964285649468 " "
y[1] (numeric) = 0.873096428564947 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.271592676710360200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48566898742601483 " "
Order of pole (three term test) = 22.618851313213572 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13 " "
y[1] (analytic) = 0.8619277510950932 " "
y[1] (numeric) = 0.8619277510950932 " "
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 = 0.48319498906725655 " "
Order of pole (three term test) = 22.628540275946076 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14 " "
y[1] (analytic) = 0.8506728815684006 " "
y[1] (numeric) = 0.8506728815684007 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.305111575413358300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48052771915538545 " "
Order of pole (three term test) = 22.638177824282057 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000002 " "
y[1] (analytic) = 0.839332945462443 " "
y[1] (numeric) = 0.8393329454624431 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.32274448492363500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47766824456280316 " "
Order of pole (three term test) = 22.647760103330675 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000003 " "
y[1] (analytic) = 0.8279090767613809 " "
y[1] (numeric) = 0.827909076761381 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.340996319267488700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4746177090412204 " "
Order of pole (three term test) = 22.657283280308057 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000004 " "
y[1] (analytic) = 0.8164024178425646 " "
y[1] (numeric) = 0.8164024178425647 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.359896786635010000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4713773327641731 " "
Order of pole (three term test) = 22.666743546070403 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000005 " "
y[1] (analytic) = 0.8048141193622972 " "
y[1] (numeric) = 0.8048141193622973 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.379477568689840000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46794841183896746 " "
Order of pole (three term test) = 22.676137116637545 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000006 " "
y[1] (analytic) = 0.7931453401407697 " "
y[1] (numeric) = 0.7931453401407698 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.399772486122292400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4643323177882551 " "
Order of pole (three term test) = 22.685460234706486 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000007 " "
y[1] (analytic) = 0.7813972470461803 " "
y[1] (numeric) = 0.7813972470461804 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.420817681175606500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46053049700144244 " "
Order of pole (three term test) = 22.694709171154322 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000008 " "
y[1] (analytic) = 0.7695710148780486 " "
y[1] (numeric) = 0.7695710148780487 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.442651819210069900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45654447015615407 " "
Order of pole (three term test) = 22.703880226529783 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000008 " "
y[1] (analytic) = 0.757667826249736 " "
y[1] (numeric) = 0.7576678262497362 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.46531631166190500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4523758316099817 " "
Order of pole (three term test) = 22.712969732532997 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2300000000000001 " "
y[1] (analytic) = 0.7456888714701863 " "
y[1] (numeric) = 0.7456888714701865 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.977711126186613500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4480262487627626 " "
Order of pole (three term test) = 22.72197405348276 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000001 " "
y[1] (analytic) = 0.7336353484248949 " "
y[1] (numeric) = 0.7336353484248951 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.02663449085104840000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4434974613896421 " "
Order of pole (three term test) = 22.730889587770736 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (analytic) = 0.7215084624561217 " "
y[1] (numeric) = 0.7215084624561219 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.07750520581780260000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4387912809451862 " "
Order of pole (three term test) = 22.739712769302102 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (analytic) = 0.709309426242358 " "
y[1] (numeric) = 0.7093094262423582 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.56521679192490200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4339095898388249 " "
Order of pole (three term test) = 22.74844006892187 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (analytic) = 0.6970394596770593 " "
y[1] (numeric) = 0.6970394596770594 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.59276926035080800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4288543406819122 " "
Order of pole (three term test) = 22.75706799582656 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (analytic) = 0.684699789746657 " "
y[1] (numeric) = 0.6846997897466572 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.24294834393317300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4236275555067079 " "
Order of pole (three term test) = 22.76559309896044 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (analytic) = 0.6722916504078613 " "
y[1] (numeric) = 0.6722916504078617 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.95420264680491300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4182313249575932 " "
Order of pole (three term test) = 22.77401196839594 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (analytic) = 0.6598162824642663 " "
y[1] (numeric) = 0.6598162824642665 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.36524894620278800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.412667807454839 " "
Order of pole (three term test) = 22.782321236697516 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (analytic) = 0.6472749334422697 " "
y[1] (numeric) = 0.6472749334422699 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.43045270954920100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.406939228331267 " "
Order of pole (three term test) = 22.79051758026866 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (analytic) = 0.6346688574663228 " "
y[1] (numeric) = 0.6346688574663232 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.24788483741256100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40104787894214633 " "
Order of pole (three term test) = 22.798597720681197 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (analytic) = 0.6219993151335184 " "
y[1] (numeric) = 0.6219993151335187 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.35477932666293700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3949961157486824 " "
Order of pole (three term test) = 22.80655842598671 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (analytic) = 0.6092675733875317 " "
y[1] (numeric) = 0.6092675733875319 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.64445138103217660000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38878635937546396 " "
Order of pole (three term test) = 22.814396512009232 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (analytic) = 0.5964749053919274 " "
y[1] (numeric) = 0.5964749053919276 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.722614361774899700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3824210936422442 " "
Order of pole (three term test) = 22.82210884361884 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (analytic) = 0.5836225904028447 " "
y[1] (numeric) = 0.5836225904028449 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.80459236116554900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37590286457044736 " "
Order of pole (three term test) = 22.82969233598574 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (analytic) = 0.5707119136410721 " "
y[1] (numeric) = 0.5707119136410724 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.83599009284072800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36923427936479386 " "
Order of pole (three term test) = 22.837143955814074 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (analytic) = 0.5577441661635272 " "
y[1] (numeric) = 0.5577441661635275 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.97167890932083300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3624180053704525 " "
Order of pole (three term test) = 22.84446072255528 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (analytic) = 0.5447206447341513 " "
y[1] (numeric) = 0.5447206447341515 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.076302359228541300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35545676900613843 " "
Order of pole (three term test) = 22.851639709600196 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (analytic) = 0.5316426516942343 " "
y[1] (numeric) = 0.5316426516942344 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.08828810308410600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3483533546735824 " "
Order of pole (three term test) = 22.85867804544976 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (analytic) = 0.5185114948321818 " "
y[1] (numeric) = 0.5185114948321821 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.2823468165714800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.34111060364380663 " "
Order of pole (three term test) = 22.865572914863446 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (analytic) = 0.5053284872527377 " "
y[1] (numeric) = 0.5053284872527379 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.394064663407284400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3337314129206539 " "
Order of pole (three term test) = 22.872321559985433 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (analytic) = 0.492094947245674 " "
y[1] (numeric) = 0.4920949472456742 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.512230945833660700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32621873408202584 " "
Order of pole (three term test) = 22.878921281447642 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (analytic) = 0.4788121981539634 " "
y[1] (numeric) = 0.47881219815396364 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.63740493206132200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3185755720992899 " "
Order of pole (three term test) = 22.885369439449487 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (analytic) = 0.4654815682414463 " "
y[1] (numeric) = 0.46548156824144654 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.770212615805579600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3108049841353321 " "
Order of pole (three term test) = 22.891663454813738 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (analytic) = 0.45210439056000506 " "
y[1] (numeric) = 0.4521043905600053 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.91135696890695600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3029100783217312 " "
Order of pole (three term test) = 22.897800810018186 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (analytic) = 0.4386820028162603 " "
y[1] (numeric) = 0.43868200281626046 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 3.796222608282500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29489401251554925 " "
Order of pole (three term test) = 22.903779050202562 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (analytic) = 0.42521574723780087 " "
y[1] (numeric) = 0.42521574723780114 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 6.52741009615212400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2867599930362283 " "
Order of pole (three term test) = 22.909595784150497 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (analytic) = 0.41170697043896304 " "
y[1] (numeric) = 0.4117069704389633 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 6.7415850613449300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.27851127338310844 " "
Order of pole (three term test) = 22.915248685245984 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (analytic) = 0.39815702328616925 " "
y[1] (numeric) = 0.3981570232861696 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 8.36521492547326600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2701511529340699 " "
Order of pole (three term test) = 22.920735492403953 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (analytic) = 0.38456726076284325 " "
y[1] (numeric) = 0.38456726076284364 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.01042937937047880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2616829756258246 " "
Order of pole (three term test) = 22.92605401097468 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (analytic) = 0.37093904183391274 " "
y[1] (numeric) = 0.3709390418339131 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 8.97901999586975400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2531101286163889 " "
Order of pole (three term test) = 22.931202113621666 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (analytic) = 0.3572737293099135 " "
y[1] (numeric) = 0.3572737293099139 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.08762001440563990000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24443604093026355 " "
Order of pole (three term test) = 22.936177741172497 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (analytic) = 0.34357268971071053 " "
y[1] (numeric) = 0.3435726897107109 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 1.13099227690649380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2356641820868695 " "
Order of pole (three term test) = 22.940978903442474 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (analytic) = 0.32983729312884613 " "
y[1] (numeric) = 0.32983729312884646 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 1.0097915376034790000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22679806071278838 " "
Order of pole (three term test) = 22.945603680030718 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (analytic) = 0.31606891309253216 " "
y[1] (numeric) = 0.3160689130925326 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.40503919067817760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21784122313835574 " "
Order of pole (three term test) = 22.950050221088254 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (analytic) = 0.30226892642829895 " "
y[1] (numeric) = 0.3022689264282994 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.46918578465062570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20879725197917873 " "
Order of pole (three term test) = 22.954316748057945 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (analytic) = 0.2884387131233128 " "
y[1] (numeric) = 0.28843871312331326 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.53963108849472100000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19966976470313622 " "
Order of pole (three term test) = 22.958401554385883 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (analytic) = 0.2745796561873791 " "
y[1] (numeric) = 0.2745796561873796 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 1.81950974816714880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1904624121834403 " "
Order of pole (three term test) = 22.96230300620401 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (analytic) = 0.2606931415146424 " "
y[1] (numeric) = 0.26069314151464285 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.70349402853438470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18117887723833628 " "
Order of pole (three term test) = 22.966019542983613 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (analytic) = 0.24678055774499763 " "
y[1] (numeric) = 0.24678055774499816 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.1369428026087650000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17182287315802272 " "
Order of pole (three term test) = 22.96954967815953 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (analytic) = 0.23284329612522825 " "
y[1] (numeric) = 0.23284329612522875 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.14565061307422980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16239814221938728 " "
Order of pole (three term test) = 22.972891999724766 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (analytic) = 0.2188827503698818 " "
y[1] (numeric) = 0.21888275036988225 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.02889085183557330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15290845418914412 " "
Order of pole (three term test) = 22.976045170795253 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (analytic) = 0.20490031652189988 " "
y[1] (numeric) = 0.20490031652190044 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.7091784031150950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1433576048159777 " "
Order of pole (three term test) = 22.979007930144608 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (analytic) = 0.19089739281301565 " "
y[1] (numeric) = 0.19089739281301615 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.61711463797035640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13374941431229334 " "
Order of pole (three term test) = 22.981779092708596 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (analytic) = 0.17687537952393062 " "
y[1] (numeric) = 0.17687537952393118 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 3.13843291139043860000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12408772582618616 " "
Order of pole (three term test) = 22.984357550059134 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (analytic) = 0.16283567884428896 " "
y[1] (numeric) = 0.16283567884428948 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 3.23857732187324600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11437640390422961 " "
Order of pole (three term test) = 22.986742270847657 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (analytic) = 0.14877969473245867 " "
y[1] (numeric) = 0.1487796947324593 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 4.29076185636367350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10461933294570912 " "
Order of pole (three term test) = 22.988932301217652 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (analytic) = 0.134708832775138 " "
y[1] (numeric) = 0.13470883277513854 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 3.91478365473803300000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.48204156489172800E-2 " "
Order of pole (three term test) = 22.99092676518618 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (analytic) = 0.12062450004679659 " "
y[1] (numeric) = 0.12062450004679724 " "
absolute error = 6.5225602696727950000000000000000E-16 " "
relative error = 5.4073262621957810000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.49835714501199900E-2 " "
Order of pole (three term test) = 22.99272486499423 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (analytic) = 0.1065281049689708 " "
y[1] (numeric) = 0.10652810496897136 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 5.2109395213053820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.51127349558426500E-2 " "
Order of pole (three term test) = 22.994325881425855 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (analytic) = 9.24210571694210600E-2 " "
y[1] (numeric) = 9.2421057169421700E-2 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 6.9072812918513380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.52118543690721200E-2 " "
Order of pole (three term test) = 22.995729174095842 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (analytic) = 7.83047673411717500E-2 " "
y[1] (numeric) = 7.8304767341172400E-2 " "
absolute error = 6.383782391594650000000000000000E-16 " "
relative error = 8.1524824201069170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.52848899100341400E-2 " "
Order of pole (three term test) = 22.996934181705825 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (analytic) = 6.418064710144200E-2 " "
y[1] (numeric) = 6.41806471014427200E-2 " "
absolute error = 7.2164496600635180000000000000000E-16 " "
relative error = 1.124396525428828100000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.53358122321543600E-2 " "
Order of pole (three term test) = 22.997940422268822 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (analytic) = 5.005010885048589000E-2 " "
y[1] (numeric) = 5.0050108850486600E-2 " "
absolute error = 7.1470607210244450000000000000000E-16 " "
relative error = 1.427981054421835000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.53686008338509600E-2 " "
Order of pole (three term test) = 22.998747493302023 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (analytic) = 3.591456563035300E-2 " "
y[1] (numeric) = 3.591456563035372000E-2 " "
absolute error = 7.1470607210244450000000000000000E-16 " "
relative error = 1.9900173079036615000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.53872424667887500E-2 " "
Order of pole (three term test) = 22.99935507198779 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (analytic) = 2.17754309835858080E-2 " "
y[1] (numeric) = 2.1775430983586500E-2 " "
absolute error = 6.9041994343876920000000000000000E-16 " "
