(%i1) batch("temp/diffeq.div_sin_c.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.div_sin_c.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,40,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[40],convfloat)
(%i173) completearray(array_norms,[40],convfloat)
(%i174) completearray(array_fact_1,[40],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[40],convfloat)
(%i184) completearray(array_x,[40],convfloat)
(%i185) completearray(array_tmp0,[40],convfloat)
(%i186) completearray(array_tmp1_g,[40],convfloat)
(%i187) completearray(array_tmp1,[40],convfloat)
(%i188) completearray(array_tmp2,[40],convfloat)
(%i189) completearray(array_tmp3,[40],convfloat)
(%i190) completearray(array_m1,[40],convfloat)
(%i191) completearray(array_y_higher,[2,40],convfloat)
(%i192) completearray(array_y_higher_work,[2,40],convfloat)
(%i193) completearray(array_y_higher_work2,[2,40],convfloat)
(%i194) completearray(array_y_set_initial,[2,40],convfloat)
(%i195) completearray(array_given_rad_poles,[2,3],convfloat)
(%i196) completearray(array_given_ord_poles,[2,3],convfloat)
(%i197) completearray(array_rad_test_poles,[2,4],convfloat)
(%i198) completearray(array_ord_test_poles,[2,4],convfloat)
(%i199) completearray(array_fact_2,[40,40],convfloat)
(%i200) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i201) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i202) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i203) 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))
(%i204) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i205) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i206) 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)
(%i207) 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)
(%i208) zero_ats_ar(arr_a):=(
block(mode_declare([iii],fixnum),iii:1,
while iii <= ats_max_terms do
(arr_a[iii]:glob__0,iii:1+iii)),0)
(%i209) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:glob__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 <= ats_max_terms
and iii_ats <= ats_max_terms
then ret_ats
:c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i210) 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:glob__0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= ats_max_terms do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= ats_max_terms
and iii_att <= ats_max_terms
then ret_att
:c(arr_aa[iii_att])*c(arr_bb[lll_att])
*c(al_att)
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/c(mmm_att)),ret_att)
(%i211) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i212) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i213) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i214) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i215) log_revs(file,revs):=printf(file,revs)
(%i216) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i217) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
elseif glob_h_reason = 7
then printf(file,"Opt Iter")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i218) logstart(file):=(printf(file,""),0)
(%i219) logend(file):=(printf(file,"
~%"),0)
(%i220) 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)
(%i221) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:c(clock_sec2),
sub1:c(t_end2-t_start2),sub2:c(t2-t_start2),
if sub1 = glob__0 then sec_left:glob__0
else (if sub2 > glob__0
then (rrr:sub1/sub2,
sec_left:rrr*c(ms2)-c(ms2))
else sec_left:glob__0),sec_left)
(%i222) 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:glob__100*sub2/sub1
else rrr:0.0,rrr)
(%i223) comp_rad_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i224) comp_ord_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret
:abs(term2)*c(last_no)
*log(abs(term1*glob_h/term2))
/log(c(last_no))
+glob__1 else ret:glob_larger_float,ret)
(%i225) c(in_val):=(ret:in_val,ret)
(%i226) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3-term1*term3*c(last_no)
+glob__m2*term2*term2
+term2*term2*c(last_no)),
if abs(temp) > glob__0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i227) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*c(last_no*last_no)
+term2*term2*c(last_no*last_no)
+glob__4*term2*term2
-glob__4*term2*term2*c(last_no)
-glob__3*term1*term3
+glob__4*term1*term3*c(last_no))
/(term1*term3-term1*term3*c(last_no)
-glob__2*term2*term2
+term2*term2*c(last_no))),
ret)
(%i228) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # glob__0 and term4 # glob__0
and term3 # glob__0
and term2 # glob__0
and term1 # glob__0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:c(last_no-3)*rm2
-glob__2*c(last_no-2)*rm1
+c(last_no-1)*rm0,
nr2
:c(last_no-4)*rm3
-glob__2*c(last_no-3)*rm2
+c(last_no-2)*rm1,
dr1
:(-glob__1)/rm3+glob__2/rm2
+glob__m1/rm1,
dr2
:(-glob__1)/rm4+glob__2/rm3
+glob__m1/rm2,
ds1
:glob__5/rm3-glob__8/rm2
+glob__3/rm1,
ds2
:glob__5/rm4-glob__8/rm3
+glob__3/rm2,
if
abs(nr1*dr2-nr2*dr1) = glob__0
or abs(dr1) = glob__0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) > glob__0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(glob__2*dr1)
-c(last_no)/glob__2,
if abs(rcs) # glob__0
then (if rcs > glob__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)
(%i229) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i230) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i231) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_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)
(%i232) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i233) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i234) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms and mmm <= ats_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)
(%i235) log10(x):=log(x)/glob_log_10
(%i236) c(x):=x
(%i237) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y) else x^y
(%i238) 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(glob__10,
c(-glob_desired_digits_correct))
*c(abs(c(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
:c(
abs(desired_abs_gbl_error)
/sqrt(c(estimated_steps))
/c(ats_max_terms)),
omniout_float(always,"step_error",32,
step_error,32,""),
step_error)
(%i239) exact_soln_y(x):=block(neg(cos(c(x)))/c(2.0))
neg(cos(c(x)))
(%o239) exact_soln_y(x) := block(--------------)
c(2.0)
(%i240) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
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])),
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," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(always,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(always,
"SOME 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] > glob__small
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] > glob__small
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)
(%i241) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i242) 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 < glob__1
then (min_size:glob__1,
omniout_float(always,"min_size",32,min_size,
32,"")),min_size)
(%i243) 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:glob__small,
no_terms:ats_max_terms,hn_div_ho:glob__0_5,
hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__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)
(%i244) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:ats_max_terms,
hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25,
hn_div_ho_3:glob__0_125,
est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3)
+c(abs(array_y[no_terms-1]))
*c(hn_div_ho_2)
+c(abs(array_y[no_terms-2]))
*c(hn_div_ho)
+c(abs(array_y[no_terms-3])),
if glob_prec*c(abs(array_y[1])) > c(est_tmp)
then est_tmp
:c(glob_prec)*c(abs(array_y[1])),
if c(est_tmp) >= c(array_max_est_error[1])
then array_max_est_error[1]:c(est_tmp))
(%i245) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
-glob_h/glob__10 then ret:true else ret:false,
return(ret))
(%i246) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_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,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(19)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i247) 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
:c(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 c(percent_done) < glob__100
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)
(%i248) 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),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+ats_max_terms,cnt:0,
while last_no < ats_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),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
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)),
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+ats_max_terms,cnt:0,
while last_no < ats_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),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
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)),
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+ats_max_terms,cnt:0,
while last_no < ats_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),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
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,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_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)
(%i249) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),array_tmp1[1]:sin(array_x[1]),
array_tmp1_g[1]:cos(array_x[1]),
array_tmp2[1]:array_tmp1[1]/array_const_2D0[1],
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp3[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_tmp1_g[1]*array_x[2]/c(1),
array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1),
array_tmp2[2]:array_tmp1[2]/array_const_2D0[1],
array_tmp3[2]:array_tmp2[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp3[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_tmp1_g[2]*array_x[2]/c(2),
array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2),
array_tmp2[3]:array_tmp1[3]/array_const_2D0[1],
array_tmp3[3]:array_tmp2[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp3[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_tmp1_g[3]*array_x[2]/c(3),
array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3),
array_tmp2[4]:array_tmp1[4]/array_const_2D0[1],
array_tmp3[4]:array_tmp2[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp3[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_tmp1_g[4]*array_x[2]/c(4),
array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4),
array_tmp2[5]:array_tmp1[5]/array_const_2D0[1],
array_tmp3[5]:array_tmp2[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp3[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp1_g[kkk]
:neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1),
array_tmp2[kkk]
:array_tmp1[kkk]/array_const_2D0[1],
array_tmp3[kkk]:array_tmp2[kkk],order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp3[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i250) exact_soln_y(x):=block(neg(cos(c(x)))/c(2.0))
neg(cos(c(x)))
(%o250) exact_soln_y(x) := block(--------------)
c(2.0)
(%i251) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],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,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(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 <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(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]:c(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]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1_g),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_tmp3),zero_ats_ar(array_m1),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_2D0),array_const_2D0[1]:c(2.0),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_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,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
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/div_sin_cpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = sin ( x ) / 2.0 ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(-5.0),"),
omniout_str(always,"x_end:c(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,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
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," (neg(cos(c(x)))/c(2.0)) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(-5.0),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:3,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),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:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(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,c(term_no-1))
/c(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 < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
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
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
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 glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(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 < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(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_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_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(),
track_estimated_error(),atomall(),
track_estimated_error(),
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:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_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,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_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,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_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,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = sin ( x ) / 2.0 ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:55:26-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"div_sin_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) / 2.0 ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
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 c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"div_sin_c diffeq.max"),
logitem_str(html_log_file,
"div_sin_c maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i252) main():=(glob_iolevel:2,compile(all),main_prog())
(%i253) 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 ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
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 ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_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 glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason 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 glob__0 in translation.