relative error = 3.1706373295628626000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.539572954123244700E-2 " "
Order of pole (three term test) = 22.99976291530274 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (analytic) = 7.634118811866375000E-3 " "
y[1] (numeric) = 7.634118811867054000E-3 " "
absolute error = 6.8001160258290840000000000000000E-16 " "
relative error = 8.90753234709822900000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.398058529133096000E-3 " "
Order of pole (three term test) = 22.99997086011499 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (analytic) = -6.5079567653726360000E-3 " "
y[1] (numeric) = -6.507956765371833000E-3 " "
absolute error = 8.0317696937726170000000000000000E-16 " "
relative error = 1.234146135774571300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.601771634404851000E-3 " "
Order of pole (three term test) = 22.999978823249364 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (analytic) = -2.06493815523581810E-2 " "
y[1] (numeric) = -2.06493815523574600E-2 " "
absolute error = 7.2164496600635180000000000000000E-16 " "
relative error = 3.494753410297361000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.459976115064488500E-2 " "
Order of pole (three term test) = 22.999786801520752 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (analytic) = -3.478874141839627400E-2 " "
y[1] (numeric) = -3.47887414183956100E-2 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 1.914797108534782000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.459191095708593300E-2 " "
Order of pole (three term test) = 22.999394871735266 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (analytic) = -4.892462243928319400E-2 " "
y[1] (numeric) = -4.892462243928244500E-2 " "
absolute error = 7.4940054162198070000000000000000E-16 " "
relative error = 1.5317451709556007000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.457422432703149000E-2 " "
Order of pole (three term test) = 22.998803190659583 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (analytic) = -6.3055611038696500E-2 " "
y[1] (numeric) = -6.30556110386957400E-2 " "
absolute error = 7.6327832942979510000000000000000E-16 " "
relative error = 1.2104843912485123000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.4542708468230396E-2 " "
Order of pole (three term test) = 22.998011994958265 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (analytic) = -7.71802941295520700E-2 " "
y[1] (numeric) = -7.71802941295513200E-2 " "
absolute error = 7.4940054162198070000000000000000E-16 " "
relative error = 9.7097393845644560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.44933761199359300E-2 " "
Order of pole (three term test) = 22.997021601099032 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (analytic) = -9.12972592553115100E-2 " "
y[1] (numeric) = -9.12972592553106500E-2 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 9.4244104489307370000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.44222471477632500E-2 " "
Order of pole (three term test) = 22.99583240522624 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (analytic) = -0.10540509473122606 " "
y[1] (numeric) = -0.10540509473122525 " "
absolute error = 8.0491169285323850000000000000000E-16 " "
relative error = 7.6363642090137510000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.43253501356823600E-2 " "
Order of pole (three term test) = 22.994444883002355 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (analytic) = -0.11950238978550487 " "
y[1] (numeric) = -0.11950238978550401 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 7.2000471758671210000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.41987239745390900E-2 " "
Order of pole (three term test) = 22.992859589417773 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (analytic) = -0.1335877347003901 " "
y[1] (numeric) = -0.1335877347003892 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.6486524507068510000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.40384194464408500E-2 " "
Order of pole (three term test) = 22.991077158568807 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (analytic) = -0.14765972095312796 " "
y[1] (numeric) = -0.1476597209531271 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 5.827065353574810000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1038405008043925 " "
Order of pole (three term test) = 22.98909830340402 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (analytic) = -0.1617169413568199 " "
y[1] (numeric) = -0.16171694135681905 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 5.3205485885737760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11360104734654398 " "
Order of pole (three term test) = 22.986923815439088 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (analytic) = -0.1757579902011398 " "
y[1] (numeric) = -0.17575799020113897 " "
absolute error = 8.3266726846886740000000000000000E-16 " "
relative error = 4.7375784595394604000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12331615498441781 " "
Order of pole (three term test) = 22.984554564440227 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (analytic) = -0.18978146339290425 " "
y[1] (numeric) = -0.1897814633929033 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 4.9725065560152420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.132981937804491 " "
Order of pole (three term test) = 22.981991498076223 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (analytic) = -0.20378595859647985 " "
y[1] (numeric) = -0.20378595859647902 " "
absolute error = 8.3266726846886740000000000000000E-16 " "
relative error = 4.08598940870919600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14259452962251112 " "
Order of pole (three term test) = 22.979235641539454 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (analytic) = -0.21777007537401705 " "
y[1] (numeric) = -0.21777007537401616 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.0785145441801010000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15215008552991718 " "
Order of pole (three term test) = 22.976288097135797 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (analytic) = -0.23173241532549127 " "
y[1] (numeric) = -0.23173241532549035 " "
absolute error = 9.1593399531575410000000000000000E-16 " "
relative error = 3.9525501601889990000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16164478343175245 " "
Order of pole (three term test) = 22.973150043843706 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (analytic) = -0.24567158222854268 " "
y[1] (numeric) = -0.2456715822285417 " "
absolute error = 9.714451465470120000000000000000E-16 " "
relative error = 3.9542430497447550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1710748255754501 " "
Order of pole (three term test) = 22.969822736842662 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (analytic) = -0.2595861821780968 " "
y[1] (numeric) = -0.25958618217809587 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 3.63536133939493240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18043644006988438 " "
Order of pole (three term test) = 22.9663075070111 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (analytic) = -0.27347482372575427 " "
y[1] (numeric) = -0.27347482372575327 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 3.65372105757222570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18972588239407828 " "
Order of pole (three term test) = 22.962605760394084 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (analytic) = -0.287336118018934 " "
y[1] (numeric) = -0.28733611801893305 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 3.28427062159028200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1989394368949588 " "
Order of pole (three term test) = 22.958718977640903 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (analytic) = -0.30116867893975763 " "
y[1] (numeric) = -0.3011686789397569 " "
absolute error = 7.2164496600635180000000000000000E-16 " "
relative error = 2.3961487912582752000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20807341827357195 " "
Order of pole (three term test) = 22.95464871341284 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000007 " "
y[1] (analytic) = -0.3149711232436606 " "
y[1] (numeric) = -0.31497112324365983 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 2.46738846797839360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21712417305915077 " "
Order of pole (three term test) = 22.95039659576132 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000007 " "
y[1] (analytic) = -0.32874207069771433 " "
y[1] (numeric) = -0.32874207069771344 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.7017485708935174000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22608808107045686 " "
Order of pole (three term test) = 22.94596432547669 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000007 " "
y[1] (analytic) = -0.3424801442186489 " "
y[1] (numeric) = -0.3424801442186481 " "
absolute error = 8.3266726846886740000000000000000E-16 " "
relative error = 2.4312862585612240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2349615568638018 " "
Order of pole (three term test) = 22.94135367540799 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000007 " "
y[1] (analytic) = -0.356183970010561 " "
y[1] (numeric) = -0.35618397001056007 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 2.64944424900256550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2437410511671803 " "
Order of pole (three term test) = 22.936566489753755 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0500000000000007 " "
y[1] (analytic) = -0.36985217770229095 " "
y[1] (numeric) = -0.36985217770228995 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 2.70162184354349850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2524230522999296 " "
Order of pole (three term test) = 22.931604683324434 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0600000000000007 " "
y[1] (analytic) = -0.38348340048445967 " "
y[1] (numeric) = -0.3834834004844587 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 2.4608355139732452000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2610040875773546 " "
Order of pole (three term test) = 22.92647024077644 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0700000000000007 " "
y[1] (analytic) = -0.3970762752461485 " "
y[1] (numeric) = -0.3970762752461475 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 2.5163949207069450000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2694807246997565 " "
Order of pole (three term test) = 22.921165215818316 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0800000000000007 " "
y[1] (analytic) = -0.4106294427112085 " "
y[1] (numeric) = -0.4106294427112075 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 2.4333392061839282000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2778495731253069 " "
Order of pole (three term test) = 22.915691730389337 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0900000000000007 " "
y[1] (analytic) = -0.42414154757418737 " "
y[1] (numeric) = -0.4241415475741864 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 2.3558190134341153000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2861072854262187 " "
Order of pole (three term test) = 22.91005197381069 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1000000000000008 " "
y[1] (analytic) = -0.43761123863585893 " "
y[1] (numeric) = -0.437611238635858 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 2.15645643350726970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2942505586276734 " "
Order of pole (three term test) = 22.904248201909795 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1100000000000008 " "
y[1] (analytic) = -0.4510371689383418 " "
y[1] (numeric) = -0.45103716893834084 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 2.09226563999737320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3022761355289654 " "
Order of pole (three term test) = 22.89828273611804 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1200000000000008 " "
y[1] (analytic) = -0.4644179958997938 " "
y[1] (numeric) = -0.4644179958997929 " "
absolute error = 9.436895709313831000000000000000E-16 " "
relative error = 2.03198321181119830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3101808060063405 " "
Order of pole (three term test) = 22.89215796254221 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1300000000000008 " "
y[1] (analytic) = -0.47775238144866966 " "
y[1] (numeric) = -0.47775238144866866 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 2.0914615205743278000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3179614082970019 " "
Order of pole (three term test) = 22.885876331010063 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1400000000000008 " "
y[1] (analytic) = -0.4910389921575262 " "
y[1] (numeric) = -0.4910389921575252 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 2.03487042398069970000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3256148302637735 " "
Order of pole (three term test) = 22.879440354090463 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1500000000000008 " "
y[1] (analytic) = -0.5042764993763649 " "
y[1] (numeric) = -0.5042764993763639 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.98145407013482740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3331380106399127 " "
Order of pole (three term test) = 22.872852606088358 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1600000000000008 " "
y[1] (analytic) = -0.5174635793654949 " "
y[1] (numeric) = -0.5174635793654938 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 2.14550949843947130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.34052794025357686 " "
Order of pole (three term test) = 22.86611572201512 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1700000000000008 " "
y[1] (analytic) = -0.5305989134279065 " "
y[1] (numeric) = -0.5305989134279054 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 2.09239596337018250000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3477816632314513 " "
Order of pole (three term test) = 22.85923239653456 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1800000000000008 " "
y[1] (analytic) = -0.5436811880411396 " "
y[1] (numeric) = -0.5436811880411386 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.8378431039019740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.354896278181061 " "
Order of pole (three term test) = 22.852205382885085 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1900000000000008 " "
y[1] (analytic) = -0.5567090949886349 " "
y[1] (numeric) = -0.5567090949886339 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.7948345575044708000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3618689393512848 " "
Order of pole (three term test) = 22.845037491778466 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2000000000000008 " "
y[1] (analytic) = -0.5696813314905538 " "
y[1] (numeric) = -0.5696813314905529 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.5590793845679190000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3686968577706231 " "
Order of pole (three term test) = 22.837731590275578 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2100000000000009 " "
y[1] (analytic) = -0.5825966003340566 " "
y[1] (numeric) = -0.5825966003340557 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.52451699716553480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37537730236274613 " "
Order of pole (three term test) = 22.8302906006396 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2200000000000009 " "
y[1] (analytic) = -0.5954536100030217 " "
y[1] (numeric) = -0.5954536100030207 " "
absolute error = 9.9920072216264090000000000000000E-16 " "
relative error = 1.6780496505136150000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38190760103888766 " "
Order of pole (three term test) = 22.82271749916718 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2300000000000009 " "
y[1] (analytic) = -0.6082510748071961 " "
y[1] (numeric) = -0.608251074807195 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.82527096228654570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38828514176664725 " "
Order of pole (three term test) = 22.815015314997947 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2400000000000009 " "
y[1] (analytic) = -0.6209877150107639 " "
y[1] (numeric) = -0.6209877150107628 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.7878341194010780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.394507373614766 " "
Order of pole (three term test) = 22.807187128902854 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2500000000000009 " "
y[1] (analytic) = -0.6336622569603187 " "
y[1] (numeric) = -0.6336622569603175 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.92728115596783770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4005718077734673 " "
Order of pole (three term test) = 22.79923607205198 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.260000000000001 " "
y[1] (analytic) = -0.6462734332122276 " "
y[1] (numeric) = -0.6462734332122264 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.88967279842776920000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4064760185499457 " "
Order of pole (three term test) = 22.79116532476204 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.270000000000001 " "
y[1] (analytic) = -0.6588199826593746 " "
y[1] (numeric) = -0.6588199826593735 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.68516902013758130000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41221764433861163 " "
Order of pole (three term test) = 22.782978115224353 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.280000000000001 " "
y[1] (analytic) = -0.6713006506572706 " "
y[1] (numeric) = -0.6713006506572694 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.81922261790145840000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4177943885657042 " "
Order of pole (three term test) = 22.77467771821356 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290000000000001 " "
y[1] (analytic) = -0.6837141891495162 " "
y[1] (numeric) = -0.683714189149515 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.7861927490590770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42320402060788803 " "
Order of pole (three term test) = 22.766267453777804 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.300000000000001 " "
y[1] (analytic) = -0.6960593567926067 " "
y[1] (numeric) = -0.6960593567926056 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.59501199688053500000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4284443766844741 " "
Order of pole (three term test) = 22.757750685910725 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.310000000000001 " "
y[1] (analytic) = -0.7083349190800656 " "
y[1] (numeric) = -0.7083349190800644 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.72410719024517070000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43351336072290153 " "
Order of pole (three term test) = 22.749130821205913 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.320000000000001 " "
y[1] (analytic) = -0.7205396484658935 " "
y[1] (numeric) = -0.7205396484658924 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.54082155921459820000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4384089451971412 " "
Order of pole (three term test) = 22.74041130749432 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.330000000000001 " "
y[1] (analytic) = -0.7326723244873226 " "
y[1] (numeric) = -0.7326723244873214 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.51530634844440180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4431291719386764 " "
Order of pole (three term test) = 22.73159563246517 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.340000000000001 " "
y[1] (analytic) = -0.7447317338868611 " "
y[1] (numeric) = -0.74473173388686 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.49076905697403870000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4476721529197464 " "
Order of pole (three term test) = 22.72268732227094 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.350000000000001 " "
y[1] (analytic) = -0.7567166707336187 " "
y[1] (numeric) = -0.7567166707336176 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.4671581419619340000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.452036071008531 " "
Order of pole (three term test) = 22.71368994011691 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.360000000000001 " "
y[1] (analytic) = -0.768625936543898 " "
y[1] (numeric) = -0.7686259365438969 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.44442565862041960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4562191806959794 " "
Order of pole (three term test) = 22.70460708483601 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.370000000000001 " "
y[1] (analytic) = -0.7804583404010424 " "
y[1] (numeric) = -0.7804583404010413 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.42252695262973660000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46021980879399066 " "
Order of pole (three term test) = 22.695442389449223 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.380000000000001 " "
y[1] (analytic) = -0.7922126990745265 " "
y[1] (numeric) = -0.7922126990745254 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.40142038359412080000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4640363551046669 " "