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__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 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 glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 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 glob__0 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.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
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 ats_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.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms 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 always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles 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 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: encountered undefined variable glob__small 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__1 in translation.
warning: encountered undefined variable glob__m1 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 glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error 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.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 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 closed_form_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 glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct 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 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 glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher 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 glob__0 in translation.
warning: encountered undefined variable glob_large_float 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 always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp1_g in translation.
warning: encountered undefined variable array_const_2D0 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 glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_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: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
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 glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
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_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
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__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
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: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
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_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 info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float 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: encountered undefined variable glob__100 in translation.
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 : $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__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST 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: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/div_sin_cpostode.ode#################"
"diff ( y , x , 1 ) = sin ( x ) / 2.0 ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(-5.0),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (neg(cos(c(x)))/c(2.0)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -5. " "
y[1] (closed_form) = -0.14183109273161312 " "
y[1] (numeric) = -0.14183109273161312 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.989999999999997 " "
y[1] (closed_form) = -0.13702945977271203 " "
y[1] (numeric) = -0.13702945977271364 " "
absolute error = 1.609823385706477000000000000000E-15 " "
relative error = 1.1748009430794358000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (closed_form) = -0.13221412398202445 " "
y[1] (numeric) = -0.13221412398202767 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 2.43517611768217000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (closed_form) = -0.12738556688911676 " "
y[1] (numeric) = -0.12738556688912156 " "
absolute error = 4.801714581503802000000000000000E-15 " "
relative error = 3.7694337739874980000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (closed_form) = -0.12254427134567442 " "
y[1] (numeric) = -0.12254427134568084 " "
absolute error = 6.4254157550180930000000000000000E-15 " "
relative error = 5.243342413692436000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (closed_form) = -0.11769072147721739 " "
y[1] (numeric) = -0.11769072147722544 " "
absolute error = 8.049116928532385000000000000000E-15 " "
relative error = 6.839211135340466000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (closed_form) = -0.1128254026346879 " "
y[1] (numeric) = -0.11282540263469756 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 8.560962415098214000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (closed_form) = -0.1079488013459158 " "
y[1] (numeric) = -0.10794880134592708 " "
absolute error = 1.126876369994533900000000000000E-14 " "
relative error = 1.043898918695282700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (closed_form) = -0.10306140526696614 " "
y[1] (numeric) = -0.10306140526697906 " "
absolute error = 1.29202204490752600000000000000E-14 " "
relative error = 1.253642953500123400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (closed_form) = -9.81637031333739800E-2 " "
y[1] (numeric) = -9.81637031333885600E-2 " "
absolute error = 1.45716771982051800000000000000E-14 " "
relative error = 1.48442619146170500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (closed_form) = -9.3256184711271300E-2 " "
y[1] (numeric) = -9.3256184711287490E-2 " "
absolute error = 1.61953783717194700000000000000E-14 " "
relative error = 1.736654616727209600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (closed_form) = -8.83393407484107100E-2 " "
y[1] (numeric) = -8.83393407484285400E-2 " "
absolute error = 1.783295733304157700000000000000E-14 " "
relative error = 2.018688070565254300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (closed_form) = -8.34136629250911400E-2 " "
y[1] (numeric) = -8.34136629251106100E-2 " "
absolute error = 1.947053629436368300000000000000E-14 " "
relative error = 2.334214277563738400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (closed_form) = -7.84796438049902200E-2 " "
y[1] (numeric) = -7.84796438050113300E-2 " "
absolute error = 2.112199304349360300000000000000E-14 " "
relative error = 2.691397669436229000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (closed_form) = -7.35377767859082800E-2 " "
y[1] (numeric) = -7.35377767859310300E-2 " "
absolute error = 2.274569421700789500000000000000E-14 " "
relative error = 3.09306253345512500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (closed_form) = -6.85885560504290200E-2 " "
y[1] (numeric) = -6.85885560504534200E-2 " "
absolute error = 2.439715096613781500000000000000E-14 " "
relative error = 3.55702938959672250000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (closed_form) = -6.36324765165016300E-2 " "
y[1] (numeric) = -6.3632476516527700E-2 " "
absolute error = 2.60624855030755500000000000000E-14 " "
relative error = 4.09578362022682500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (closed_form) = -5.8670033787949500E-2 " "
y[1] (numeric) = -5.867003378797722000E-2 " "
absolute error = 2.77139422522054700000000000000E-14 " "
relative error = 4.723696316994070400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (closed_form) = -5.3701724104910100E-2 " "
y[1] (numeric) = -5.370172410493946000E-2 " "
absolute error = 2.93653990013353900000000000000E-14 " "
relative error = 5.46824138159289100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (closed_form) = -4.87280442942114870E-2 " "
y[1] (numeric) = -4.872804429424250000E-2 " "
absolute error = 3.10168557504653100000000000000E-14 " "
relative error = 6.36529871036705400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (closed_form) = -4.37494917196900150E-2 " "
y[1] (numeric) = -4.37494917197226940E-2 " "
absolute error = 3.26752513934991400000000000000E-14 " "
relative error = 7.46871566025376900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (closed_form) = -3.876656423245436500E-2 " "
y[1] (numeric) = -3.87665642324887100E-2 " "
absolute error = 3.43475248243407800000000000000E-14 " "
relative error = 8.86009000394879500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (closed_form) = -3.37797601211008300E-2 " "
y[1] (numeric) = -3.37797601211368400E-2 " "
absolute error = 3.601285936127851500000000000000E-14 " "
relative error = 1.06610761095318610000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (closed_form) = -2.878957806188488000E-2 " "
y[1] (numeric) = -2.878957806192256600E-2 " "
absolute error = 3.768166334516820400000000000000E-14 " "
relative error = 1.30886473098595830000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (closed_form) = -2.379651706885398400E-2 " "
y[1] (numeric) = -2.37965170688933300E-2 " "
absolute error = 3.93469978821059400000000000000E-14 " "
relative error = 1.653477177700310200000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (closed_form) = -1.880107644394656300E-2 " "
y[1] (numeric) = -1.880107644398758300E-2 " "
absolute error = 4.10192713129475800000000000000E-14 " "
relative error = 2.18175121170546970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (closed_form) = -1.380375572706225600E-2 " "
y[1] (numeric) = -1.380375572710494400E-2 " "
absolute error = 4.26880752968372700000000000000E-14 " "
relative error = 3.09249715373818960000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (closed_form) = -8.805054646108335000E-3 " "
y[1] (numeric) = -8.80505464615269000E-3 " "
absolute error = 4.43551445572509800000000000000E-14 " "
relative error = 5.0374638591090530000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (closed_form) = -3.805473067027323000E-3 " "
y[1] (numeric) = -3.8054730670733483000E-3 " "
absolute error = 4.60252495837476500000000000000E-14 " "
relative error = 1.2094488325915459000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.709999999999903 " "
y[1] (closed_form) = 1.194489056189175100E-3 " "
y[1] (numeric) = 1.1944890561414803000E-3 " "
absolute error = 4.76947040889408300000000000000E-14 " "
relative error = 3.992895861357081000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6999999999999 " "
y[1] (closed_form) = 6.194331731495458000E-3 " "
y[1] (numeric) = 6.194331731446093000E-3 " "
absolute error = 4.936502595587200000000000000E-14 " "
relative error = 7.9693868678153780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6899999999998965 " "
y[1] (closed_form) = 1.119355497879051700E-2 " "
y[1] (numeric) = 1.119355497873948100E-2 " "
absolute error = 5.103556466323766000000000000000E-14 " "
relative error = 4.5593705270523577000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.679999999999893 " "
y[1] (closed_form) = 1.619165887991562700E-2 " "
y[1] (numeric) = 1.619165887986292500E-2 " "
absolute error = 5.27043686471273500000000000000E-14 " "
relative error = 3.25503205310869240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.66999999999989 " "
y[1] (closed_form) = 2.11881436286457500E-2 " "
y[1] (numeric) = 2.118814362859137700E-2 " "
absolute error = 5.43731726310170400000000000000E-14 " "
relative error = 2.5662074782948940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6599999999998865 " "
y[1] (closed_form) = 2.618250958066973000E-2 " "
y[1] (numeric) = 2.618250958061369400E-2 " "
absolute error = 5.603850716795478000000000000000E-14 " "
relative error = 2.14030312851780290000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.649999999999883 " "
y[1] (closed_form) = 3.117425730355433700E-2 " "
y[1] (numeric) = 3.117425730349663000E-2 " "
absolute error = 5.77073111518444600000000000000E-14 " "
relative error = 1.8511206406596561000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.63999999999988 " "
y[1] (closed_form) = 3.61628876266870400E-2 " "
y[1] (numeric) = 3.616288762662766600E-2 " "
absolute error = 5.93761151357341500000000000000E-14 " "
relative error = 1.64190746459960540000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.629999999999876 " "
y[1] (closed_form) = 4.11479016911927060E-2 " "
y[1] (numeric) = 4.11479016911316700E-2 " "
absolute error = 6.10345107787679800000000000000E-14 " "
relative error = 1.4832958248228680000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.619999999999873 " "
y[1] (closed_form) = 4.612880099981906400E-2 " "
y[1] (numeric) = 4.61288009997563700E-2 " "
absolute error = 6.26929064218018100000000000000E-14 " "
relative error = 1.35908380584285530000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.60999999999987 " "
y[1] (closed_form) = 5.11050874667859700E-2 " "
y[1] (numeric) = 5.11050874667216200E-2 " "
absolute error = 6.43443631709317300000000000000E-14 " "
relative error = 1.2590598384700970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.599999999999866 " "
y[1] (closed_form) = 5.60762634675936300E-2 " "
y[1] (numeric) = 5.60762634675276300E-2 " "
absolute error = 6.60027588139655600000000000000E-14 " "
relative error = 1.1770177742336280000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.589999999999863 " "
y[1] (closed_form) = 6.104183188878458000E-2 " "
y[1] (numeric) = 6.10418318887169400E-2 " "
absolute error = 6.76472766691915700000000000000E-14 " "
relative error = 1.10821177176402230000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.57999999999986 " "
y[1] (closed_form) = 6.60012961776546900E-2 " "
y[1] (numeric) = 6.60012961775853900E-2 " "
absolute error = 6.92917945244175800000000000000E-14 " "
relative error = 1.04985505645079940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.569999999999856 " "
y[1] (closed_form) = 7.09541603919079200E-2 " "
y[1] (numeric) = 7.09541603918369700E-2 " "
absolute error = 7.0943251273547500000000000000E-14 " "
relative error = 9.9984625118104200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.559999999999853 " "
y[1] (closed_form) = 7.58999292492502100E-2 " "
y[1] (numeric) = 7.58999292491775900E-2 " "
absolute error = 7.26224635982930500000000000000E-14 " "
relative error = 9.56818594122872200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.54999999999985 " "
y[1] (closed_form) = 8.0838108176917300E-2 " "
y[1] (numeric) = 8.08381081768430300E-2 " "
absolute error = 7.42739203474229700000000000000E-14 " "
relative error = 9.18798349224992300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.539999999999846 " "
y[1] (closed_form) = 8.57682033611315800E-2 " "
y[1] (numeric) = 8.57682033610556700E-2 " "
absolute error = 7.59114993087450800000000000000E-14 " "
relative error = 8.85077410204288200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.529999999999843 " "
y[1] (closed_form) = 9.06897217964829900E-2 " "
y[1] (numeric) = 9.06897217964054500E-2 " "
absolute error = 7.75352004822593700000000000000E-14 " "
relative error = 8.54950251763438900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.51999999999984 " "
y[1] (closed_form) = 9.56021713352292800E-2 " "
y[1] (numeric) = 9.5602171335150100E-2 " "
absolute error = 7.91727794435814800000000000000E-14 " "
relative error = 8.28148339497038400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.509999999999836 " "
y[1] (closed_form) = 0.10050506073651022 " "
y[1] (numeric) = 0.10050506073642941 " "
absolute error = 8.08103584049035800000000000000E-14 " "
relative error = 8.04042680166729200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.499999999999833 " "
y[1] (closed_form) = 0.10539789971547146 " "
y[1] (numeric) = 0.10539789971538904 " "
absolute error = 8.24201817906100600000000000000E-14 " "
relative error = 7.81990741875395300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.48999999999983 " "
y[1] (closed_form) = 0.11028019899229244 " "
y[1] (numeric) = 0.11028019899220838 " "
absolute error = 8.40577607519321600000000000000E-14 " "
relative error = 7.62219886434980200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.479999999999826 " "
y[1] (closed_form) = 0.11515147034111403 " "
y[1] (numeric) = 0.11515147034102834 " "
absolute error = 8.56953397132542700000000000000E-14 " "
relative error = 7.44196660792939400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.469999999999823 " "
y[1] (closed_form) = 0.12001122663886075 " "
y[1] (numeric) = 0.12001122663877342 " "
absolute error = 8.73329186745763800000000000000E-14 " "
relative error = 7.27706241495053400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.45999999999982 " "
y[1] (closed_form) = 0.1248589819139526 " "
y[1] (numeric) = 0.12485898191386367 " "
absolute error = 8.89288642724750400000000000000E-14 " "
relative error = 7.12234417654958500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.449999999999816 " "
y[1] (closed_form) = 0.12969425139490184 " "
y[1] (numeric) = 0.1296942513948113 " "
absolute error = 9.05386876581815200000000000000E-14 " "
relative error = 6.98093297770794700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.439999999999813 " "
y[1] (closed_form) = 0.13451655155878978 " "
y[1] (numeric) = 0.1345165515586976 " "
absolute error = 9.21762666195036200000000000000E-14 " "
relative error = 6.85241076665710200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.42999999999981 " "
y[1] (closed_form) = 0.13932540017961856 " "
y[1] (numeric) = 0.1393254001795248 " "
absolute error = 9.37583344295944700000000000000E-14 " "
relative error = 6.7294502157338900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.419999999999806 " "
y[1] (closed_form) = 0.1441203163765335 " "
y[1] (numeric) = 0.14412031637643816 " "
absolute error = 9.53404022396853200000000000000E-14 " "
relative error = 6.61533395406903100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.409999999999803 " "
y[1] (closed_form) = 0.14890082066191063 " "
y[1] (numeric) = 0.14890082066181368 " "
absolute error = 9.6950225625391800000000000000E-14 " "
relative error = 6.51106052971486500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.3999999999998 " "
y[1] (closed_form) = 0.15366643498930518 " "
y[1] (numeric) = 0.15366643498920662 " "
absolute error = 9.85600490110982700000000000000E-14 " "
relative error = 6.41389572276846300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.389999999999796 " "
y[1] (closed_form) = 0.1584166828012557 " "
y[1] (numeric) = 0.15841668280115562 " "
absolute error = 1.00086605669957860000000000000E-13 " "
relative error = 6.3179334335338400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.379999999999793 " "
y[1] (closed_form) = 0.16315108907693956 " "
y[1] (numeric) = 0.16315108907683787 " "
absolute error = 1.01696429055664340000000000000E-13 " "
relative error = 6.23326694483209100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.36999999999979 " "
y[1] (closed_form) = 0.16786918037967452 " "
y[1] (numeric) = 0.16786918037957121 " "
absolute error = 1.03306252441370820000000000000E-13 " "
relative error = 6.1539737197572610000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.359999999999786 " "
y[1] (closed_form) = 0.172570484904262 " "
y[1] (numeric) = 0.1725704849041571 " "
absolute error = 1.04888320251461660000000000000E-13 " "
relative error = 6.07799881362396500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.349999999999783 " "
y[1] (closed_form) = 0.1772545325241673 " "
y[1] (numeric) = 0.17725453252406084 " "
absolute error = 1.06470388061552510000000000000E-13 " "
relative error = 6.0066383942557900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.33999999999978 " "
y[1] (closed_form) = 0.1819208548385318 " "
y[1] (numeric) = 0.1819208548384238 " "
absolute error = 1.0799694472041210000000000000E-13 " "
relative error = 5.93647962001208600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.329999999999776 " "
y[1] (closed_form) = 0.18656898521901263 " "
y[1] (numeric) = 0.18656898521890306 " "