Order of pole (three term test) = 22.68619951971253 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.390000000000001 " "
y[1] (analytic) = -0.8038878371382783 " "
y[1] (numeric) = -0.803887837138277 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.51917378354065520000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4676672930603696 " "
Order of pole (three term test) = 22.676882172650565 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.400000000000001 " "
y[1] (analytic) = -0.8154825870882204 " "
y[1] (numeric) = -0.8154825870882192 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.49757376358982340000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4711111703343293 " "
Order of pole (three term test) = 22.667494075077943 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.410000000000001 " "
y[1] (analytic) = -0.8269957894590203 " "
y[1] (numeric) = -0.8269957894590191 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.476724963601750200000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4743666094215538 " "
Order of pole (three term test) = 22.658038982108526 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.420000000000001 " "
y[1] (analytic) = -0.8384262929400352 " "
y[1] (numeric) = -0.8384262929400339 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.58900983994483630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4774323081898135 " "
Order of pole (three term test) = 22.648520675653412 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.430000000000001 " "
y[1] (analytic) = -0.8497729544904423 " "
y[1] (numeric) = -0.849772954490441 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.56779245857391230000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4803070404004765 " "
Order of pole (three term test) = 22.638942962908295 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.440000000000001 " "
y[1] (analytic) = -0.8610346394535421 " "
y[1] (numeric) = -0.8610346394535409 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 1.4183463372190680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4829896561989876 " "
Order of pole (three term test) = 22.62930967483056 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.450000000000001 " "
y[1] (analytic) = -0.8722102216702231 " "
y[1] (numeric) = -0.8722102216702218 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.52746161011388550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4854790825747956 " "
Order of pole (three term test) = 22.61962466460699 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.460000000000001 " "
y[1] (analytic) = -0.8832985835915765 " "
y[1] (numeric) = -0.8832985835915751 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.63397741015744470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4877743237905416 " "
Order of pole (three term test) = 22.609891806112557 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.470000000000001 " "
y[1] (analytic) = -0.8942986163906504 " "
y[1] (numeric) = -0.894298616390649 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.61387919600922300000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4898744617803424 " "
Order of pole (three term test) = 22.600114992360883 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.480000000000001 " "
y[1] (analytic) = -0.9052092200733316 " "
y[1] (numeric) = -0.9052092200733302 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.59442690154634280000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4917786565170034 " "
Order of pole (three term test) = 22.590298133947112 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.490000000000001 " "
y[1] (analytic) = -0.916029303588344 " "
y[1] (numeric) = -0.9160293035883426 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.57559362605424470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.493486146348019 " "
Order of pole (three term test) = 22.580445157483723 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.500000000000001 " "
y[1] (analytic) = -0.9267577849363527 " "
y[1] (numeric) = -0.9267577849363513 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.55735398771085030000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4949962483002228 " "
Order of pole (three term test) = 22.570560004029932 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5100000000000011 " "
y[1] (analytic) = -0.9373935912781635 " "
y[1] (numeric) = -0.937393591278162 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.53968401900927840000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49630835835296866 " "
Order of pole (three term test) = 22.560646627515315 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5200000000000011 " "
y[1] (analytic) = -0.947935659042005 " "
y[1] (numeric) = -0.9479356590420036 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.5225610707284812000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49742195167972975 " "
Order of pole (three term test) = 22.5507089931583 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5300000000000011 " "
y[1] (analytic) = -0.9583829340298861 " "
y[1] (numeric) = -0.9583829340298847 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.39012036029080900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4983365828580234 " "
Order of pole (three term test) = 22.540751075880134 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5400000000000011 " "
y[1] (analytic) = -0.968734371523014 " "
y[1] (numeric) = -0.9687343715230127 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.3752661913457640000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4990518860475728 " "
Order of pole (three term test) = 22.53077685871495 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5500000000000012 " "
y[1] (analytic) = -0.9789889363862657 " "
y[1] (numeric) = -0.9789889363862643 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.4742658250463060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4995675751366399 " "
Order of pole (three term test) = 22.52079033121665 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5600000000000012 " "
y[1] (analytic) = -0.9891456031717 " "
y[1] (numeric) = -0.9891456031716986 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.34688727855460880000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4998834438564642 " "
Order of pole (three term test) = 22.51079548786305 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5700000000000012 " "
y[1] (analytic) = -0.9992033562211025 " "
y[1] (numeric) = -0.9992033562211011 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.33332981845527900000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49999936586376986 " "
Order of pole (three term test) = 22.500796326458246 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5800000000000012 " "
y[1] (analytic) = -1.0091611897675494 " "
y[1] (numeric) = -1.009161189767548 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.320173271682260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49991529479129915 " "
Order of pole (three term test) = 22.490796846533474 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5900000000000012 " "
y[1] (analytic) = -1.0190181080359846 " "
y[1] (numeric) = -1.0190181080359832 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.30740329248706680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4996312642663604 " "
Order of pole (three term test) = 22.480801047747384 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6000000000000012 " "
y[1] (analytic) = -1.028773125342795 " "
y[1] (numeric) = -1.0287731253427936 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.29500625233213200000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49914738789737645 " "
Order of pole (three term test) = 22.47081292828621 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6100000000000012 " "
y[1] (analytic) = -1.0384252661943794 " "
y[1] (numeric) = -1.0384252661943778 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4967973960913550000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49846385922844333 " "
Order of pole (three term test) = 22.460836483264565 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6200000000000012 " "
y[1] (analytic) = -1.0479735653846955 " "
y[1] (numeric) = -1.0479735653846942 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.27127980471638340000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49758095166191507 " "
Order of pole (three term test) = 22.450875703127444 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6300000000000012 " "
y[1] (analytic) = -1.0574170680917818 " "
y[1] (numeric) = -1.0574170680917805 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2599263523846860000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4964990183490461 " "
Order of pole (three term test) = 22.440934572054083 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6400000000000012 " "
y[1] (analytic) = -1.0667548299732368 " "
y[1] (numeric) = -1.0667548299732355 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2488976774387911000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49521849204873636 " "
Order of pole (three term test) = 22.431017066364383 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6500000000000012 " "
y[1] (analytic) = -1.075985917260654 " "
y[1] (numeric) = -1.0759859172606525 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4445470052548020000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4937398849544322 " "
Order of pole (three term test) = 22.421127152928378 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6600000000000013 " "
y[1] (analytic) = -1.085109406852997 " "
y[1] (numeric) = -1.0851094068529954 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.43240140087163260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4920637884892571 " "
Order of pole (three term test) = 22.411268787579566 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6700000000000013 " "
y[1] (analytic) = -1.0941243864089094 " "
y[1] (numeric) = -1.0941243864089079 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4205992058880249000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4901908730694491 " "
Order of pole (three term test) = 22.401445913532665 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6800000000000013 " "
y[1] (analytic) = -1.1030299544379483 " "
y[1] (numeric) = -1.1030299544379467 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.40912966889210460000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48812188783620475 " "
Order of pole (three term test) = 22.39166245980631 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6900000000000013 " "
y[1] (analytic) = -1.111825220390732 " "
y[1] (numeric) = -1.1118252203907304 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.3979825299600440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48585766035603073 " "
Order of pole (three term test) = 22.381922339651545 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7000000000000013 " "
y[1] (analytic) = -1.1205093047479944 " "
y[1] (numeric) = -1.1205093047479928 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.38714799412110930000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4833990962897302 " "
Order of pole (three term test) = 22.372229448986584 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7100000000000013 " "
y[1] (analytic) = -1.1290813391085368 " "
y[1] (numeric) = -1.1290813391085353 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.376616706554040000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.480747179030149 " "
Order of pole (three term test) = 22.362587664838433 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7200000000000013 " "
y[1] (analytic) = -1.1375404662760662 " "
y[1] (numeric) = -1.1375404662760646 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.36637972938538770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4779029693088327 " "
Order of pole (three term test) = 22.353000843792213 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7300000000000013 " "
y[1] (analytic) = -1.1458858403449153 " "
y[1] (numeric) = -1.1458858403449137 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.35642851997138440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4748676047717476 " "
Order of pole (three term test) = 22.34347282044851 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7400000000000013 " "
y[1] (analytic) = -1.1541166267846317 " "
y[1] (numeric) = -1.15411662678463 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.539148469205560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4716422995242374 " "
Order of pole (three term test) = 22.33400740588963 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7500000000000013 " "
y[1] (analytic) = -1.16223200252343 " "
y[1] (numeric) = -1.1622320025234283 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.5284012447974560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4682283436453977 " "
Order of pole (three term test) = 22.32460838615519 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7600000000000013 " "
y[1] (analytic) = -1.1702311560304997 " "
y[1] (numeric) = -1.1702311560304979 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.51795380788336630000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46462710267206125 " "
Order of pole (three term test) = 22.31527952072776 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7700000000000014 " "
y[1] (analytic) = -1.1781132873971556 " "
y[1] (numeric) = -1.1781132873971538 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.50779798377863480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4608400170526012 " "
Order of pole (three term test) = 22.306024541029135 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7800000000000014 " "
y[1] (analytic) = -1.1858776084168294 " "
y[1] (numeric) = -1.1858776084168279 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.31068520346737770000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45686860157077197 " "
Order of pole (three term test) = 22.29684714892779 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7900000000000014 " "
y[1] (analytic) = -1.1935233426638898 " "
y[1] (numeric) = -1.1935233426638883 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.30228892801213660000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4527144447398143 " "
Order of pole (three term test) = 22.287751015258213 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8000000000000014 " "
y[1] (analytic) = -1.2010497255712833 " "
y[1] (numeric) = -1.2010497255712818 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.29412812923786760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4483792081670731 " "
Order of pole (three term test) = 22.278739778352573 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8100000000000014 " "
y[1] (analytic) = -1.208456004506991 " "
y[1] (numeric) = -1.2084560045069894 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.28619679051479060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44386462588937453 " "
Order of pole (three term test) = 22.269817042585498 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8200000000000014 " "
y[1] (analytic) = -1.2157414388492913 " "
y[1] (numeric) = -1.2157414388492898 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.27848914646389600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4391725036794364 " "
Order of pole (three term test) = 22.260986376932326 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8300000000000014 " "
y[1] (analytic) = -1.2229053000608212 " "
y[1] (numeric) = -1.2229053000608197 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.27099967135469560000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4343047183235817 " "
Order of pole (three term test) = 22.252251313541574 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8400000000000014 " "
y[1] (analytic) = -1.2299468717614295 " "
y[1] (numeric) = -1.229946871761428 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.2637230681755060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4292632168710501 " "
Order of pole (three term test) = 22.243615346322134 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8500000000000014 " "
y[1] (analytic) = -1.2368654497998137 " "
y[1] (numeric) = -1.2368654497998122 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.25665425833245160000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4240500158552034 " "
Order of pole (three term test) = 22.235081929545757 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8600000000000014 " "
y[1] (analytic) = -1.243660342323936 " "
y[1] (numeric) = -1.2436603423239343 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.42832956792760950000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41866720048693934 " "
Order of pole (three term test) = 22.226654476465356 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8700000000000014 " "
y[1] (analytic) = -1.2503308698502058 " "
y[1] (numeric) = -1.2503308698502043 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.24312073864210960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41311692382063525 " "
Order of pole (three term test) = 22.21833635794981 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8800000000000014 " "
y[1] (analytic) = -1.2568763653314297 " "
y[1] (numeric) = -1.256876365331428 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.23664687899939760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40740140589295554 " "
Order of pole (three term test) = 22.210130901135624 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8900000000000015 " "
y[1] (analytic) = -1.2632961742235138 " "
y[1] (numeric) = -1.2632961742235123 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.23036249629314270000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40152293283486457 " "
Order of pole (three term test) = 22.202041388096116 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9000000000000015 " "
y[1] (analytic) = -1.2695896545509189 " "
y[1] (numeric) = -1.2695896545509173 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.22426346883317420000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3954838559572075 " "
Order of pole (three term test) = 22.194071054528642 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9100000000000015 " "
y[1] (analytic) = -1.2757561769708567 " "
y[1] (numeric) = -1.2757561769708552 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.21834584267172680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3892865908102154 " "
Order of pole (three term test) = 22.186223088460356 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9200000000000015 " "
y[1] (analytic) = -1.281795124836224 " "
y[1] (numeric) = -1.2817951248362225 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.21260582472086940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38293361621731775 " "
Order of pole (three term test) = 22.178500628973048 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9300000000000015 " "
y[1] (analytic) = -1.2877058942572668 " "
y[1] (numeric) = -1.2877058942572652 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.20703977624621160000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37642747328364684 " "
Order of pole (three term test) = 22.17090676494755 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9400000000000015 " "
y[1] (analytic) = -1.2934878941619685 " "
y[1] (numeric) = -1.293487894161967 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.2016442067146170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36977076437962836 " "
Order of pole (three term test) = 22.16344453382822 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9500000000000015 " "
y[1] (analytic) = -1.299140546355157 " "
y[1] (numeric) = -1.2991405463551555 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.19641576797519470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36296615210006905 " "
Order of pole (three term test) = 22.156116920408014 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9600000000000015 " "
y[1] (analytic) = -1.3046632855763236 " "
y[1] (numeric) = -1.304663285576322 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.1913512487542831000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.356016358199154 " "
Order of pole (three term test) = 22.148926855634596 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9700000000000015 " "
y[1] (analytic) = -1.3100555595561483 " "
y[1] (numeric) = -1.3100555595561467 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.18644756944646350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3489241625017808 " "
Order of pole (three term test) = 22.141877215438015 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9800000000000015 " "
y[1] (analytic) = -1.3153168290717265 " "
y[1] (numeric) = -1.315316829071725 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.18170177718486380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3416924017916672 " "
Order of pole (three term test) = 22.13497081958035 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9900000000000015 " "
y[1] (analytic) = -1.3204465680004915 " "
y[1] (numeric) = -1.32044656800049 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.17711104117515520000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33432396867667447 " "
Order of pole (three term test) = 22.12821043052786 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0000000000000013 " "
y[1] (analytic) = -1.3254442633728247 " "