absolute error = 1.09579012530502950000000000000E-13 " "
relative error = 5.87337774292273400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.319999999999773 " "
y[1] (closed_form) = 0.19119845885644518 " "
y[1] (numeric) = 0.19119845885633405 " "
absolute error = 1.11133324764978170000000000000E-13 " "
relative error = 5.81245923370223500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.30999999999977 " "
y[1] (closed_form) = 0.1958088128073236 " "
y[1] (numeric) = 0.1958088128072109 " "
absolute error = 1.12687636999453390000000000000E-13 " "
relative error = 5.754982903161684000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.299999999999766 " "
y[1] (closed_form) = 0.20039958604009472 " "
y[1] (numeric) = 0.2003995860399805 " "
absolute error = 1.14214193658312980000000000000E-13 " "
relative error = 5.69932283370394300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.289999999999763 " "
y[1] (closed_form) = 0.20497031948126096 " "
y[1] (numeric) = 0.2049703194811452 " "
absolute error = 1.1576850589278820000000000000E-13 " "
relative error = 5.648061933346019000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.2799999999997596 " "
y[1] (closed_form) = 0.20952055606128706 " "
y[1] (numeric) = 0.2095205560611698 " "
absolute error = 1.17267306976032160000000000000E-13 " "
relative error = 5.59693565063516800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.269999999999756 " "
y[1] (closed_form) = 0.2140498407603069 " "
y[1] (numeric) = 0.21404984076018813 " "
absolute error = 1.18766108059276120000000000000E-13 " "
relative error = 5.54852587777771100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.259999999999753 " "
y[1] (closed_form) = 0.21855772065362497 " "
y[1] (numeric) = 0.2185577206535047 " "
absolute error = 1.20264909142520080000000000000E-13 " "
relative error = 5.50266120926098700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.2499999999997495 " "
y[1] (closed_form) = 0.2230437449570085 " "
y[1] (numeric) = 0.22304374495688672 " "
absolute error = 1.21763710225764040000000000000E-13 " "
relative error = 5.45918515891283600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.239999999999746 " "
y[1] (closed_form) = 0.22750746507176545 " "
y[1] (numeric) = 0.22750746507164218 " "
absolute error = 1.232625113090080000000000000E-13 " "
relative error = 5.417954583166130000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.229999999999743 " "
y[1] (closed_form) = 0.23194843462960416 " "
y[1] (numeric) = 0.2319484346294794 " "
absolute error = 1.24761312392251970000000000000E-13 " "
relative error = 5.37883830048182500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.2199999999997395 " "
y[1] (closed_form) = 0.2363662095372696 " "
y[1] (numeric) = 0.23636620953714335 " "
absolute error = 1.26260113475495930000000000000E-13 " "
relative error = 5.34171587904520500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.209999999999736 " "
y[1] (closed_form) = 0.24076034802095247 " "
y[1] (numeric) = 0.2407603480208248 " "
absolute error = 1.276756478318930000000000000E-13 " "
relative error = 5.30301807923877400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.199999999999733 " "
y[1] (closed_form) = 0.2451304106704662 " "
y[1] (numeric) = 0.24513041067033703 " "
absolute error = 1.29174448915136960000000000000E-13 " "
relative error = 5.269621527652429000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.1899999999997295 " "
y[1] (closed_form) = 0.24947596048318754 " "
y[1] (numeric) = 0.2494759604830569 " "
absolute error = 1.3064549442276530000000000000E-13 " "
relative error = 5.23679693104416900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.179999999999726 " "
y[1] (closed_form) = 0.2537965629077565 " "
y[1] (numeric) = 0.2537965629076243 " "
absolute error = 1.32172051081624900000000000000E-13 " "
relative error = 5.207795155589378000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.169999999999723 " "
y[1] (closed_form) = 0.25809178588753107 " "
y[1] (numeric) = 0.25809178588739745 " "
absolute error = 1.3361534101363760000000000000E-13 " "
relative error = 5.17704740405273000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.1599999999997195 " "
y[1] (closed_form) = 0.26236119990379264 " "
y[1] (numeric) = 0.2623611999036576 " "
absolute error = 1.3505863094565030000000000000E-13 " "
relative error = 5.147812671811840000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.149999999999716 " "
y[1] (closed_form) = 0.2666043780186974 " "
y[1] (numeric) = 0.266604378018561 " "
absolute error = 1.36390898575200480000000000000E-13 " "
relative error = 5.11585367010121500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.139999999999713 " "
y[1] (closed_form) = 0.2708208959179699 " "
y[1] (numeric) = 0.27082089591783204 " "
absolute error = 1.37834188507213180000000000000E-13 " "
relative error = 5.08949606861068700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.1299999999997095 " "
y[1] (closed_form) = 0.27501033195333385 " "
y[1] (numeric) = 0.27501033195319463 " "
absolute error = 1.39221967287994630000000000000E-13 " "
relative error = 5.06242679317295700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.119999999999706 " "
y[1] (closed_form) = 0.27917226718467697 " "
y[1] (numeric) = 0.27917226718453636 " "
absolute error = 1.40609746068776080000000000000E-13 " "
relative error = 5.03666597999723500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.109999999999703 " "
y[1] (closed_form) = 0.2833062854219444 " "
y[1] (numeric) = 0.2833062854218025 " "
absolute error = 1.41942013698326260000000000000E-13 " "
relative error = 5.01019641999554700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.099999999999700 " "
y[1] (closed_form) = 0.28741197326675744 " "
y[1] (numeric) = 0.28741197326661416 " "
absolute error = 1.43274281327876450000000000000E-13 " "
relative error = 4.984979564330760000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.089999999999696 " "
y[1] (closed_form) = 0.29148892015375294 " "
y[1] (numeric) = 0.2914889201536083 " "
absolute error = 1.4466206010865790000000000000E-13 " "
relative error = 4.96286651418353600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.079999999999693 " "
y[1] (closed_form) = 0.29553671839163964 " "
y[1] (numeric) = 0.29553671839149365 " "
absolute error = 1.45994327738208090000000000000E-13 " "
relative error = 4.93997255341852900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.069999999999690 " "
y[1] (closed_form) = 0.29955496320396696 " "
y[1] (numeric) = 0.2995549632038196 " "
absolute error = 1.47382106518989530000000000000E-13 " "
relative error = 4.92003554014349750000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.059999999999686 " "
y[1] (closed_form) = 0.30354325276960215 " "
y[1] (numeric) = 0.30354325276945354 " "
absolute error = 1.4860335184607720000000000000E-13 " "
relative error = 4.8956236216810700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.049999999999683 " "
y[1] (closed_form) = 0.30750118826291223 " "
y[1] (numeric) = 0.3075011882627623 " "
absolute error = 1.4993561947562740000000000000E-13 " "
relative error = 4.875936262966016300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.039999999999680 " "
y[1] (closed_form) = 0.31142837389364614 " "
y[1] (numeric) = 0.31142837389349487 " "
absolute error = 1.51267887105177580000000000000E-13 " "
relative error = 4.85722881360951650000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.029999999999676 " "
y[1] (closed_form) = 0.3153244169465135 " "
y[1] (numeric) = 0.31532441694636093 " "
absolute error = 1.5254464358349650000000000000E-13 " "
relative error = 4.83770476960468700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.019999999999673 " "
y[1] (closed_form) = 0.31918892782045555 " "
y[1] (numeric) = 0.3191889278203018 " "
absolute error = 1.53765888910584180000000000000E-13 " "
relative error = 4.81739419849418500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.009999999999670 " "
y[1] (closed_form) = 0.3230215200676055 " "
y[1] (numeric) = 0.3230215200674505 " "
absolute error = 1.54987134237671850000000000000E-13 " "
relative error = 4.79804361657497200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9999999999996665 " "
y[1] (closed_form) = 0.32682181043193215 " "
y[1] (numeric) = 0.32682181043177616 " "
absolute error = 1.5598633495983450000000000000E-13 " "
relative error = 4.77282512919443240000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9899999999996676 " "
y[1] (closed_form) = 0.3305894188875647 " "
y[1] (numeric) = 0.33058941888740917 " "
absolute error = 1.55542245749984430000000000000E-13 " "
relative error = 4.70499770601808700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9799999999996687 " "
y[1] (closed_form) = 0.3343239686767988 " "
y[1] (numeric) = 0.3343239686766437 " "
absolute error = 1.55098156540134370000000000000E-13 " "
relative error = 4.639157555887729600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.96999999999967 " "
y[1] (closed_form) = 0.33802508634776757 " "
y[1] (numeric) = 0.3380250863476129 " "
absolute error = 1.5465406733028430000000000000E-13 " "
relative error = 4.57522454919729900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.959999999999671 " "
y[1] (closed_form) = 0.3416924017917882 " "
y[1] (numeric) = 0.341692401791634 " "
absolute error = 1.54209978120434240000000000000E-13 " "
relative error = 4.51312283538580900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.949999999999672 " "
y[1] (closed_form) = 0.34532554828037243 " "
y[1] (numeric) = 0.3453255482802186 " "
absolute error = 1.53821400061815440000000000000E-13 " "
relative error = 4.454388064474358000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.939999999999673 " "
y[1] (closed_form) = 0.34892416250189895 " "
y[1] (numeric) = 0.34892416250174546 " "
absolute error = 1.5348833315442790000000000000E-13 " "
relative error = 4.398902387666906400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.929999999999674 " "
y[1] (closed_form) = 0.35248788459794445 " "
y[1] (numeric) = 0.35248788459779135 " "
absolute error = 1.53099755095809100000000000000E-13 " "
relative error = 4.3434047462493100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9199999999996753 " "
y[1] (closed_form) = 0.3560163581992691 " "
y[1] (numeric) = 0.3560163581991163 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 4.29100193488623700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9099999999996764 " "
y[1] (closed_form) = 0.35950923046145306 " "
y[1] (numeric) = 0.3595092304613007 " "
absolute error = 1.52378110129802740000000000000E-13 " "
relative error = 4.238503415731933000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8999999999996775 " "
y[1] (closed_form) = 0.36296615210018096 " "
y[1] (numeric) = 0.362966152100029 " "
absolute error = 1.51934020919952670000000000000E-13 " "
relative error = 4.18590053206994100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8899999999996786 " "
y[1] (closed_form) = 0.36638677742616965 " "
y[1] (numeric) = 0.36638677742601805 " "
absolute error = 1.51600954012565130000000000000E-13 " "
relative error = 4.13772994422851760000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8799999999996797 " "
y[1] (closed_form) = 0.369770764379737 " "
y[1] (numeric) = 0.3697707643795859 " "
absolute error = 1.5110135365148380000000000000E-13 " "
relative error = 4.08635209181410300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.869999999999681 " "
y[1] (closed_form) = 0.37311777456500766 " "
y[1] (numeric) = 0.3731177745648569 " "
absolute error = 1.50768286744096260000000000000E-13 " "
relative error = 4.040769350103104500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.859999999999682 " "
y[1] (closed_form) = 0.3764274732837523 " "
y[1] (numeric) = 0.3764274732836019 " "
absolute error = 1.5043521983670870000000000000E-13 " "
relative error = 3.996393210208387700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.849999999999683 " "
y[1] (closed_form) = 0.3796995295688571 " "
y[1] (numeric) = 0.379699529568707 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 3.95318248352216350000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.839999999999684 " "
y[1] (closed_form) = 0.3829336162174202 " "
y[1] (numeric) = 0.38293361621727057 " "
absolute error = 1.4965806371947110000000000000E-13 " "
relative error = 3.90819863760665400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.829999999999685 " "
y[1] (closed_form) = 0.3861294098234719 " "
y[1] (numeric) = 0.3861294098233225 " "
absolute error = 1.4938050796331480000000000000E-13 " "
relative error = 3.86866434316949900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8199999999996863 " "
y[1] (closed_form) = 0.38928659081031464 " "
y[1] (numeric) = 0.38928659081016564 " "
absolute error = 1.489919299046960000000000000E-13 " "
relative error = 3.82730701292751200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8099999999996874 " "
y[1] (closed_form) = 0.3924048434624808 " "
y[1] (numeric) = 0.3924048434623321 " "
absolute error = 1.48658862997308460000000000000E-13 " "
relative error = 3.78840540513160800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7999999999996885 " "
y[1] (closed_form) = 0.3954838559573036 " "
y[1] (numeric) = 0.3954838559571553 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 3.75048927675910300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7899999999996896 " "
y[1] (closed_form) = 0.39852332039609956 " "
y[1] (numeric) = 0.39852332039595156 " "
absolute error = 1.47992729182533370000000000000E-13 " "
relative error = 3.71352745519235140000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7799999999996907 " "
y[1] (closed_form) = 0.40152293283495755 " "
y[1] (numeric) = 0.4015229328348099 " "
absolute error = 1.47659662275145820000000000000E-13 " "
relative error = 3.67749013070294600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.769999999999692 " "
y[1] (closed_form) = 0.40448239331513336 " "
y[1] (numeric) = 0.40448239331498603 " "
absolute error = 1.47326595367758270000000000000E-13 " "
relative error = 3.642348784585432400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.759999999999693 " "
y[1] (closed_form) = 0.4074014058930452 " "
y[1] (numeric) = 0.40740140589289825 " "
absolute error = 1.46938017309139470000000000000E-13 " "
relative error = 3.60671355532128500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.749999999999694 " "
y[1] (closed_form) = 0.4102796786698678 " "
y[1] (numeric) = 0.41027967866972115 " "
absolute error = 1.46660461552983180000000000000E-13 " "
relative error = 3.574646008022097600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.739999999999695 " "
y[1] (closed_form) = 0.413116923820722 " "
y[1] (numeric) = 0.4131169238205757 " "
absolute error = 1.46327394645595630000000000000E-13 " "
relative error = 3.542033410112641600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7299999999996962 " "
y[1] (closed_form) = 0.41591285762345714 " "
y[1] (numeric) = 0.41591285762331104 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 3.51288370538776930000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7199999999996973 " "
y[1] (closed_form) = 0.4186672004870228 " "
y[1] (numeric) = 0.418667200486877 " "
absolute error = 1.45772283133283050000000000000E-13 " "
relative error = 3.48181760987511300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7099999999996984 " "
y[1] (closed_form) = 0.4213796769794279 " "
y[1] (numeric) = 0.42137967697928236 " "
absolute error = 1.45550238528358020000000000000E-13 " "
relative error = 3.45413522483344400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6999999999996995 " "
y[1] (closed_form) = 0.4240500158552837 " "
y[1] (numeric) = 0.4240500158551384 " "
absolute error = 1.45272682772201730000000000000E-13 " "
relative error = 3.425838399727338400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6899999999997006 " "
y[1] (closed_form) = 0.42667795008292775 " "
y[1] (numeric) = 0.42667795008278275 " "
absolute error = 1.44995127016045440000000000000E-13 " "
relative error = 3.398233421433300400000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6799999999997017 " "
y[1] (closed_form) = 0.42926321687112734 " "
y[1] (numeric) = 0.4292632168709826 " "
absolute error = 1.44717571259889160000000000000E-13 " "
relative error = 3.371301466608913600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.669999999999703 " "
y[1] (closed_form) = 0.43180555769535794 " "
y[1] (numeric) = 0.4318055576952135 " "
absolute error = 1.44440015503732870000000000000E-13 " "
relative error = 3.345024465980504500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.659999999999704 " "
y[1] (closed_form) = 0.4343047183236558 " "
y[1] (numeric) = 0.4343047183235116 " "
absolute error = 1.44217970898807830000000000000E-13 " "
relative error = 3.32066323054157200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.649999999999705 " "
y[1] (closed_form) = 0.43676044884204074 " "
y[1] (numeric) = 0.43676044884189674 " "
absolute error = 1.4399592629388280000000000000E-13 " "
relative error = 3.29690856110372200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.639999999999706 " "
y[1] (closed_form) = 0.4391725036795072 " "
y[1] (numeric) = 0.43917250367936356 " "
absolute error = 1.43662859386495260000000000000E-13 " "
relative error = 3.27121707718148500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6299999999997072 " "
y[1] (closed_form) = 0.4415406416325817 " "
y[1] (numeric) = 0.4415406416324383 " "
absolute error = 1.43440814781570230000000000000E-13 " "
relative error = 3.24864352806125900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6199999999997083 " "
y[1] (closed_form) = 0.4438646258894422 " "
y[1] (numeric) = 0.4438646258892991 " "
absolute error = 1.43107747874182680000000000000E-13 " "
relative error = 3.224130501217908300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6099999999997094 " "
y[1] (closed_form) = 0.44614422405359977 " "
y[1] (numeric) = 0.4461442240534569 " "
absolute error = 1.42885703269257650000000000000E-13 " "
relative error = 3.20267966199404060000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5999999999997105 " "
y[1] (closed_form) = 0.44837920816713756 " "
y[1] (numeric) = 0.448379208166995 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 3.17928739257535450000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5899999999997116 " "
y[1] (closed_form) = 0.45056935473350673 " "
y[1] (numeric) = 0.45056935473336435 " "
absolute error = 1.42386102908176330000000000000E-13 " "
relative error = 3.16013731098937770000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5799999999997127 " "
y[1] (closed_form) = 0.4527144447398758 " "
y[1] (numeric) = 0.45271444473973366 " "
absolute error = 1.4216405830325130000000000000E-13 " "
relative error = 3.140258941482130000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.569999999999714 " "
y[1] (closed_form) = 0.45481426367903166 " "
y[1] (numeric) = 0.45481426367888966 " "
absolute error = 1.41997524849557520000000000000E-13 " "
relative error = 3.1220991993726700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.559999999999715 " "
y[1] (closed_form) = 0.45686860157083026 " "
y[1] (numeric) = 0.4568686015706884 " "
absolute error = 1.41830991395863750000000000000E-13 " "
relative error = 3.104415381319985400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.549999999999716 " "
y[1] (closed_form) = 0.4588772529831943 " "
y[1] (numeric) = 0.4588772529830527 " "
absolute error = 1.41608946790938720000000000000E-13 " "
relative error = 3.0859875025473300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.539999999999717 " "
y[1] (closed_form) = 0.46084001705265654 " "
y[1] (numeric) = 0.4608400170525152 " "
absolute error = 1.41331391034782430000000000000E-13 " "