y[1] (numeric) = -1.3254442633728234 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.00514798423888440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32682181043180486 " "
Order of pole (three term test) = 22.121598752346035 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.010000000000001 " "
y[1] (analytic) = -1.330309415423354 " "
y[1] (numeric) = -1.3303094154233526 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.00147199899822610000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3191889278203286 " "
Order of pole (three term test) = 22.11513842961799 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.020000000000001 " "
y[1] (analytic) = -1.3350415376409281 " "
y[1] (numeric) = -1.335041537640927 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.31601859060479100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.31142837389352 " "
Order of pole (three term test) = 22.10883204638667 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0300000000000007 " "
y[1] (analytic) = -1.3396401568172693 " "
y[1] (numeric) = -1.3396401568172682 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.28747196756803400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3035432527694767 " "
Order of pole (three term test) = 22.1026821251213 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0400000000000005 " "
y[1] (analytic) = -1.3441048130942916 " "
y[1] (numeric) = -1.3441048130942908 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.60795505713152800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2955367183915154 " "
Order of pole (three term test) = 22.096691125708375 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0500000000000003 " "
y[1] (analytic) = -1.3484350600100883 " "
y[1] (numeric) = -1.3484350600100874 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.58673484575134400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2874119732666343 " "
Order of pole (three term test) = 22.09086144446779 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.06 " "
y[1] (analytic) = -1.3526304645435763 " "
y[1] (numeric) = -1.3526304645435754 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.56630501073201100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2791722671845551 " "
Order of pole (three term test) = 22.085195413194313 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.07 " "
y[1] (analytic) = -1.356690607157798 " "
y[1] (numeric) = -1.356690607157797 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.5466541524955090000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2708208959178492 " "
Order of pole (three term test) = 22.0796952982249 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0799999999999996 " "
y[1] (analytic) = -1.3606150818418756 " "
y[1] (numeric) = -1.360615081841875 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.89582853861463300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2623611999036733 " "
Order of pole (three term test) = 22.07436329953221 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0899999999999994 " "
y[1] (analytic) = -1.3644034961516114 " "
y[1] (numeric) = -1.3644034961516107 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.882234739605751400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.253796562907639 " "
Order of pole (three term test) = 22.06920154984463 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999999 " "
y[1] (analytic) = -1.368055471248731 " "
y[1] (numeric) = -1.3680554712487305 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.24613452585155600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24513041067035074 " "
Order of pole (three term test) = 22.064212113793207 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.109999999999999 " "
y[1] (analytic) = -1.371570641938768 " "
y[1] (numeric) = -1.3715706419387677 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.23781507325299200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2363662095371557 " "
Order of pole (three term test) = 22.05939698708584 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999999988 " "
y[1] (analytic) = -1.3749486567075833 " "
y[1] (numeric) = -1.3749486567075828 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.229860312845916000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22750746507165343 " "
Order of pole (three term test) = 22.05475809570901 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999999986 " "
y[1] (analytic) = -1.3781891777565143 " "
y[1] (numeric) = -1.3781891777565138 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.222265977831675000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21855772065351514 " "
Order of pole (three term test) = 22.050297295157417 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999999983 " "
y[1] (analytic) = -1.3812918810361565 " "
y[1] (numeric) = -1.3812918810361565 " "
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 = 0.2095205560611794 " "
Order of pole (three term test) = 22.0460163696918 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.149999999999998 " "
y[1] (analytic) = -1.3842564562787683 " "
y[1] (numeric) = -1.3842564562787683 " "
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 = 0.20039958603998936 " "
Order of pole (three term test) = 22.041917031625275 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999998 " "
y[1] (analytic) = -1.3870826070292952 " "
y[1] (numeric) = -1.3870826070292952 " "
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 = 0.191198458856342 " "
Order of pole (three term test) = 22.038000920638403 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1699999999999977 " "
y[1] (analytic) = -1.3897700506750175 " "
y[1] (numeric) = -1.3897700506750177 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.597707511520940500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18192085483843157 " "
Order of pole (three term test) = 22.034269603123377 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1799999999999975 " "
y[1] (analytic) = -1.3923185184738103 " "
y[1] (numeric) = -1.3923185184738105 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.594783104432349600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17257048490416377 " "
Order of pole (three term test) = 22.030724571557446 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1899999999999973 " "
y[1] (analytic) = -1.3947277555810174 " "
y[1] (numeric) = -1.3947277555810174 " "
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 = 0.16315108907684436 " "
Order of pole (three term test) = 22.027367243905967 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999997 " "
y[1] (analytic) = -1.3969975210749352 " "
y[1] (numeric) = -1.3969975210749355 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.589441653083082400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15366643498921218 " "
Order of pole (three term test) = 22.02419896305524 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.209999999999997 " "
y[1] (analytic) = -1.3991275879809066 " "
y[1] (numeric) = -1.3991275879809069 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.587021847274599200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14412031637644368 " "
Order of pole (three term test) = 22.02122099627536 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999999966 " "
y[1] (analytic) = -1.4011177432940154 " "
y[1] (numeric) = -1.4011177432940158 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.16953526550889900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1345165515587028 " "
Order of pole (three term test) = 22.018434534713343 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999999964 " "
y[1] (analytic) = -1.4029677880003892 " "
y[1] (numeric) = -1.4029677880003897 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.165355709862809000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.124858981913869 " "
Order of pole (three term test) = 22.015840692916647 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.239999999999996 " "
y[1] (analytic) = -1.4046775370970992 " "
y[1] (numeric) = -1.4046775370970994 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.5807514469399700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1151514703410334 " "
Order of pole (three term test) = 22.013440508387415 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999996 " "
y[1] (analytic) = -1.4062468196106597 " "
y[1] (numeric) = -1.4062468196106601 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.157974856597473600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1053978997153938 " "
Order of pole (three term test) = 22.01123494116745 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999996 " "
y[1] (analytic) = -1.4076754786141277 " "
y[1] (numeric) = -1.4076754786141283 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.73215471104824650000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.56021713351550800E-2 " "
Order of pole (three term test) = 22.00922487345424 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2699999999999956 " "
y[1] (analytic) = -1.4089633712427934 " "
y[1] (numeric) = -1.408963371242794 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.7278291854210697000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.57682033610603400E-2 " "
Order of pole (three term test) = 22.00741110924807 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2799999999999954 " "
y[1] (analytic) = -1.410110368708467 " "
y[1] (numeric) = -1.4101103687084677 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.72398352325578640000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.58999292491822200E-2 " "
Order of pole (three term test) = 22.005794374030433 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999995 " "
y[1] (analytic) = -1.411116356312358 " "
y[1] (numeric) = -1.4111163563123585 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.147077190789510000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.60012961775897500E-2 " "
Order of pole (three term test) = 22.00437531447386 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999995 " "
y[1] (analytic) = -1.411981233456544 " "
y[1] (numeric) = -1.4119812334565445 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.145149519890770000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.60762634675322400E-2 " "
Order of pole (three term test) = 22.00315449818326 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999999947 " "
y[1] (analytic) = -1.4127049136540315 " "
y[1] (numeric) = -1.412704913654032 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.14353836783510400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.61288009997609770E-2 " "
Order of pole (three term test) = 22.00213241346888 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999999945 " "
y[1] (analytic) = -1.4132873245374036 " "
y[1] (numeric) = -1.4132873245374042 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.71336438960232300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.61628876266323400E-2 " "
Order of pole (three term test) = 22.00130946915095 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999999943 " "
y[1] (analytic) = -1.4137284078660577 " "
y[1] (numeric) = -1.4137284078660584 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.71189381969472400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.618250958061879000E-2 " "
Order of pole (three term test) = 22.00068599439625 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.339999999999994 " "
y[1] (analytic) = -1.4140281195320281 " "
y[1] (numeric) = -1.4140281195320288 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.71089510578863600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.619165887986818200E-2 " "
Order of pole (three term test) = 22.000262238586355 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999994 " "
y[1] (analytic) = -1.4141864295643982 " "
y[1] (numeric) = -1.4141864295643989 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.71036774819200030000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.1943317314515890000E-3 " "
Order of pole (three term test) = 22.00003837121795 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3599999999999937 " "
y[1] (analytic) = -1.4142033221322967 " "
y[1] (numeric) = -1.4142033221322974 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.71031148315162900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.8054730670677510000E-3 " "
Order of pole (three term test) = 22.000014481834988 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3699999999999934 " "
y[1] (analytic) = -1.4140787955464809 " "
y[1] (numeric) = -1.4140787955464815 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.710726282531248500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.380375572709931500E-2 " "
Order of pole (three term test) = 22.00019057999291 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3799999999999932 " "
y[1] (analytic) = -1.4138128622595052 " "
y[1] (numeric) = -1.413812862259506 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.28214980503622100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.379651706888721600E-2 " "
Order of pole (three term test) = 22.000566595254796 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999993 " "
y[1] (analytic) = -1.4134055488644774 " "
y[1] (numeric) = -1.4134055488644781 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.712970140171462400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.377976012113040000E-2 " "
Order of pole (three term test) = 22.00114237721955 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999993 " "
y[1] (analytic) = -1.4128568960923968 " "
y[1] (numeric) = -1.4128568960923977 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.28640042849775600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.374949171971618000E-2 " "
Order of pole (three term test) = 22.001917695582073 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999999926 " "
y[1] (analytic) = -1.412166958808084 " "
y[1] (numeric) = -1.412166958808085 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.28947175233286400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.37017241049328400E-2 " "
Order of pole (three term test) = 22.002892240225364 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999999924 " "
y[1] (analytic) = -1.4113358060046923 " "
y[1] (numeric) = -1.4113358060046932 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.29317569866269100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.36324765165203500E-2 " "
Order of pole (three term test) = 22.00406562134454 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.429999999999992 " "
y[1] (analytic) = -1.4103635207968095 " "
y[1] (numeric) = -1.4103635207968102 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.72313559555730700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.35377767859237300E-2 " "
Order of pole (three term test) = 22.005437369602816 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.439999999999992 " "
y[1] (analytic) = -1.4092502004121457 " "
y[1] (numeric) = -1.4092502004121465 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.30248922044056400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.34136629251034500E-2 " "
Order of pole (three term test) = 22.00700693631916 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999999917 " "
y[1] (analytic) = -1.407995956181812 " "
y[1] (numeric) = -1.407995956181813 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.30810348425060600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.32561847112793400E-2 " "
Order of pole (three term test) = 22.008773693687832 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4599999999999915 " "
y[1] (analytic) = -1.4066009135291866 " "
y[1] (numeric) = -1.4066009135291873 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.73576981479240200000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10306140526697116 " "
Order of pole (three term test) = 22.010736935029428 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4699999999999913 " "
y[1] (analytic) = -1.4050652119573714 " "
y[1] (numeric) = -1.405065211957372 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.7409458942273197000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11282540263468936 " "
Order of pole (three term test) = 22.012895875073593 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999991 " "
y[1] (analytic) = -1.4033890050352444 " "
y[1] (numeric) = -1.403389005035245 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.74660847694445800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.12254427134567225 " "
Order of pole (three term test) = 22.015249650273088 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999991 " "
y[1] (analytic) = -1.4015724603821007 " "
y[1] (numeric) = -1.4015724603821014 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.752760443034751400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13221412398201882 " "
Order of pole (three term test) = 22.01779731914923 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999999907 " "
y[1] (analytic) = -1.3996157596508922 " "
y[1] (numeric) = -1.3996157596508927 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.1729366205538600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14183109273160427 " "
Order of pole (three term test) = 22.02053786266843 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999999905 " "
y[1] (analytic) = -1.397519098510061 " "
y[1] (numeric) = -1.3975190985100614 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.17769689389948300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15139133093515283 " "
Order of pole (three term test) = 22.02347018464981 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999999902 " "
y[1] (analytic) = -1.395282686623974 " "
y[1] (numeric) = -1.3952826866239745 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.182790226721588500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16089101462485178 " "
Order of pole (three term test) = 22.026593112203695 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.52999999999999 " "
y[1] (analytic) = -1.3929067476319568 " "
y[1] (numeric) = -1.392906747631957 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.59410962221644300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17032634405388575 " "
Order of pole (three term test) = 22.029905396200682 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.53999999999999 " "
y[1] (analytic) = -1.3903915191259277 " "
y[1] (numeric) = -1.390391519125928 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.596993378272474300000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17969354521628506 " "
Order of pole (three term test) = 22.03340571177135 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999999896 " "
y[1] (analytic) = -1.3877372526266418 " "
y[1] (numeric) = -1.387737252626642 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.60004788013549420000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18898887135648068 " "
Order of pole (three term test) = 22.037092658836126 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5599999999999894 " "
y[1] (analytic) = -1.3849442135585375 " "
y[1] (numeric) = -1.3849442135585375 " "
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 = 0.19820860446795124 " "
Order of pole (three term test) = 22.040964762665357 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999989 " "
y[1] (analytic) = -1.3820126812231932 " "
y[1] (numeric) = -1.3820126812231932 " "
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 = 0.20734905678038096 " "
Order of pole (three term test) = 22.04502047446914 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999989 " "
y[1] (analytic) = -1.3789429487714 " "
y[1] (numeric) = -1.3789429487714002 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.61025229595515100000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21640657223471618 " "
Order of pole (three term test) = 22.049258172016817 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999999888 " "
y[1] (analytic) = -1.3757353231738452 " "
y[1] (numeric) = -1.3757353231738454 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.61400671469836600000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22537752794553942 " "
Order of pole (three term test) = 22.053676160285878 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999999885 " "
y[1] (analytic) = -1.3723901251904154 " "
y[1] (numeric) = -1.3723901251904154 " "
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 = 0.2342583356501782 " "
Order of pole (three term test) = 22.058272672139914 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999999883 " "
y[1] (analytic) = -1.368907689338121 " "
y[1] (numeric) = -1.368907689338121 " "
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 = 0.24304544314395984 " "
Order of pole (three term test) = 22.06304586903548 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.619999999999988 " "
y[1] (analytic) = -1.3652883638576454 " "
y[1] (numeric) = -1.3652883638576452 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.62635682543752520000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2517353357010468 " "
Order of pole (three term test) = 22.06799384175746 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.629999999999988 " "
y[1] (analytic) = -1.3615325106785205 " "
y[1] (numeric) = -1.3615325106785203 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.630843209277281800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2603245374802794 " "