relative error = 3.066821148447132500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5299999999997183 " "
y[1] (closed_form) = 0.4627566975044456 " "
y[1] (numeric) = 0.4627566975043044 " "
absolute error = 1.41164857581088650000000000000E-13 " "
relative error = 3.05052003228397430000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5199999999997194 " "
y[1] (closed_form) = 0.4646271026721135 " "
y[1] (numeric) = 0.46462710267197255 " "
absolute error = 1.40942812976163620000000000000E-13 " "
relative error = 3.03346085851618300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5099999999997205 " "
y[1] (closed_form) = 0.46645104551670213 " "
y[1] (numeric) = 0.4664510455165614 " "
absolute error = 1.4072076837123860000000000000E-13 " "
relative error = 3.0168389528499800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4999999999997216 " "
y[1] (closed_form) = 0.468228343645447 " "
y[1] (numeric) = 0.4682283436453065 " "
absolute error = 1.40498723766313560000000000000E-13 " "
relative error = 3.000645425957005300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4899999999997227 " "
y[1] (closed_form) = 0.4699588193300164 " "
y[1] (numeric) = 0.46995881932987604 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 2.98605291656576300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4799999999997238 " "
y[1] (closed_form) = 0.47164229952428377 " "
y[1] (numeric) = 0.4716422995241436 " "
absolute error = 1.40165656858926000000000000000E-13 " "
relative error = 2.971863571191608600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.469999999999725 " "
y[1] (closed_form) = 0.47327861588163267 " "
y[1] (numeric) = 0.47327861588149267 " "
absolute error = 1.39999123405232240000000000000E-13 " "
relative error = 2.958069912887129600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.459999999999726 " "
y[1] (closed_form) = 0.47486760477179096 " "
y[1] (numeric) = 0.47486760477165124 " "
absolute error = 1.39721567649075950000000000000E-13 " "
relative error = 2.94232679266934800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.449999999999727 " "
y[1] (closed_form) = 0.47640910729719377 " "
y[1] (numeric) = 0.4764091072970542 " "
absolute error = 1.39555034195382180000000000000E-13 " "
relative error = 2.9293107973337900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.439999999999728 " "
y[1] (closed_form) = 0.47790296930887316 " "
y[1] (numeric) = 0.4779029693087337 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 2.91783104203304670000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4299999999997293 " "
y[1] (closed_form) = 0.4793490414218728 " "
y[1] (numeric) = 0.4793490414217335 " "
absolute error = 1.3927747843922590000000000000E-13 " "
relative error = 2.905554541761322700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4199999999997304 " "
y[1] (closed_form) = 0.4807471790301865 " "
y[1] (numeric) = 0.48074717903004743 " "
absolute error = 1.39055433834300860000000000000E-13 " "
relative error = 2.892485695180116000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4099999999997315 " "
y[1] (closed_form) = 0.4820972423212185 " "
y[1] (numeric) = 0.48209724232107953 " "
absolute error = 1.38944411531838340000000000000E-13 " "
relative error = 2.882082686531123300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3999999999997326 " "
y[1] (closed_form) = 0.4833990962897647 " "
y[1] (numeric) = 0.48339909628962585 " "
absolute error = 1.38833389229375830000000000000E-13 " "
relative error = 2.87202417826107600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3899999999997337 " "
y[1] (closed_form) = 0.48465261075151317 " "
y[1] (numeric) = 0.48465261075137445 " "
absolute error = 1.3872236692691330000000000000E-13 " "
relative error = 2.862305161460026400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3799999999997348 " "
y[1] (closed_form) = 0.48585766035606237 " "
y[1] (numeric) = 0.4858576603559237 " "
absolute error = 1.38666855775682050000000000000E-13 " "
relative error = 2.854063382968164000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.369999999999736 " "
y[1] (closed_form) = 0.487014124599456 " "
y[1] (numeric) = 0.4870141245993175 " "
absolute error = 1.38500322321988280000000000000E-13 " "
relative error = 2.843866642182044700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.359999999999737 " "
y[1] (closed_form) = 0.48812188783623345 " "
y[1] (numeric) = 0.48812188783609506 " "
absolute error = 1.38389300019525760000000000000E-13 " "
relative error = 2.835138178969672000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.349999999999738 " "
y[1] (closed_form) = 0.48918083929099415 " "
y[1] (numeric) = 0.4891808392908558 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 2.82786605192451700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.339999999999739 " "
y[1] (closed_form) = 0.4901908730694751 " "
y[1] (numeric) = 0.4901908730693369 " "
absolute error = 1.382227665658320000000000000E-13 " "
relative error = 2.81977438095306100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3299999999997403 " "
y[1] (closed_form) = 0.4911518881691402 " "
y[1] (numeric) = 0.49115188816900207 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.811996606145741000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3199999999997414 " "
y[1] (closed_form) = 0.49206378848928023 " "
y[1] (numeric) = 0.4920637884891422 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.8056572408222596000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3099999999997425 " "
y[1] (closed_form) = 0.4929264828406231 " "
y[1] (numeric) = 0.4929264828404851 " "
absolute error = 1.38000721960906960000000000000E-13 " "
relative error = 2.799620770335572400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2999999999997436 " "
y[1] (closed_form) = 0.49373988495445265 " "
y[1] (numeric) = 0.49373988495431476 " "
absolute error = 1.37889699658444440000000000000E-13 " "
relative error = 2.792759990843452500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2899999999997447 " "
y[1] (closed_form) = 0.49450391349123535 " "
y[1] (numeric) = 0.49450391349109746 " "
absolute error = 1.37889699658444440000000000000E-13 " "
relative error = 2.788445063759610000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.279999999999746 " "
y[1] (closed_form) = 0.49521849204875407 " "
y[1] (numeric) = 0.49521849204861634 " "
absolute error = 1.37723166204750670000000000000E-13 " "
relative error = 2.781058632018771300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.269999999999747 " "
y[1] (closed_form) = 0.4958835491697487 " "
y[1] (numeric) = 0.495883549169611 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.776209359717912000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.259999999999748 " "
y[1] (closed_form) = 0.49649901834906124 " "
y[1] (numeric) = 0.4964990183489236 " "
absolute error = 1.37612143902288150000000000000E-13 " "
relative error = 2.771649868712139400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.249999999999749 " "
y[1] (closed_form) = 0.49706483804028667 " "
y[1] (numeric) = 0.49706483804014906 " "
absolute error = 1.37612143902288150000000000000E-13 " "
relative error = 2.768494839523024000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.23999999999975 " "
y[1] (closed_form) = 0.49758095166192745 " "
y[1] (numeric) = 0.4975809516617899 " "
absolute error = 1.3755663275105690000000000000E-13 " "
relative error = 2.764507610100744300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2299999999997513 " "
y[1] (closed_form) = 0.49804730760305144 " "
y[1] (numeric) = 0.4980473076029139 " "
absolute error = 1.3755663275105690000000000000E-13 " "
relative error = 2.761919011530745000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2199999999997524 " "
y[1] (closed_form) = 0.49846385922845315 " "
y[1] (numeric) = 0.4984638592283156 " "
absolute error = 1.3755663275105690000000000000E-13 " "
relative error = 2.759610956829925400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2099999999997535 " "
y[1] (closed_form) = 0.49883056488331723 " "
y[1] (numeric) = 0.4988305648831797 " "
absolute error = 1.3755663275105690000000000000E-13 " "
relative error = 2.757582282136884500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1999999999997546 " "
y[1] (closed_form) = 0.4991473878973837 " "
y[1] (numeric) = 0.4991473878972461 " "
absolute error = 1.37612143902288150000000000000E-13 " "
relative error = 2.75694408583339900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1899999999997557 " "
y[1] (closed_form) = 0.49941429658861525 " "
y[1] (numeric) = 0.4994142965884776 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.75658218024385100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.179999999999757 " "
y[1] (closed_form) = 0.4996312642663651 " "
y[1] (numeric) = 0.4996312642662275 " "
absolute error = 1.37612143902288150000000000000E-13 " "
relative error = 2.754274076590289600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.169999999999758 " "
y[1] (closed_form) = 0.49979826923404636 " "
y[1] (numeric) = 0.4997982692339087 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.754464421505472500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.159999999999759 " "
y[1] (closed_form) = 0.49991529479130137 " "
y[1] (numeric) = 0.4999152947911637 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.753819626802801500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.14999999999976 " "
y[1] (closed_form) = 0.499982329235672 " "
y[1] (numeric) = 0.49998232923553426 " "
absolute error = 1.37723166204750670000000000000E-13 " "
relative error = 2.754560674480025000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.139999999999761 " "
y[1] (closed_form) = 0.4999993658637696 " "
y[1] (numeric) = 0.4999993658636319 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.7533565930767300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1299999999997623 " "
y[1] (closed_form) = 0.49996640297194556 " "