Order of pole (three term test) = 22.07311461118272 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999999877 " "
y[1] (analytic) = -1.3576405053829346 " "
y[1] (numeric) = -1.3576405053829341 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.27103683257301800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.26880961291546757 " "
Order of pole (three term test) = 22.078406129071784 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999999875 " "
y[1] (analytic) = -1.3536127371681737 " "
y[1] (numeric) = -1.353612737168173 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.92115504297543400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2771871680895701 " "
Order of pole (three term test) = 22.083866278888042 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6599999999999873 " "
y[1] (analytic) = -1.3494496088077026 " "
y[1] (numeric) = -1.349449608807702 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.93633708459593400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28545385209221597 " "
Order of pole (three term test) = 22.08949287664437 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999987 " "
y[1] (analytic) = -1.3451515366108886 " "
y[1] (numeric) = -1.3451515366108877 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.60281310712317400000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29360635836002613 " "
Order of pole (three term test) = 22.09528367177668 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999987 " "
y[1] (analytic) = -1.3407189503813692 " "
y[1] (numeric) = -1.3407189503813683 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.62464284142087800000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3016414259991914 " "
Order of pole (three term test) = 22.10123634804414 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999999866 " "
y[1] (analytic) = -1.3361522933740737 " "
y[1] (numeric) = -1.3361522933740728 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.64728432607994500000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.30955584108978873 " "
Order of pole (three term test) = 22.1073485244556 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999999864 " "
y[1] (analytic) = -1.3314520222508976 " "
y[1] (numeric) = -1.3314520222508965 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.33843808166860900000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3173464379713065 " "
Order of pole (three term test) = 22.11361775622199 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.709999999999986 " "
y[1] (analytic) = -1.3266186070350359 " "
y[1] (numeric) = -1.3266186070350348 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.36881842857972000000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.32501010050886564 " "
Order of pole (three term test) = 22.120041535734213 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.719999999999986 " "
y[1] (analytic) = -1.3216525310639824 " "
y[1] (numeric) = -1.3216525310639813 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.40026405224210700000000000000E-14 "%"
Correct digits = 17
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33254376333963087 " "
Order of pole (three term test) = 22.12661729356609 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999999858 " "
y[1] (analytic) = -1.3165542909411962 " "
y[1] (numeric) = -1.316554290941195 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.01193519987524280000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3399444130989183 " "
Order of pole (three term test) = 22.133342399502162 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999999856 " "
y[1] (analytic) = -1.3113243964864407 " "
y[1] (numeric) = -1.3113243964864394 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.01597105424093570000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3472090896254974 " "
Order of pole (three term test) = 22.140214163589732 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999999853 " "
y[1] (analytic) = -1.305963370684803 " "
y[1] (numeric) = -1.3059633706848017 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.02014165133252680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.35433488714561967 " "
Order of pole (three term test) = 22.147229837214798 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999985 " "
y[1] (analytic) = -1.3004717496343965 " "
y[1] (numeric) = -1.300471749634395 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.19519107963105330000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3613189554352858 " "
Order of pole (three term test) = 22.15438661420142 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999985 " "
y[1] (analytic) = -1.2948500824927491 " "
y[1] (numeric) = -1.2948500824927474 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.37186293874310170000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36815850096029945 " "
Order of pole (three term test) = 22.16168163193426 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7799999999999847 " "
y[1] (analytic) = -1.2890989314218906 " "
y[1] (numeric) = -1.2890989314218888 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.3779833309154238000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3748507879936435 " "
Order of pole (three term test) = 22.16911197250347 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999999845 " "
y[1] (analytic) = -1.2832188715321355 " "
y[1] (numeric) = -1.2832188715321335 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.55733483091565960000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38139313970973426 " "
Order of pole (three term test) = 22.176674663871896 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999999843 " "
y[1] (analytic) = -1.2772104908245725 " "
y[1] (numeric) = -1.2772104908245705 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.5646610004237480000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3877829392551148 " "
Order of pole (three term test) = 22.18436668106382 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.809999999999984 " "
y[1] (analytic) = -1.2710743901322659 " "
y[1] (numeric) = -1.2710743901322636 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.74690487550398760000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3940176307951639 " "
Order of pole (three term test) = 22.192184947374948 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.819999999999984 " "
y[1] (analytic) = -1.264811183060171 " "
y[1] (numeric) = -1.2648111830601687 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.75555535797684350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40009472053639344 " "
Order of pole (three term test) = 22.20012633560297 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999999836 " "
y[1] (analytic) = -1.2584214959237758 " "
y[1] (numeric) = -1.2584214959237734 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.94091618912022260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4060117777239332 " "
Order of pole (three term test) = 22.208187669298482 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999999834 " "
y[1] (analytic) = -1.2519059676864697 " "
y[1] (numeric) = -1.2519059676864668 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.30574814605271430000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4117664356138017 " "
Order of pole (three term test) = 22.216365724035505 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999983 " "
y[1] (analytic) = -1.245265249895646 " "
y[1] (numeric) = -1.2452652498956431 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.3180441791556491000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4173563924195706 " "
Order of pole (three term test) = 22.224657228701165 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999983 " "
y[1] (analytic) = -1.2385000066175507 " "
y[1] (numeric) = -1.2385000066175476 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.50999148352074500000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4227794122330496 " "
Order of pole (three term test) = 22.233058866804168 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999983 " "
y[1] (analytic) = -1.2316109143708731 " "
y[1] (numeric) = -1.23161091437087 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.5240312769868350000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42803332591861865 " "
Order of pole (three term test) = 22.24156727780127 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8799999999999826 " "
y[1] (analytic) = -1.2245986620590978 " "
y[1] (numeric) = -1.2245986620590945 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.71980459971687850000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4331160319808556 " "
Order of pole (three term test) = 22.25017905844154 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999999824 " "
y[1] (analytic) = -1.217463950901612 " "
y[1] (numeric) = -1.2174639509016085 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.9181263857295180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4380254974051033 " "
Order of pole (three term test) = 22.258890764127518 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.899999999999982 " "
y[1] (analytic) = -1.2102074943635859 " "
y[1] (numeric) = -1.2102074943635823 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.93562359789283360000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4427597584706513 " "
Order of pole (three term test) = 22.267698910293106 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.909999999999982 " "
y[1] (analytic) = -1.2028300180846263 " "
y[1] (numeric) = -1.2028300180846225 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.13823086136178800000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44731692153619557 " "
Order of pole (three term test) = 22.27659997379727 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999999817 " "
y[1] (analytic) = -1.1953322598062133 " "
y[1] (numeric) = -1.1953322598062093 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.3436752466619807000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4516951637972714 " "
Order of pole (three term test) = 22.28559039433328 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999999815 " "
y[1] (analytic) = -1.1877149692979265 " "
y[1] (numeric) = -1.1877149692979223 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.552070658896730000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4558927340153506 " "
Order of pole (three term test) = 22.294666575852812 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999999813 " "
y[1] (analytic) = -1.1799789082824694 " "
y[1] (numeric) = -1.1799789082824648 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.9517119083194830000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45990795321831224 " "
Order of pole (three term test) = 22.303824888004254 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999981 " "
y[1] (analytic) = -1.1721248503594963 " "
y[1] (numeric) = -1.1721248503594914 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.1676288211553930000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4637392153720109 " "
Order of pole (three term test) = 22.313061667584865 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999981 " "
y[1] (analytic) = -1.1641535809282546 " "
y[1] (numeric) = -1.1641535809282497 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.1961656849911320000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4673849880226676 " "
Order of pole (three term test) = 22.322373220005954 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9699999999999807 " "
y[1] (analytic) = -1.1560658971090452 " "
y[1] (numeric) = -1.1560658971090398 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.6096598226165747000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4708438129098323 " "
Order of pole (three term test) = 22.33175582077073 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9799999999999804 " "
y[1] (analytic) = -1.1478626076635094 " "
y[1] (numeric) = -1.1478626076635041 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.6426031152353240000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4741143065496668 " "
Order of pole (three term test) = 22.341205716963962 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999999802 " "
y[1] (analytic) = -1.1395445329137566 " "
y[1] (numeric) = -1.139544532913751 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.8713454918096690000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.477195160788321 " "
Order of pole (three term test) = 22.350719128753187 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.99999999999998 " "
y[1] (analytic) = -1.1311125046603296 " "
y[1] (numeric) = -1.1311125046603239 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.1039659664840140000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4800851433251774 " "
Order of pole (three term test) = 22.360292250900518 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00999999999998 " "
y[1] (analytic) = -1.1225673660990272 " "
y[1] (numeric) = -1.1225673660990214 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.1428180636613440000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4827830982057535 " "
Order of pole (three term test) = 22.36992125428474 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999999796 " "
y[1] (analytic) = -1.1139099717365846 " "
y[1] (numeric) = -1.1139099717365786 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.3821264600309910000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48528794628406974 " "
Order of pole (three term test) = 22.3796022874329 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999999794 " "
y[1] (analytic) = -1.1051411873052235 " "
y[1] (numeric) = -1.1051411873052173 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.6257508174688690000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4875986856542918 " "
Order of pole (three term test) = 22.3893314780608 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999979 " "
y[1] (analytic) = -1.09626188967608 " "
y[1] (numeric) = -1.0962618896760734 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.0764113123728210000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4897143920514813 " "
Order of pole (three term test) = 22.399104934621917 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999979 " "
y[1] (analytic) = -1.0872729667715173 " "
y[1] (numeric) = -1.0872729667715104 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.3308690301710260000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4916342192212884 " "
Order of pole (three term test) = 22.40891874786393 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0599999999999787 " "
y[1] (analytic) = -1.078175317476335 " "
y[1] (numeric) = -1.0781753174763282 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 6.3842889380808470000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4933573992584427 " "
Order of pole (three term test) = 22.418768992392405 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0699999999999785 " "
y[1] (analytic) = -1.0689698515478818 " "
y[1] (numeric) = -1.0689698515478747 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.6469857380095930000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4948832429139044 " "
Order of pole (three term test) = 22.42865172824085 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0799999999999783 " "
y[1] (analytic) = -1.0596574895250792 " "
y[1] (numeric) = -1.0596574895250717 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.1244875274128740000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49621113987055565 " "
Order of pole (three term test) = 22.4385630024467 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.089999999999978 " "
y[1] (analytic) = -1.0502391626363687 " "
y[1] (numeric) = -1.0502391626363612 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.1883784532466380000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49734055898731927 " "
Order of pole (three term test) = 22.44849885063243 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.099999999999978 " "
y[1] (analytic) = -1.0407158127065912 " "
y[1] (numeric) = -1.0407158127065834 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.4675152212442940000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49827104851160686 " "
Order of pole (three term test) = 22.458455298591225 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999999777 " "
y[1] (analytic) = -1.0310883920628033 " "
y[1] (numeric) = -1.0310883920627953 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.7525902132493780000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49900223626001544 " "
Order of pole (three term test) = 22.468428363876676 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999999775 " "
y[1] (analytic) = -1.0213578634390466 " "
y[1] (numeric) = -1.0213578634390383 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 8.0438509129042980000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49953382976719407 " "
Order of pole (three term test) = 22.478414057395607 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999999772 " "
y[1] (analytic) = -1.0115251998800745 " "
y[1] (numeric) = -1.011525199880066 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3415568768346600000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4998656164028284 " "
Order of pole (three term test) = 22.488408385003787 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999977 " "
y[1] (analytic) = -1.0015913846440494 " "
y[1] (numeric) = -1.0015913846440407 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.6459805114575370000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4999974634566875 " "
Order of pole (three term test) = 22.49840734910341 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999977 " "
y[1] (analytic) = -0.9915574111042167 " "
y[1] (numeric) = -0.9915574111042077 " "
absolute error = 8.992806499463768000000000000000E-15 " "
relative error = 9.0693755084228680000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.499929318191708 " "
Order of pole (three term test) = 22.508406950242154 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1599999999999766 " "
y[1] (analytic) = -0.9814242826495685 " "
y[1] (numeric) = -0.9814242826495594 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 9.2761397520637220000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49966120786508705 " "
Order of pole (three term test) = 22.51840318871289 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1699999999999764 " "
y[1] (analytic) = -0.9711930125845062 " "
y[1] (numeric) = -0.971193012584497 " "
absolute error = 9.2148511043887990000000000000E-15 " "
relative error = 9.4881768968524060000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4991932397173808 " "
Order of pole (three term test) = 22.52839206615352 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999976 " "
y[1] (analytic) = -0.9608646240275104 " "
y[1] (numeric) = -0.9608646240275008 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.9367983512139180000000000000E-13 "%"
Correct digits = 16
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4985256009296087 " "
Order of pole (three term test) = 22.53836958714624 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.189999999999976 " "
y[1] (analytic) = -0.9504401498088296 " "
y[1] (numeric) = -0.9504401498088199 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 1.0279408565248949000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4976585585483842 " "
Order of pole (three term test) = 22.548331760815692 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999999758 " "
y[1] (analytic) = -0.9399206323671987 " "
y[1] (numeric) = -0.9399206323671888 " "
absolute error = 9.880984919163893000000000000000E-15 " "
relative error = 1.0512573699205371000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4965924593790992 " "
Order of pole (three term test) = 22.55827460242522 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999999755 " "
y[1] (analytic) = -0.9293071236455959 " "
y[1] (numeric) = -0.9293071236455857 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 1.099104006271097000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49532772984720713 " "
Order of pole (three term test) = 22.56819413497077 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999999753 " "
y[1] (analytic) = -0.9186006849860484 " "
y[1] (numeric) = -0.918600684986038 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 1.1360862888573803000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49386487582765787 " "
Order of pole (three term test) = 22.57808639077158 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.229999999999975 " "
y[1] (analytic) = -0.9078023870235002 " "
y[1] (numeric) = -0.9078023870234897 " "
absolute error = 1.054711873393898700000000000000E-14 " "
relative error = 1.161829808414676000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49220448244255477 " "
Order of pole (three term test) = 22.587947413057215 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999975 " "
y[1] (analytic) = -0.8969133095787494 " "
y[1] (numeric) = -0.8969133095787385 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.213069928289569000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4903472138271136 " "
Order of pole (three term test) = 22.59777325755024 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2499999999999747 " "
y[1] (analytic) = -0.8859345415504657 " "
y[1] (numeric) = -0.8859345415504547 " "