y[1] (numeric) = 0.49996640297180794 " "
absolute error = 1.37612143902288150000000000000E-13 " "
relative error = 2.75242782483546100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1199999999997634 " "
y[1] (closed_form) = 0.4998834438564616 " "
y[1] (numeric) = 0.499883443856324 " "
absolute error = 1.37612143902288150000000000000E-13 " "
relative error = 2.752884609273089000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1099999999997645 " "
y[1] (closed_form) = 0.4997504968131602 " "
y[1] (numeric) = 0.49975049681302236 " "
absolute error = 1.37834188507213180000000000000E-13 " "
relative error = 2.758060059693041600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0999999999997656 " "
y[1] (closed_form) = 0.49956757513663486 " "
y[1] (numeric) = 0.4995675751364969 " "
absolute error = 1.3794521080967570000000000000E-13 " "
relative error = 2.76129231910111100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0899999999997667 " "
y[1] (closed_form) = 0.49933469711890077 " "
y[1] (numeric) = 0.4993346971187627 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.764803525745467300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.079999999999768 " "
y[1] (closed_form) = 0.4990518860475657 " "
y[1] (numeric) = 0.4990518860474276 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.766370330859340700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.069999999999769 " "
y[1] (closed_form) = 0.498719170203501 " "
y[1] (numeric) = 0.498719170203363 " "
absolute error = 1.38000721960906960000000000000E-13 " "
relative error = 2.76710281468819700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.05999999999977 " "
y[1] (closed_form) = 0.4983365828580139 " "
y[1] (numeric) = 0.4983365828578758 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.77145505696739700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.049999999999771 " "
y[1] (closed_form) = 0.49790416226952017 " "
y[1] (numeric) = 0.49790416226938206 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.77386201460610200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.039999999999772 " "
y[1] (closed_form) = 0.4974219516797182 " "
y[1] (numeric) = 0.49742195167958 " "
absolute error = 1.382227665658320000000000000E-13 " "
relative error = 2.778783005033749000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0299999999997733 " "
y[1] (closed_form) = 0.4968899993092652 " "
y[1] (numeric) = 0.49688999930912686 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 2.783992212775353000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0199999999997744 " "
y[1] (closed_form) = 0.4963083583529549 " "
y[1] (numeric) = 0.49630835835281645 " "
absolute error = 1.38444811170757020000000000000E-13 " "
relative error = 2.78949183185628600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0099999999997755 " "
y[1] (closed_form) = 0.4956770869743982 " "
y[1] (numeric) = 0.49567708697425966 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 2.795284210512154500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9999999999997766 " "
y[1] (closed_form) = 0.49499624830020694 " "
y[1] (numeric) = 0.49499624830006844 " "
absolute error = 1.38500322321988280000000000000E-13 " "
relative error = 2.798007516169903600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9899999999997777 " "
y[1] (closed_form) = 0.49426591041368123 " "
y[1] (numeric) = 0.4942659104135427 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 2.803265014923924700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.979999999999779 " "
y[1] (closed_form) = 0.493486146348001 " "
y[1] (numeric) = 0.49348614634786236 " "
absolute error = 1.3861134462445080000000000000E-13 " "
relative error = 2.808819369099444000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.96999999999978 " "
y[1] (closed_form) = 0.4926570340789231 " "
y[1] (numeric) = 0.49265703407878436 " "
absolute error = 1.3872236692691330000000000000E-13 " "
relative error = 2.815799985202081500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.959999999999781 " "
y[1] (closed_form) = 0.49177865651698344 " "
y[1] (numeric) = 0.49177865651684466 " "
absolute error = 1.38777878078144570000000000000E-13 " "
relative error = 2.82195813582145400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.949999999999782 " "
y[1] (closed_form) = 0.4908511014992063 " "
y[1] (numeric) = 0.49085110149906747 " "
absolute error = 1.38833389229375830000000000000E-13 " "
relative error = 2.82842167014267800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9399999999997832 " "
y[1] (closed_form) = 0.48987446178032046 " "
y[1] (numeric) = 0.48987446178018146 " "
absolute error = 1.3899992268306960000000000000E-13 " "
relative error = 2.837460074524211000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9299999999997843 " "
y[1] (closed_form) = 0.4888488350234839 " "
y[1] (numeric) = 0.4888488350233448 " "
absolute error = 1.39110944985532110000000000000E-13 " "
relative error = 2.84568428968127400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9199999999997854 " "
y[1] (closed_form) = 0.48777432379051777 " "
y[1] (numeric) = 0.4877743237903784 " "
absolute error = 1.3938850074168840000000000000E-13 " "
relative error = 2.85764325720332400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9099999999997865 " "
y[1] (closed_form) = 0.4866510355316498 " "
y[1] (numeric) = 0.48665103553151023 " "
absolute error = 1.39555034195382180000000000000E-13 " "
relative error = 2.867661301550977000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8999999999997876 " "
y[1] (closed_form) = 0.48547908257476985 " "
y[1] (numeric) = 0.4854790825746302 " "
absolute error = 1.3966605649784470000000000000E-13 " "
relative error = 2.876870734720776700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8899999999997887 " "
y[1] (closed_form) = 0.484258582114197 " "
y[1] (numeric) = 0.4842585821140572 " "
absolute error = 1.3977707880030720000000000000E-13 " "
relative error = 2.886414076340421700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.87999999999979 " "
y[1] (closed_form) = 0.4829896561989602 " "
y[1] (numeric) = 0.48298965619882034 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 2.896296003596916500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.869999999999791 " "
y[1] (closed_form) = 0.4816724317205936 " "
y[1] (numeric) = 0.48167243172045365 " "
absolute error = 1.39943612254000980000000000000E-13 " "
relative error = 2.905368940341988600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.859999999999792 " "
y[1] (closed_form) = 0.48030704040044725 " "
y[1] (numeric) = 0.48030704040030714 " "
absolute error = 1.40110145707694760000000000000E-13 " "
relative error = 2.91709539778722500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.849999999999793 " "
y[1] (closed_form) = 0.47889361877651543 " "
y[1] (numeric) = 0.4788936187763753 " "
absolute error = 1.40110145707694760000000000000E-13 " "
relative error = 2.92570500449870760000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8399999999997942 " "
y[1] (closed_form) = 0.4774323081897826 " "
y[1] (numeric) = 0.4774323081896424 " "
absolute error = 1.40221168010157270000000000000E-13 " "
relative error = 2.936985319276264600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8299999999997953 " "
y[1] (closed_form) = 0.4759232547700898 " "
y[1] (numeric) = 0.47592325476994934 " "
absolute error = 1.4044321261508230000000000000E-13 " "
relative error = 2.95096344226608500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8199999999997964 " "
y[1] (closed_form) = 0.47436660942152137 " "
y[1] (numeric) = 0.47436660942138076 " "
absolute error = 1.40609746068776080000000000000E-13 " "
relative error = 2.9641577479546100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8099999999997975 " "
y[1] (closed_form) = 0.472762527807315 " "
y[1] (numeric) = 0.47276252780717415 " "
absolute error = 1.4083179067370110000000000000E-13 " "
relative error = 2.97891187203187700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7999999999997986 " "
y[1] (closed_form) = 0.47111117033429534 " "
y[1] (numeric) = 0.47111117033415434 " "
absolute error = 1.40998324127394880000000000000E-13 " "
relative error = 2.992888579299531300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7899999999997998 " "
y[1] (closed_form) = 0.4694127021368336 " "
y[1] (numeric) = 0.4694127021366925 " "
absolute error = 1.4110934642985740000000000000E-13 " "
relative error = 3.00608283047108740000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.779999999999801 " "
y[1] (closed_form) = 0.46766729306033417 " "
y[1] (numeric) = 0.46766729306019283 " "
absolute error = 1.41331391034782430000000000000E-13 " "
relative error = 3.02204993019576260000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.769999999999802 " "
y[1] (closed_form) = 0.46587511764425016 " "
y[1] (numeric) = 0.46587511764410866 " "
absolute error = 1.4149792448847620000000000000E-13 " "
relative error = 3.037250094059033600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.759999999999803 " "
y[1] (closed_form) = 0.46403635510462965 " "
y[1] (numeric) = 0.464036355104488 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 3.052874120395757700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.749999999999804 " "
y[1] (closed_form) = 0.4621511893161944 " "
y[1] (numeric) = 0.46215118931605265 " "
absolute error = 1.4177548024463250000000000000E-13 " "
relative error = 3.06772942539443700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7399999999998053 " "
y[1] (closed_form) = 0.46021980879395225 " "
y[1] (numeric) = 0.4602198087938103 " "
absolute error = 1.41942013698326260000000000000E-13 " "
relative error = 3.08422216919124300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7299999999998064 " "
y[1] (closed_form) = 0.4582424066743459 " "
y[1] (numeric) = 0.45824240667420374 " "
absolute error = 1.4216405830325130000000000000E-13 " "