absolute error = 1.09912079437890500000000000000E-14 " "
relative error = 1.240634316453384900000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48829381286401713 " "
Order of pole (three term test) = 22.607559994043882 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2599999999999745 " "
y[1] (analytic) = -0.8748671808063035 " "
y[1] (numeric) = -0.8748671808062922 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.2943993213621077000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4860451008862726 " "
Order of pole (three term test) = 22.617303707974017 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2699999999999743 " "
y[1] (analytic) = -0.8637123340731141 " "
y[1] (numeric) = -0.8637123340731027 " "
absolute error = 1.143529715363911200000000000000E-14 " "
relative error = 1.3239705747528555000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4836019773486885 " "
Order of pole (three term test) = 22.627000501984988 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999974 " "
y[1] (analytic) = -0.8524711168262754 " "
y[1] (numeric) = -0.8524711168262636 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.3805000343988108000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4809654194681054 " "
Order of pole (three term test) = 22.63664649748848 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.289999999999974 " "
y[1] (analytic) = -0.8411446531781441 " "
y[1] (numeric) = -0.8411446531781323 " "
absolute error = 1.187938636348917500000000000000E-14 " "
relative error = 1.412288162161481000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4781364818325217 " "
Order of pole (three term test) = 22.646237836214915 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999999736 " "
y[1] (analytic) = -0.8297340757656467 " "
y[1] (numeric) = -0.8297340757656345 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.4718514795969467000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47511629597927296 " "
Order of pole (three term test) = 22.655770681756664 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999999734 " "
y[1] (analytic) = -0.8182405256370154 " "
y[1] (numeric) = -0.818240525637003 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.5196629213789264000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.471906069942432 " "
Order of pole (three term test) = 22.665241221102626 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.319999999999973 " "
y[1] (analytic) = -0.8066651521376853 " "
y[1] (numeric) = -0.8066651521376726 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.5689958153251807000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46850708776961125 " "
Order of pole (three term test) = 22.67464566616334 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.329999999999973 " "
y[1] (analytic) = -0.7950091127953601 " "
y[1] (numeric) = -0.7950091127953473 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.6199294924266908000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46492070900836063 " "
Order of pole (three term test) = 22.683980255286162 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999999728 " "
y[1] (analytic) = -0.7832735732042608 " "
y[1] (numeric) = -0.7832735732042477 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.6725486648277976000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4611483681623668 " "
Order of pole (three term test) = 22.693241254759915 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3499999999999726 " "
y[1] (analytic) = -0.7714597069085669 " "
y[1] (numeric) = -0.7714597069085536 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.7269438930114955000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45719157411767086 " "
Order of pole (three term test) = 22.702424960308267 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3599999999999723 " "
y[1] (analytic) = -0.7595686952850631 " "
y[1] (numeric) = -0.7595686952850494 " "
absolute error = 1.365574320288942500000000000000E-14 " "
relative error = 1.7978285950508371000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4530519095391342 " "
Order of pole (three term test) = 22.711527698571473 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999972 " "
y[1] (analytic) = -0.7476017274250025 " "
y[1] (numeric) = -0.7476017274249886 " "
absolute error = 1.387778780781445700000000000000E-14 " "
relative error = 1.856307616572038800000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4487310302373935 " "
Order of pole (three term test) = 22.720545828575574 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.379999999999972 " "
y[1] (analytic) = -0.7355600000151988 " "
y[1] (numeric) = -0.7355600000151847 " "
absolute error = 1.409983241273948800000000000000E-14 " "
relative error = 1.9168840628158332000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4442306645065587 " "
Order of pole (three term test) = 22.72947574318882 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999999717 " "
y[1] (analytic) = -0.7234447172183583 " "
y[1] (numeric) = -0.7234447172183439 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.995024495530421000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43955261243291766 " "
Order of pole (three term test) = 22.738313870564426 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999999715 " "
y[1] (analytic) = -0.7112570905526645 " "
y[1] (numeric) = -0.7112570905526499 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 2.0604285172981276000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4346987451749267 " "
Order of pole (three term test) = 22.747056675569276 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999999713 " "
y[1] (analytic) = -0.6989983387706278 " "
y[1] (numeric) = -0.6989983387706128 " "
absolute error = 1.498801083243961300000000000000E-14 " "
relative error = 2.144212654181692200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42967100421477206 " "
Order of pole (three term test) = 22.755700661197956 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.419999999999971 " "
y[1] (analytic) = -0.6866696877372105 " "
y[1] (numeric) = -0.6866696877371954 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 2.1988786463922885000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.42447140058180144 " "
Order of pole (three term test) = 22.764242369971438 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.429999999999971 " "
y[1] (analytic) = -0.6742723703072424 " "
y[1] (numeric) = -0.6742723703072271 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 2.272238699747682000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4191020140481414 " "
Order of pole (three term test) = 22.772678385320123 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999999706 " "
y[1] (analytic) = -0.6618076262021355 " "
y[1] (numeric) = -0.6618076262021197 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 2.382137395446404200000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4135649922968147 " "
Order of pole (three term test) = 22.781005332950347 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4499999999999704 " "
y[1] (analytic) = -0.6492767018859127 " "
y[1] (numeric) = -0.6492767018858968 " "
absolute error = 1.58761892521397390000000000000E-14 " "
relative error = 2.445211603315687300000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.40786255006269573 " "
Order of pole (three term test) = 22.789219882194075 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999997 " "
y[1] (analytic) = -0.6366808504405634 " "
y[1] (numeric) = -0.6366808504405473 " "
absolute error = 1.60982338570647700000000000000E-14 " "
relative error = 2.5284620773383226000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4019969682466464 " "
Order of pole (three term test) = 22.79731874734114 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.46999999999997 " "
y[1] (analytic) = -0.6240213314407359 " "
y[1] (numeric) = -0.6240213314407195 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 2.633131262759215000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3959705930031864 " "
Order of pole (three term test) = 22.805298688953467 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.47999999999997 " "
y[1] (analytic) = -0.6112994108277803 " "
y[1] (numeric) = -0.6112994108277635 " "
absolute error = 1.676436767183986400000000000000E-14 " "
relative error = 2.742415152852624700000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3897858348020627 " "
Order of pole (three term test) = 22.81315651516081 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999999696 " "
y[1] (analytic) = -0.5985163607831563 " "
y[1] (numeric) = -0.5985163607831393 " "
absolute error = 1.698641227676489500000000000000E-14 " "
relative error = 2.838086540280743700000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3834451674640933 " "
Order of pole (three term test) = 22.82088908293744 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999999694 " "
y[1] (analytic) = -0.585673459601216 " "
y[1] (numeric) = -0.5856734596011988 " "
absolute error = 1.720845688168992600000000000000E-14 " "
relative error = 2.9382340277818175000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3769511271716723 " "
Order of pole (three term test) = 22.828493299359362 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.509999999999969 " "
y[1] (analytic) = -0.5727719915613751 " "
y[1] (numeric) = -0.5727719915613576 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 3.0625666142053000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.37030631145433074 " "
Order of pole (three term test) = 22.83596612284141 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.519999999999969 " "
y[1] (analytic) = -0.5598132467996866 " "
y[1] (numeric) = -0.5598132467996687 " "
absolute error = 1.78745906964650200000000000000E-14 " "
relative error = 3.1929560078561237000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36351337814975926 " "
Order of pole (three term test) = 22.843304564353794 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999999687 " "
y[1] (analytic) = -0.5467985211798274 " "
y[1] (numeric) = -0.5467985211798094 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 3.2892577983056670000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3565750443407084 " "
Order of pole (three term test) = 22.850505688617783 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999999685 " "
y[1] (analytic) = -0.5337291161635144 " "
y[1] (numeric) = -0.533729116163496 " "
absolute error = 1.831867990631508300000000000000E-14 " "
relative error = 3.4322054674459496000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3494940852681913 " "
Order of pole (three term test) = 22.857566615279655 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5499999999999683 " "
y[1] (analytic) = -0.5206063386803577 " "
y[1] (numeric) = -0.5206063386803391 " "
absolute error = 1.854072451124011400000000000000E-14 " "
relative error = 3.5613712576449750000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.34227333322142645 " "
Order of pole (three term test) = 22.86448452006292 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999968 " "
y[1] (analytic) = -0.5074315009971702 " "
y[1] (numeric) = -0.5074315009971513 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 3.719475708847038000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3349156764049561 " "
Order of pole (three term test) = 22.871256635897883 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999968 " "
y[1] (analytic) = -0.49420592058674107 " "
y[1] (numeric) = -0.4942059205867219 " "
absolute error = 1.91513471747839500000000000000E-14 " "
relative error = 3.875175585117779400000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.327424057783407 " "
Order of pole (three term test) = 22.877880254028508 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999999677 " "
y[1] (analytic) = -0.48093091999609017 " "
y[1] (numeric) = -0.48093091999607074 " "
absolute error = 1.94289029309402400000000000000E-14 " "
relative error = 4.039853152111365600000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.31980147390434027 " "
Order of pole (three term test) = 22.88435272509586 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999999674 " "
y[1] (analytic) = -0.4676078267142141 " "
y[1] (numeric) = -0.46760782671419443 " "
absolute error = 1.96509475358652700000000000000E-14 " "
relative error = 4.2024419638029836000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3120509736996746 " "
Order of pole (three term test) = 22.8906714601978 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999999672 " "
y[1] (analytic) = -0.45423797303933855 " "
y[1] (numeric) = -0.45423797303931857 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 4.399459232687738000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3041756572661535 " "
Order of pole (three term test) = 22.896833931924554 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.609999999999967 " "
y[1] (analytic) = -0.44082269594568935 " "
y[1] (numeric) = -0.44082269594566914 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 4.583715682975474000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.29617867462534686 " "
Order of pole (three term test) = 22.90283767536959 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.619999999999967 " "
y[1] (analytic) = -0.42736333694979667 " "
y[1] (numeric) = -0.4273633369497762 " "
absolute error = 2.048361480433413800000000000000E-14 " "
relative error = 4.7930210744166846000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28806322446368676 " "
Order of pole (three term test) = 22.90868028911557 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999999666 " "
y[1] (analytic) = -0.41386124197634394 " "
y[1] (numeric) = -0.4138612419763232 " "
absolute error = 2.076117056049042700000000000000E-14 " "
relative error = 5.016456834988459000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2798325528530325 " "
Order of pole (three term test) = 22.9143594361949 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999999664 " "
y[1] (analytic) = -0.4003177612235769 " "
y[1] (numeric) = -0.4003177612235558 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 5.269373360653082000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.27148995195228887 " "
Order of pole (three term test) = 22.919872845024475 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999966 " "
y[1] (analytic) = -0.38673424902828446 " "
y[1] (numeric) = -0.38673424902826303 " "
absolute error = 2.14273043752655200000000000000E-14 " "
relative error = 5.5405758422234800000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2630387586905815 " "
Order of pole (three term test) = 22.925218310314264 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999966 " "
y[1] (analytic) = -0.3731120637303666 " "
y[1] (numeric) = -0.3731120637303449 " "
absolute error = 2.17048601314218100000000000000E-14 " "
relative error = 5.817249625867648000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.25448235343253484 " "
Order of pole (three term test) = 22.930393693949437 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6699999999999657 " "
y[1] (analytic) = -0.3594525675370014 " "
y[1] (numeric) = -0.3594525675369794 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 6.115526184220473000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24582415862616733 " "
Order of pole (three term test) = 22.935396925845524 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999999655 " "
y[1] (analytic) = -0.3457571263864253 " "
y[1] (numeric) = -0.34575712638640305 " "
absolute error = 2.22599716437343900000000000000E-14 " "
relative error = 6.438036975948309000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23706763743396192 " "
Order of pole (three term test) = 22.9402260047765 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999999653 " "
y[1] (analytic) = -0.33202710981134054 " "
y[1] (numeric) = -0.332027109811318 " "
absolute error = 2.253752739989067800000000000000E-14 " "
relative error = 6.7878575977415260000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.22821629234764235 " "
Order of pole (three term test) = 22.944878999175167 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.699999999999965 " "
y[1] (analytic) = -0.31826389080196305 " "
y[1] (numeric) = -0.3182638908019402 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 7.1860474808024190000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21927366378722668 " "
Order of pole (three term test) = 22.949354047905796 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.709999999999965 " "
y[1] (analytic) = -0.30446884566872434 " "
y[1] (numeric) = -0.3044688456687012 " "
absolute error = 2.314815006343451400000000000000E-14 " "
relative error = 7.60279759086443000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21024332868490642 " "
Order of pole (three term test) = 22.953649361008576 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999999647 " "
y[1] (analytic) = -0.290643353904642 " "
y[1] (numeric) = -0.29064335390461854 " "
absolute error = 2.34812169708220600000000000000E-14 " "
relative error = 8.079048309677186000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20112889905431885 " "
Order of pole (three term test) = 22.957763220415533 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999999645 " "
y[1] (analytic) = -0.2767887980473711 " "
y[1] (numeric) = -0.2767887980473474 " "
absolute error = 2.370326157574709200000000000000E-14 " "
relative error = 8.563663610291913000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1919340205457928 " "
Order of pole (three term test) = 22.96169398063774 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7399999999999642 " "
y[1] (analytic) = -0.262906563540952 " "
y[1] (numeric) = -0.26290656354092806 " "
absolute error = 2.392530618067212300000000000000E-14 " "
relative error = 9.10030767525717000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1826623709881345 " "
Order of pole (three term test) = 22.965440069423547 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999964 " "
y[1] (analytic) = -0.248998038597267 " "
y[1] (numeric) = -0.2489980385972427 " "
absolute error = 2.4286128663675300000000000000E-14 " "
relative error = 9.753542156593463000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17331765891754655 " "
Order of pole (three term test) = 22.96899998838736 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999964 " "
y[1] (analytic) = -0.2350646140572199 " "
y[1] (numeric) = -0.2350646140571953 " "
absolute error = 2.459143999544721700000000000000E-14 " "
relative error = 1.046156610771756500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16390362209426318 " "
Order of pole (three term test) = 22.972372313609064 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7699999999999636 " "
y[1] (analytic) = -0.22110768325165364 " "
y[1] (numeric) = -0.22110768325162872 " "
absolute error = 2.492450690283476400000000000000E-14 " "
relative error = 1.127256481380022500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.15442402600749425 " "
Order of pole (three term test) = 22.97555569620354 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999999634 " "
y[1] (analytic) = -0.20712864186201796 " "
y[1] (numeric) = -0.20712864186199276 " "
absolute error = 2.520206265899105300000000000000E-14 " "
relative error = 1.216734799805224800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.14488266236928263 " "
Order of pole (three term test) = 22.978548862860197 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.789999999999963 " "
y[1] (analytic) = -0.19312888778080273 " "
y[1] (numeric) = -0.19312888778077722 " "
absolute error = 2.55073739907629700000000000000E-14 " "
relative error = 1.320743586516860700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1352833475978654 " "
Order of pole (three term test) = 22.98135061635227 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.799999999999963 " "
y[1] (analytic) = -0.17910982097174954 " "
y[1] (numeric) = -0.1791098209717238 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 1.438065988317091300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1256299212911636 " "
Order of pole (three term test) = 22.983959836015735 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999999627 " "
y[1] (analytic) = -0.16507284332985694 " "
y[1] (numeric) = -0.16507284332983088 " "
absolute error = 2.60624855030755500000000000000E-14 " "
relative error = 1.578847554651746400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11592624469098838 " "
Order of pole (three term test) = 22.986375478197502 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999999625 " "
y[1] (analytic) = -0.15101935854119164 " "
y[1] (numeric) = -0.15101935854116522 " "
absolute error = 2.642330798607872600000000000000E-14 " "
relative error = 1.7496636352664400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1061761991385995 " "
Order of pole (three term test) = 22.988596576672904 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8299999999999623 " "
y[1] (analytic) = -0.13695077194252114 " "
y[1] (numeric) = -0.1369507719424945 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.945615363320984400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.6383684522218900E-2 " "
Order of pole (three term test) = 22.99062224303217 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999962 " "
y[1] (analytic) = -0.12286849038078185 " "
y[1] (numeric) = -0.12286849038075479 " "
absolute error = 2.70616862252381900000000000000E-14 " "
relative error = 2.2024919604181098000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.65526177171278100E-2 " "
Order of pole (three term test) = 22.99245166703577 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999962 " "
y[1] (analytic) = -0.10877392207239434 " "
y[1] (numeric) = -0.10877392207236707 " "
absolute error = 2.726985304235541000000000000000E-14 " "
relative error = 2.50702121637261500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.66869310189699100E-2 " "
Order of pole (three term test) = 22.99408411693849 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8599999999999617 " "
y[1] (analytic) = -9.46684764624442500E-2 " "
y[1] (numeric) = -9.46684764624167300E-2 " "
absolute error = 2.751965322289607000000000000000E-14 " "
relative error = 2.90695004834194600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.67905705708826600E-2 " "
Order of pole (three term test) = 22.995518939782148 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8699999999999615 " "
y[1] (analytic) = -8.05535640837382600E-2 " "
y[1] (numeric) = -8.05535640837102800E-2 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 3.47316975217511500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.686749478509716000E-2 " "
Order of pole (three term test) = 22.996755561656702 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999999613 " "
y[1] (analytic) = -6.64305964157514400E-2 " "
y[1] (numeric) = -6.64305964157232200E-2 " "
absolute error = 2.822742040109460500000000000000E-14 " "
relative error = 4.2491595626261100000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.69216727596198260E-2 " "
Order of pole (three term test) = 22.997793487929922 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.889999999999961 " "
y[1] (analytic) = -5.23009857434817400E-2 " "
y[1] (numeric) = -5.23009857434532200E-2 " "
absolute error = 2.852579283896261600000000000000E-14 " "
relative error = 5.45415969382905500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.69570826906527600E-2 " "
Order of pole (three term test) = 22.998632303445135 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.899999999999961 " "
y[1] (analytic) = -3.81661450162217300E-2 " "
y[1] (numeric) = -3.81661450161928760E-2 " "
absolute error = 2.885192085244625600000000000000E-14 " "
relative error = 7.5595585669402410000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.69777102813639100E-2 " "
Order of pole (three term test) = 22.999271672687303 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999999606 " "
y[1] (analytic) = -2.40274877062650600E-2 " "
y[1] (numeric) = -2.402748770623593400E-2 " "
absolute error = 2.91260071616505900000000000000E-14 " "
relative error = 1.21219527891199860000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.698754714766067800E-2 " "
Order of pole (three term test) = 22.999711339917262 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999999604 " "
y[1] (analytic) = -9.886427667560538000E-3 " "
y[1] (numeric) = -9.886427667531202000E-3 " "
absolute error = 2.933590870224378500000000000000E-14 " "
relative error = 2.9672910872044420000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.9905892215959810000E-3 " "
Order of pole (three term test) = 22.999951129273985 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.92999999999996 " "
y[1] (analytic) = 4.255621005671894600E-3 " "
y[1] (numeric) = 4.2556210057016225000E-3 " "
absolute error = 2.972795620781454300000000000000E-14 " "
relative error = 6.9855741778210760000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.009164846950697600E-3 " "
Order of pole (three term test) = 22.999990944844935 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.93999999999996 " "
y[1] (analytic) = 1.839724412035026500E-2 " "
y[1] (numeric) = 1.83972441203802180E-2 " "
absolute error = 2.995520498316750500000000000000E-14 " "
relative error = 1.62824414282964820000000000E-10 "%"
Correct digits = 13
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 1.300771528968024400E-2 " "
Order of pole (three term test) = 22.999830770704392 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9499999999999598 " "
y[1] (analytic) = 3.25370275259474500E-2 " "
y[1] (numeric) = 3.253702752597776300E-2 " "
absolute error = 3.03160274661706800000000000000E-14 " "
relative error = 9.31739306609813200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 2.300106281972798300E-2 " "
Order of pole (three term test) = 22.999470670919887 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9599999999999596 " "
y[1] (analytic) = 4.66735572559062730E-2 " "
y[1] (numeric) = 4.66735572559368150E-2 " "
absolute error = 3.05450109649996200000000000000E-14 " "
relative error = 6.54439317695981300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 3.29852102313249130E-2 " "
Order of pole (three term test) = 22.99891078952654 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9699999999999593 " "
y[1] (analytic) = 6.080541966903386000E-2 " "
y[1] (numeric) = 6.08054196690647900E-2 " "
absolute error = 3.09266501297145170000000000000E-14 " "
relative error = 5.086166709817878000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 4.29561639986253700E-2 " "
Order of pole (three term test) = 22.998151350469442 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.979999999999959 " "
y[1] (analytic) = 7.49312015908656400E-2 " "
y[1] (numeric) = 7.49312015908968600E-2 " "
absolute error = 3.12250225675825300000000000000E-14 " "
relative error = 4.167158927742186700000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 5.29099358730684000E-2 " "
Order of pole (three term test) = 22.997192657514073 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.989999999999959 " "
y[1] (analytic) = 8.90494904549807800E-2 " "
y[1] (numeric) = 8.90494904550123100E-2 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 3.540765223726315400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 6.28425444786178100E-2 " "
Order of pole (three term test) = 22.996035094124853 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999999587 " "
y[1] (analytic) = 0.10315887444425809 " "
y[1] (numeric) = 0.10315887444428992 " "
absolute error = 3.183564523112636400000000000000E-14 " "
relative error = 3.08607915728362900000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 7.275001690426599E-2 " "
Order of pole (three term test) = 22.9946791233117 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999959 " "
y[1] (analytic) = 0.11725794263205702 " "
y[1] (numeric) = 0.11725794263208855 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 2.688972123474252500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 8.26283902931399400E-2 " "
Order of pole (three term test) = 22.993125287444848 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999959 " "
y[1] (analytic) = 0.1313452851233068 " "
y[1] (numeric) = 0.1313452851233386 " "
absolute error = 3.180788965551073500000000000000E-14 " "
relative error = 2.421700149011784300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 9.24737134275933100E-2 " "
Order of pole (three term test) = 22.99137420803794 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999999585 " "
y[1] (analytic) = 0.1454194931954983 " "
y[1] (numeric) = 0.14541949319553035 " "
absolute error = 3.205768983605139500000000000000E-14 " "
relative error = 2.20449742545546100000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.10228204830964205 " "
Order of pole (three term test) = 22.989426585499373 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999958 " "
y[1] (analytic) = 0.1594791594395526 " "
y[1] (numeric) = 0.15947915943958507 " "
absolute error = 3.24740234702858300000000000000E-14 " "
relative error = 2.036254993091712300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.11204947173610914 " "
Order of pole (three term test) = 22.987283198852225 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999958 " "
y[1] (analytic) = 0.17352287790056187 " "
y[1] (numeric) = 0.17352287790059467 " "
absolute error = 3.280709037767337600000000000000E-14 " "
relative error = 1.890649277755388500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1217720768678551 " "
Order of pole (three term test) = 22.98494490542255 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.059999999999958 " "
y[1] (analytic) = 0.18754924421838315 " "
y[1] (numeric) = 0.18754924421841615 " "
absolute error = 3.30013794069827800000000000000E-14 " "
relative error = 1.75961143136123900000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.13144597479245995 " "
Order of pole (three term test) = 22.982412640496555 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999958 " "
y[1] (analytic) = 0.20155685576807303 " "
y[1] (numeric) = 0.2015568557681063 " "
absolute error = 3.32789351631390700000000000000E-14 " "
relative error = 1.651094180662968600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1410672960797373 " "
Order of pole (three term test) = 22.979687416946447 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999957 " "
y[1] (analytic) = 0.21554431180014955 " "
y[1] (numeric) = 0.21554431180018313 " "
absolute error = 3.358424649491098500000000000000E-14 " "
relative error = 1.558113327808434400000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1506321923294548 " "
Order of pole (three term test) = 22.976770324825306 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.089999999999957 " "
y[1] (analytic) = 0.2295102135806657 " "
y[1] (numeric) = 0.22951021358069962 " "
absolute error = 3.39173134022985300000000000000E-14 " "
relative error = 1.47781281160185300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.1601368377106437 " "
Order of pole (three term test) = 22.97366253093108 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999957 " "
y[1] (analytic) = 0.2434531645310818 " "
y[1] (numeric) = 0.2434531645311159 " "
absolute error = 3.411160243160793500000000000000E-14 " "
relative error = 1.401156665895500800000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.16957743049187682 " "
Order of pole (three term test) = 22.970365278339898 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999957 " "
y[1] (analytic) = 0.2573717703679216 " "
y[1] (numeric) = 0.25737177036795605 " "
absolute error = 3.44724249146111100000000000000E-14 " "
relative error = 1.339401942385974300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.17895019456191597 " "
Order of pole (three term test) = 22.966879885908835 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999957 " "
y[1] (analytic) = 0.27126463924220034 " "
y[1] (numeric) = 0.27126463924223515 " "
absolute error = 3.48054918219986600000000000000E-14 " "
relative error = 1.283082524844764100000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.18825138094010122 " "
Order of pole (three term test) = 22.963207747748406 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999956 " "
y[1] (analytic) = 0.2851303818786082 " "
y[1] (numeric) = 0.28513038187864315 " "
absolute error = 3.49720252756924300000000000000E-14 " "
relative error = 1.226527494028380200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.19747726927589543 " "
Order of pole (three term test) = 22.95935033266488 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999956 " "
y[1] (analytic) = 0.29896761171443575 " "
y[1] (numeric) = 0.29896761171447117 " "
absolute error = 3.541611448554249400000000000000E-14 " "
relative error = 1.184613754060116300000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.20662416933697414 " "
Order of pole (three term test) = 22.955309183572886 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999956 " "
y[1] (analytic) = 0.3127749450382309 " "
y[1] (numeric) = 0.3127749450382666 " "
absolute error = 3.56936702416987800000000000000E-14 " "
relative error = 1.141193398254323200000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.21568842248527034 " "
Order of pole (three term test) = 22.951085916878156 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999956 " "
y[1] (analytic) = 0.32655100112816715 " "
y[1] (numeric) = 0.32655100112820307 " "
absolute error = 3.591571484662381400000000000000E-14 " "
relative error = 1.099850091487772000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2246664031403799 " "
Order of pole (three term test) = 22.9466822218311 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.1699999999999555 " "
y[1] (analytic) = 0.34029440239011544 " "
y[1] (numeric) = 0.3402944023901517 " "
absolute error = 3.62487817540113600000000000000E-14 " "
relative error = 1.065218278626151500000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.23355452022974477 " "
Order of pole (three term test) = 22.94209985985098 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999955 " "
y[1] (analytic) = 0.35400377449540243 " "
y[1] (numeric) = 0.354003774495439 " "
absolute error = 3.65818486613989100000000000000E-14 " "
relative error = 1.03337453713714600000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.24234921862503697 " "
Order of pole (three term test) = 22.937340663821505 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999955 " "
y[1] (analytic) = 0.36767774651824214 " "
y[1] (numeric) = 0.36767774651827895 " "
absolute error = 3.68038932663239400000000000000E-14 " "
relative error = 1.000982344317592000000000000E-11 "%"
Correct digits = 14
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2510469805641591 " "
Order of pole (three term test) = 22.932406537357632 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999955 " "
y[1] (analytic) = 0.3813149510728271 " "
y[1] (numeric) = 0.38131495107286417 " "
absolute error = 3.70814490224802300000000000000E-14 " "
relative error = 9.724624989959563000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.25964432705830415 " "
Order of pole (three term test) = 22.927299454044157 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999955 " "
y[1] (analytic) = 0.3949140244500661 " "
y[1] (numeric) = 0.39491402445010354 " "
absolute error = 3.741451592986777500000000000000E-14 " "
relative error = 9.474091476485043000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2681378192835035 " "
Order of pole (three term test) = 22.922021456646327 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2199999999999545 " "
y[1] (analytic) = 0.40847360675395405 " "
y[1] (numeric) = 0.4084736067539918 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 9.241131425167637000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2765240599561133 " "
Order of pole (three term test) = 22.91657465629271 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999954 " "
y[1] (analytic) = 0.4219923420375602 " "
y[1] (numeric) = 0.4219923420375982 " "
absolute error = 3.80251385934116100000000000000E-14 " "
relative error = 9.010859867695683000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.28479969469167854 " "
Order of pole (three term test) = 22.910961231630825 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999954 " "
y[1] (analytic) = 0.4354688784386217 " "
y[1] (numeric) = 0.43546887843866 " "
absolute error = 3.8302694349567900000000000000E-14 " "
relative error = 8.795736330665609000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.2929614133466462 " "
Order of pole (three term test) = 22.905183427955702 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999954 " "
y[1] (analytic) = 0.44890186831472884 " "
y[1] (numeric) = 0.4489018683147674 " "
absolute error = 3.85802501057241900000000000000E-14 " "
relative error = 8.594361669859492000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3010059513423751 " "
Order of pole (three term test) = 22.89924355631177 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999954 " "
y[1] (analytic) = 0.4622899683780881 " "
y[1] (numeric) = 0.462289968378127 " "
absolute error = 3.891331701311173700000000000000E-14 " "
relative error = 8.417512746304311000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.30893009097092616 " "
Order of pole (three term test) = 22.893143992568497 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999953 " "
y[1] (analytic) = 0.47563183982984997 " "
y[1] (numeric) = 0.47563183982988916 " "
absolute error = 3.919087276926802600000000000000E-14 " "
relative error = 8.23974963141407100000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3167306626821016 " "
Order of pole (three term test) = 22.886887176470033 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999953 " "
y[1] (analytic) = 0.48892614849398736 " "
y[1] (numeric) = 0.4889261484940269 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 8.083826115334395000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3244045463512237 " "
Order of pole (three term test) = 22.880475610659417 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999953 " "
y[1] (analytic) = 0.5021715649507126 " "
y[1] (numeric) = 0.5021715649507523 " "
absolute error = 3.974598428158060400000000000000E-14 " "
relative error = 7.914821757277638000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3319486725271418 " "
Order of pole (three term test) = 22.873911859677477 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999953 " "
y[1] (analytic) = 0.5153667646694174 " "
y[1] (numeric) = 0.5153667646694575 " "
absolute error = 4.00790511889681500000000000000E-14 " "
relative error = 7.7768016753422000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.33936002365997175 " "
Order of pole (three term test) = 22.86719854893709 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3099999999999525 " "
y[1] (analytic) = 0.5285104281411264 " "
y[1] (numeric) = 0.5285104281411667 " "
absolute error = 4.03010957938931800000000000000E-14 " "
relative error = 7.625411656613843000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.34663563530807795 " "
Order of pole (three term test) = 22.86033836367304 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999952 " "
y[1] (analytic) = 0.5416012410104449 " "
y[1] (numeric) = 0.5416012410104856 " "
absolute error = 4.06341627012807300000000000000E-14 " "
relative error = 7.502597783097968000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3537725973238077 " "
Order of pole (three term test) = 22.85333404786797 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999952 " "
y[1] (analytic) = 0.5546378942069956 " "
y[1] (numeric) = 0.5546378942070364 " "
absolute error = 4.074518500374324500000000000000E-14 " "
relative error = 7.346267795495559000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.36076805501751336 " "
Order of pole (three term test) = 22.846188403154816 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999952 " "
y[1] (analytic) = 0.567619084076322 " "
y[1] (numeric) = 0.5676190840763631 " "
absolute error = 4.10782519111307900000000000000E-14 " "
relative error = 7.236939888653817000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3676192102993882 " "
Order of pole (three term test) = 22.838904287696188 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999952 " "
y[1] (analytic) = 0.5805435125102553 " "
y[1] (numeric) = 0.5805435125102966 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 7.114074246988722000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3743233227986675 " "
Order of pole (three term test) = 22.831484615041127 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3599999999999515 " "
y[1] (analytic) = 0.593409887076722 " "
y[1] (numeric) = 0.5934098870767637 " "
absolute error = 4.16333634234433700000000000000E-14 " "
relative error = 7.01595378340243000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.38087771095973855 " "
Order of pole (three term test) = 22.823932352959797 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999951 " "
y[1] (analytic) = 0.6062169211489878 " "
y[1] (numeric) = 0.6062169211490297 " "
absolute error = 4.1855408028368400000000000000E-14 " "
relative error = 6.9043615524684010000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.3872797531147274 " "
Order of pole (three term test) = 22.816250522256322 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999951 " "
y[1] (analytic) = 0.6189633340343177 " "
y[1] (numeric) = 0.6189633340343599 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 6.8159893512233250000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39352688853213175 " "
Order of pole (three term test) = 22.808442195560566 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999950 " "
y[1] (analytic) = 0.6316478511020452 " "
y[1] (numeric) = 0.6316478511020878 " "
absolute error = 4.252154184314349500000000000000E-14 " "
relative error = 6.731843030725988000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.39961661844107815 " "
Order of pole (three term test) = 22.80051049609909 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999950 " "
y[1] (analytic) = 0.6442692039110341 " "
y[1] (numeric) = 0.6442692039110769 " "
absolute error = 4.274358644806852700000000000000E-14 " "
relative error = 6.634429550348476000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4055465070307989 " "
Order of pole (three term test) = 22.792458596445925 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.40999999999995 " "
y[1] (analytic) = 0.656826130336521 " "
y[1] (numeric) = 0.6568261303365641 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 6.5583038441826300000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41131418242492196 " "
Order of pole (three term test) = 22.784289717253568 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999995 " "
y[1] (analytic) = 0.6693173746963276 " "
y[1] (numeric) = 0.669317374696371 " "
absolute error = 4.34097202628436200000000000000E-14 " "
relative error = 6.485670610678351000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4169173376301912 " "
Order of pole (three term test) = 22.776007125964814 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.42999999999995 " "
y[1] (analytic) = 0.6817416878764271 " "
y[1] (numeric) = 0.6817416878764708 " "
absolute error = 4.37427871702311700000000000000E-14 " "
relative error = 6.416328640028833000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4223537314592317 " "
Order of pole (three term test) = 22.767614135505703 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.43999999999995 " "
y[1] (analytic) = 0.6940978274558551 " "
y[1] (numeric) = 0.6940978274558992 " "
absolute error = 4.407585407761871500000000000000E-14 " "
relative error = 6.350092499089685000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4276211894269965 " "
Order of pole (three term test) = 22.75911410296053 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4499999999999496 " "
y[1] (analytic) = 0.7063845578309507 " "
y[1] (numeric) = 0.7063845578309949 " "
absolute error = 4.41868763800812300000000000000E-14 " "
relative error = 6.255357070058696000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4327176046205308 " "
Order of pole (three term test) = 22.750510428228985 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999950 " "
y[1] (analytic) = 0.7186006503389148 " "
y[1] (numeric) = 0.7186006503389593 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 6.179916614890566000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43764093854170766 " "
Order of pole (three term test) = 22.741806552666237 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999950 " "
y[1] (analytic) = 0.730744883380677 " "
y[1] (numeric) = 0.7307448833807217 " "
absolute error = 4.47419878923938100000000000000E-14 " "
relative error = 6.122791812841986000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4423892219226028 " "
Order of pole (three term test) = 22.733005957706478 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999949 " "
y[1] (analytic) = 0.7428160425430532 " "
y[1] (numeric) = 0.7428160425430982 " "
absolute error = 4.49640324973188400000000000000E-14 " "
relative error = 6.053185435169536000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.44696055551317315 " "
Order of pole (three term test) = 22.724112163470338 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999949 " "
y[1] (analytic) = 0.7548129207201864 " "
y[1] (numeric) = 0.7548129207202315 " "
absolute error = 4.51860771022438700000000000000E-14 " "
relative error = 5.986394225887214000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45135311084093294 " "
Order of pole (three term test) = 22.715128727356937 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999999485 " "
y[1] (analytic) = 0.7667343182342562 " "
y[1] (numeric) = 0.7667343182343016 " "
absolute error = 4.5408121707168900000000000000E-14 " "
relative error = 5.922275894959433000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4555651309423173 " "
Order of pole (three term test) = 22.706059242620928 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999948 " "
y[1] (analytic) = 0.7785790429554457 " "
y[1] (numeric) = 0.7785790429554914 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 5.874957594661843000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4595949310654457 " "
Order of pole (three term test) = 22.69690733693529 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999948 " "
y[1] (analytic) = 0.7903459104211534 " "
y[1] (numeric) = 0.7903459104211994 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 5.815584367987550000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46344089934399857 " "
Order of pole (three term test) = 22.687676670940277 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999948 " "
y[1] (analytic) = 0.8020337439544383 " "
y[1] (numeric) = 0.8020337439544846 " "
absolute error = 4.62963001268690300000000000000E-14 " "
relative error = 5.7723631300853360000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4671014974419435 " "
Order of pole (three term test) = 22.678370936779217 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999948 " "
y[1] (analytic) = 0.8136413747816871 " "
y[1] (numeric) = 0.8136413747817336 " "
absolute error = 4.65183447317940600000000000000E-14 " "
relative error = 5.7173032460739450000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4705752611688485 " "
Order of pole (three term test) = 22.668993856621686 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999947 " "
y[1] (analytic) = 0.8251676421494899 " "
y[1] (numeric) = 0.8251676421495366 " "
absolute error = 4.67403893367190900000000000000E-14 " "
relative error = 5.6643507269582760000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47386080106553924 " "
Order of pole (three term test) = 22.65954918117472 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999947 " "
y[1] (analytic) = 0.8366113934407151 " "
y[1] (numeric) = 0.8366113934407622 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 5.626681230159748000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4769568029598634 " "
Order of pole (three term test) = 22.65004068818259 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999947 " "
y[1] (analytic) = 0.8479714842897702 " "
y[1] (numeric) = 0.8479714842898175 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 5.57748718267863000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47986202849234305 " "
Order of pole (three term test) = 22.640472180915697 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999947 " "
y[1] (analytic) = 0.8592467786970368 " "
y[1] (numeric) = 0.8592467786970843 " "
absolute error = 4.7517545453956700000000000000E-14 " "
relative error = 5.530139493337686000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48257531561150074 " "
Order of pole (three term test) = 22.630847486649376 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999947 " "
y[1] (analytic) = 0.8704361491424704 " "
y[1] (numeric) = 0.8704361491425181 " "
absolute error = 4.77395900588817300000000000000E-14 " "
relative error = 5.484559678031922000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4850955790386657 " "
Order of pole (three term test) = 22.62117045513301 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999946 " "
y[1] (analytic) = 0.8815384766983506 " "
y[1] (numeric) = 0.8815384766983987 " "
absolute error = 4.80726569662692800000000000000E-14 " "
relative error = 5.453268148466652000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4874218107020701 " "
Order of pole (three term test) = 22.61144495705018 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999946 " "
y[1] (analytic) = 0.8925526511411741 " "
y[1] (numeric) = 0.8925526511412224 " "
absolute error = 4.82947015711943100000000000000E-14 " "
relative error = 5.4108518426836860000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48955308014006405 " "
Order of pole (three term test) = 22.601674882470427 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999946 " "
y[1] (analytic) = 0.9034775710626748 " "
y[1] (numeric) = 0.9034775710627233 " "
absolute error = 4.85167461761193400000000000000E-14 " "
relative error = 5.370000067522839000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4914885348732898 " "
Order of pole (three term test) = 22.591864139293346 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999946 " "
y[1] (analytic) = 0.9143121439799647 " "
y[1] (numeric) = 0.9143121439800135 " "
absolute error = 4.87387907810443700000000000000E-14 " "
relative error = 5.330651145995539000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49322740074565924 " "
Order of pole (three term test) = 22.582016651685382 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6399999999999455 " "
y[1] (analytic) = 0.9250552864447809 " "
y[1] (numeric) = 0.9250552864448299 " "
absolute error = 4.90718576884319200000000000000E-14 " "
relative error = 5.304748635838552000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49476898223400795 " "
Order of pole (three term test) = 22.572136358510285 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999945 " "
y[1] (analytic) = 0.9357059241518294 " "
y[1] (numeric) = 0.9357059241518787 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 5.2680977026023870000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49611266272629484 " "
Order of pole (three term test) = 22.56222721175358 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999945 " "
y[1] (analytic) = 0.9462629920462151 " "
y[1] (numeric) = 0.9462629920462646 " "
absolute error = 4.95159468982819800000000000000E-14 " "
relative error = 5.232789120412271000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4972579047682387 " "
Order of pole (three term test) = 22.55229317494187 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999945 " "
y[1] (analytic) = 0.956725434429946 " "
y[1] (numeric) = 0.9567254344299958 " "
absolute error = 4.98490138056695300000000000000E-14 " "
relative error = 5.210378235148677000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4982042502782923 " "
Order of pole (three term test) = 22.54233822155742 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999945 " "
y[1] (analytic) = 0.9670922050675025 " "
y[1] (numeric) = 0.9670922050675526 " "
absolute error = 5.00710584105945600000000000000E-14 " "
relative error = 5.177485471212088000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4989513207308691 " "
Order of pole (three term test) = 22.532366333448834 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999944 " "
y[1] (analytic) = 0.9773622672904596 " "
y[1] (numeric) = 0.97736226729051 " "
absolute error = 5.04041253179821100000000000000E-14 " "
relative error = 5.157158916899607000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49949881730774937 " "
Order of pole (three term test) = 22.522381499238424 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999944 " "
y[1] (analytic) = 0.9875345941011536 " "
y[1] (numeric) = 0.9875345941012043 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 5.126521159391554000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4998465210176018 " "
Order of pole (three term test) = 22.51238771272673 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999944 " "
y[1] (analytic) = 0.9976081682753803 " "
y[1] (numeric) = 0.9976081682754311 " "
absolute error = 5.073719222536965000000000000000E-14 " "
relative error = 5.085883800759351000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4999942927835788 " "
Order of pole (three term test) = 22.50238897129512 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999944 " "
y[1] (analytic) = 1.0075819824641168 " "
y[1] (numeric) = 1.0075819824641679 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 5.068595907983694000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.499942073498944 " "
Order of pole (three term test) = 22.49238927430684 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999944 " "
y[1] (analytic) = 1.0174550392942558 " "
y[1] (numeric) = 1.017455039294307 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 5.019411881647509000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49968988405071496 " "
Order of pole (three term test) = 22.482392621507362 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999943 " "
y[1] (analytic) = 1.0272263514683417 " "
y[1] (numeric) = 1.027226351468393 " "
absolute error = 5.12923037376822300000000000000E-14 " "
relative error = 4.993281535696957300000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49923782531130867 " "
Order of pole (three term test) = 22.472403011424515 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999943 " "
y[1] (analytic) = 1.0368949418632998 " "
y[1] (numeric) = 1.0368949418633513 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 4.968135754431977600000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4985860780981935 " "
Order of pole (three term test) = 22.46242443976915 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999943 " "
y[1] (analytic) = 1.0464598436281478 " "
y[1] (numeric) = 1.0464598436281995 " "
absolute error = 5.173639294753230000000000000000E-14 " "
relative error = 4.943944410533584000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49773490310156465 " "
Order of pole (three term test) = 22.452460897836872 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999943 " "
y[1] (analytic) = 1.0559201002806802 " "
y[1] (numeric) = 1.055920100280732 " "
absolute error = 5.173639294753230000000000000000E-14 " "
relative error = 4.8996503555316306000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49668464078007224 " "
Order of pole (three term test) = 22.442516370911616 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.7799999999999425 " "
y[1] (analytic) = 1.0652747658031148 " "
y[1] (numeric) = 1.0652747658031667 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 4.877468163181886000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49543571122464136 " "
Order of pole (three term test) = 22.43259483667156 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999942 " "
y[1] (analytic) = 1.074522904736695 " "
y[1] (numeric) = 1.0745229047367473 " "
absolute error = 5.21804821573823600000000000000E-14 " "
relative error = 4.85615354752897000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4939886139904422 " "
Order of pole (three term test) = 22.42270026359811 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999942 " "
y[1] (analytic) = 1.0836635922752347 " "
y[1] (numeric) = 1.0836635922752869 " "
absolute error = 5.21804821573823600000000000000E-14 " "
relative error = 4.815191958957063000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.49234392789707365 " "
Order of pole (three term test) = 22.412836609388567 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999942 " "
y[1] (analytic) = 1.0926959143575965 " "
y[1] (numeric) = 1.092695914357649 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 4.795709956792068600000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4905023107970444 " "
Order of pole (three term test) = 22.40300781937311 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999942 " "
y[1] (analytic) = 1.1016189677590997 " "
y[1] (numeric) = 1.1016189677591521 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 4.756864968375044000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4884644993126402 " "
Order of pole (three term test) = 22.393217824936688 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8299999999999415 " "
y[1] (analytic) = 1.1104318601818395 " "
y[1] (numeric) = 1.1104318601818923 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 4.759104801217025000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4862313085412838 " "
Order of pole (three term test) = 22.38347054194655 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999941 " "
y[1] (analytic) = 1.119133710343918 " "
y[1] (numeric) = 1.1191337103439711 " "
absolute error = 5.30686605770824800000000000000E-14 " "
relative error = 4.7419410287242700000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48380363172950885 " "
Order of pole (three term test) = 22.373769869185928 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999941 " "
y[1] (analytic) = 1.1277236480675705 " "
y[1] (numeric) = 1.1277236480676238 " "
absolute error = 5.329070518200751000000000000000E-14 " "
relative error = 4.7255110126780336000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.48118243991567106 " "
Order of pole (three term test) = 22.364119686794588 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999940 " "
y[1] (analytic) = 1.1362008143661828 " "
y[1] (numeric) = 1.1362008143662363 " "
absolute error = 5.351274978693255000000000000000E-14 " "
relative error = 4.709796816752331300000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4783687815415473 " "
Order of pole (three term test) = 22.354523854716813 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999940 " "
y[1] (analytic) = 1.1445643615301893 " "
y[1] (numeric) = 1.144564361530243 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 4.694781368172126000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4753637820329723 " "
Order of pole (three term test) = 22.344986211157494 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.87999999999994 " "
y[1] (analytic) = 1.1528134532118433 " "
y[1] (numeric) = 1.1528134532118972 " "
absolute error = 5.39568389967826100000000000000E-14 " "
relative error = 4.6804484148284303000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.47216864334968367 " "
Order of pole (three term test) = 22.335510571046896 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.88999999999994 " "
y[1] (analytic) = 1.1609472645088508 " "
y[1] (numeric) = 1.1609472645089047 " "
absolute error = 5.39568389967826100000000000000E-14 " "
relative error = 4.64765632740515000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46878464350455273 " "
Order of pole (three term test) = 22.326100724514706 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999994 " "
y[1] (analytic) = 1.1689649820468602 " "
y[1] (numeric) = 1.1689649820469143 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 4.634773875504833400000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.46521313605239867 " "
Order of pole (three term test) = 22.316760435374086 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.90999999999994 " "
y[1] (analytic) = 1.176865804060799 " "
y[1] (numeric) = 1.1768658040608535 " "
absolute error = 5.44009282066326700000000000000E-14 " "
relative error = 4.62252603643688000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4614555495485829 " "
Order of pole (three term test) = 22.307493439616163 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9199999999999395 " "
y[1] (analytic) = 1.1846489404750502 " "
y[1] (numeric) = 1.1846489404751048 " "
absolute error = 5.4622972811557700000000000000E-14 " "
relative error = 4.6108995623339366000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45751338697760635 " "
Order of pole (three term test) = 22.29830344391567 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999940 " "
y[1] (analytic) = 1.192313612982458 " "
y[1] (numeric) = 1.1923136129825127 " "
absolute error = 5.4622972811557700000000000000E-14 " "
relative error = 4.581258841365032000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.45338822515193583 " "
Order of pole (three term test) = 22.289194124148356 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999939 " "
y[1] (analytic) = 1.1998590551221588 " "
y[1] (numeric) = 1.1998590551222137 " "
absolute error = 5.48450174164827300000000000000E-14 " "
relative error = 4.570954995284751000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4490817140813002 " "
Order of pole (three term test) = 22.28016912392068 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999939 " "
y[1] (analytic) = 1.2072845123562268 " "
y[1] (numeric) = 1.2072845123562819 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 4.56123320210037000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4445955763127086 " "
Order of pole (three term test) = 22.271232053112392 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999939 " "
y[1] (analytic) = 1.2145892421451263 " "
y[1] (numeric) = 1.2145892421451814 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 4.5338012317770904000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4399316062414538 " "
Order of pole (three term test) = 22.262386486432664 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999385 " "
y[1] (analytic) = 1.2217725140219653 " "
y[1] (numeric) = 1.2217725140220208 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 4.543493211229651000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4350916693933789 " "
Order of pole (three term test) = 22.253635961990227 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999938 " "
y[1] (analytic) = 1.2288336096655428 " "
y[1] (numeric) = 1.2288336096655983 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 4.517385494230301000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.43007770167869147 " "
Order of pole (three term test) = 22.244983979878178 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.989999999999938 " "
y[1] (analytic) = 1.2357718229721781 " "
y[1] (numeric) = 1.2357718229722339 " "
absolute error = 5.57331958361828600000000000000E-14 " "
relative error = 4.509990825178219000000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.4248917086176256 " "
Order of pole (three term test) = 22.236434000774008 " "
"NO COMPLEX POLE (six term test) for Equation 1"
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.999999999999938 " "
y[1] (analytic) = 1.2425864601263228 " "
y[1] (numeric) = 1.2425864601263785 " "
absolute error = 5.57331958361828600000000000000E-14 " "
relative error = 4.485256972019231500000000000E-12 "%"
Correct digits = 15
h = 1.00E-2 " "
"NO INFO (given) for Equation 1"
"NO POLE (ratio test) for Equation 1"
Radius of convergence (three term test) for eq 1 = 0.41953576453826014 " "
Order of pole (three term test) = 22.227989444555366 " "
"NO COMPLEX POLE (six term test) for Equation 1"
"Finished!"
"diff ( y , x , 1 ) = m1 * sin ( x ) - cos ( x ) ; "
Iterations = 491
"Total Elapsed Time "= 22 Seconds
"Elapsed Time(since restart) "= 22 Seconds
"Time to Timeout "= 9 Minutes 37 Seconds
Percent Done = 100.40816326530484 "%"
(%o227) true
(%o227) diffeq.max