relative error = 3.10237673843838440000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7199999999998075 " "
y[1] (closed_form) = 0.4562191806959396 " "
y[1] (numeric) = 0.45621918069579714 " "
absolute error = 1.42441614059407580000000000000E-13 " "
relative error = 3.122218882645837500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7099999999998086 " "
y[1] (closed_form) = 0.45415033317964504 " "
y[1] (numeric) = 0.4541503331795023 " "
absolute error = 1.42719169815563870000000000000E-13 " "
relative error = 3.14255345397070230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6999999999998097 " "
y[1] (closed_form) = 0.4520360710084899 " "
y[1] (numeric) = 0.4520360710083469 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 3.16339192252280400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6899999999998108 " "
y[1] (closed_form) = 0.4498766056069294 " "
y[1] (numeric) = 0.4498766056067861 " "
absolute error = 1.43274281327876450000000000000E-13 " "
relative error = 3.184746206897885500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.679999999999812 " "
y[1] (closed_form) = 0.44767215291970414 " "
y[1] (numeric) = 0.4476721529195606 " "
absolute error = 1.43551837084032740000000000000E-13 " "
relative error = 3.20662869351582500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.669999999999813 " "
y[1] (closed_form) = 0.44542293339024575 " "
y[1] (numeric) = 0.4454229333901021 " "
absolute error = 1.43662859386495260000000000000E-13 " "
relative error = 3.22531348561320650000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.659999999999814 " "
y[1] (closed_form) = 0.44312917193863294 " "
y[1] (numeric) = 0.443129171938489 " "
absolute error = 1.43940415142651550000000000000E-13 " "
relative error = 3.24827215759528600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.649999999999815 " "
y[1] (closed_form) = 0.4407910979390993 " "
y[1] (numeric) = 0.4407910979389551 " "
absolute error = 1.44217970898807830000000000000E-13 " "
relative error = 3.27179862690269940000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6399999999998163 " "
y[1] (closed_form) = 0.4384089451970965 " "
y[1] (numeric) = 0.43840894519695195 " "
absolute error = 1.44551037806195380000000000000E-13 " "
relative error = 3.29717354971416600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6299999999998174 " "
y[1] (closed_form) = 0.4359829519259136 " "
y[1] (numeric) = 0.4359829519257688 " "
absolute error = 1.44773082411120400000000000000E-13 " "
relative error = 3.32061338113334400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6199999999998185 " "
y[1] (closed_form) = 0.43351336072285596 " "
y[1] (numeric) = 0.4335133607227109 " "
absolute error = 1.4505063816727670000000000000E-13 " "
relative error = 3.34593235893385130000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6099999999998196 " "
y[1] (closed_form) = 0.431000418544986 " "
y[1] (numeric) = 0.43100041854484067 " "
absolute error = 1.453281939234330000000000000E-13 " "
relative error = 3.37188057529146600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5999999999998207 " "
y[1] (closed_form) = 0.4284443766844274 " "
y[1] (numeric) = 0.4284443766842818 " "
absolute error = 1.45605749679589280000000000000E-13 " "
relative error = 3.39847498539666500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.589999999999822 " "
y[1] (closed_form) = 0.42584549074323613 " "
y[1] (numeric) = 0.42584549074309025 " "
absolute error = 1.45883305435745570000000000000E-13 " "
relative error = 3.425733243790669600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.579999999999823 " "
y[1] (closed_form) = 0.4232040206078406 " "
y[1] (numeric) = 0.42320402060769446 " "
absolute error = 1.46160861191901860000000000000E-13 " "
relative error = 3.45367373830649200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.569999999999824 " "
y[1] (closed_form) = 0.42052023042305314 " "
y[1] (numeric) = 0.42052023042290676 " "
absolute error = 1.4638290579682690000000000000E-13 " "
relative error = 3.48099556707562650000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.559999999999825 " "
y[1] (closed_form) = 0.41779438856565576 " "
y[1] (numeric) = 0.41779438856550905 " "
absolute error = 1.46715972704214440000000000000E-13 " "
relative error = 3.51167887170313800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.549999999999826 " "
y[1] (closed_form) = 0.41502676761756263 " "
y[1] (numeric) = 0.41502676761741564 " "
absolute error = 1.46993528460370730000000000000E-13 " "
relative error = 3.54178428789493900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5399999999998273 " "
y[1] (closed_form) = 0.4122176443385623 " "
y[1] (numeric) = 0.41221764433841496 " "
absolute error = 1.47326595367758270000000000000E-13 " "
relative error = 3.5740002251518400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5299999999998284 " "
y[1] (closed_form) = 0.4093672996386416 " "
y[1] (numeric) = 0.409367299638494 " "
absolute error = 1.47604151123914560000000000000E-13 " "
relative error = 3.60566540742771400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5199999999998295 " "
y[1] (closed_form) = 0.40647601854989535 " "
y[1] (numeric) = 0.40647601854974746 " "
absolute error = 1.47881706880070850000000000000E-13 " "
relative error = 3.63814100048606500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5099999999998306 " "
y[1] (closed_form) = 0.403544090198023 " "
y[1] (numeric) = 0.4035440901978747 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 3.67557844837068550000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4999999999998317 " "
y[1] (closed_form) = 0.4005718077734165 " "
y[1] (numeric) = 0.40057180777326784 " "
absolute error = 1.48658862997308460000000000000E-13 " "
relative error = 3.71116639045644900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.489999999999833 " "
y[1] (closed_form) = 0.3975594685018414 " "
y[1] (numeric) = 0.3975594685016925 " "
absolute error = 1.4888090760223350000000000000E-13 " "
relative error = 3.74487138146337300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.479999999999834 " "
y[1] (closed_form) = 0.39450737361471455 " "
y[1] (numeric) = 0.39450737361456545 " "
absolute error = 1.49102952207158520000000000000E-13 " "
relative error = 3.779471872502339600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.469999999999835 " "
y[1] (closed_form) = 0.3914158283189813 " "
y[1] (numeric) = 0.39141582831883187 " "
absolute error = 1.49436019114546070000000000000E-13 " "
relative error = 3.817832808558890300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.459999999999836 " "
y[1] (closed_form) = 0.3882851417665949 " "
y[1] (numeric) = 0.3882851417664453 " "
absolute error = 1.49602552568239840000000000000E-13 " "
relative error = 3.852904385874455500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.449999999999837 " "
y[1] (closed_form) = 0.38511562702360175 " "
y[1] (numeric) = 0.3851156270234518 " "
absolute error = 1.4993561947562740000000000000E-13 " "
relative error = 3.89326241145853600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4399999999998383 " "
y[1] (closed_form) = 0.38190760103883487 " "
y[1] (numeric) = 0.3819076010386845 " "
absolute error = 1.50379708685477450000000000000E-13 " "
relative error = 3.93759402212541600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4299999999998394 " "
y[1] (closed_form) = 0.3786613846122194 " "
y[1] (numeric) = 0.3786613846120686 " "
absolute error = 1.50768286744096260000000000000E-13 " "
relative error = 3.98161240810164630000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4199999999998405 " "
y[1] (closed_form) = 0.3753773023626928 " "
y[1] (numeric) = 0.3753773023625417 " "
absolute error = 1.5110135365148380000000000000E-13 " "
relative error = 4.025319397321694400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4099999999998416 " "
y[1] (closed_form) = 0.3720556826957433 " "
y[1] (numeric) = 0.3720556826955918 " "
absolute error = 1.5148993171010260000000000000E-13 " "
relative error = 4.07170052107460600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3999999999998427 " "
y[1] (closed_form) = 0.36869685777056965 " "
y[1] (numeric) = 0.3686968577704178 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 4.11933290365147100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.389999999999844 " "
y[1] (closed_form) = 0.36530116346686525 " "
y[1] (numeric) = 0.365301163466713 " "
absolute error = 1.52267087827340220000000000000E-13 " "
relative error = 4.168261781108497700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.379999999999845 " "
y[1] (closed_form) = 0.3618689393512308 " "
y[1] (numeric) = 0.36186893935107817 " "
absolute error = 1.52655665885959020000000000000E-13 " "
relative error = 4.21853464847368630000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.369999999999846 " "
y[1] (closed_form) = 0.35840052864321775 " "
y[1] (numeric) = 0.3584005286430647 " "
absolute error = 1.53044243944577830000000000000E-13 " "
relative error = 4.27020140076107500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.359999999999847 " "
y[1] (closed_form) = 0.35489627818100644 " "
y[1] (numeric) = 0.354896278180853 " "
absolute error = 1.53432822003196630000000000000E-13 " "
relative error = 4.32331448471662600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.349999999999848 " "
y[1] (closed_form) = 0.3513565383867229 " "
y[1] (numeric) = 0.35135653838656916 " "
absolute error = 1.53765888910584180000000000000E-13 " "
relative error = 4.376349152818118600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3399999999998493 " "
y[1] (closed_form) = 0.3477816632313969 " "
y[1] (numeric) = 0.3477816632312427 " "
absolute error = 1.54209978120434240000000000000E-13 " "
relative error = 4.434103186683262500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3299999999998504 " "
y[1] (closed_form) = 0.3441720101995649 " "
y[1] (numeric) = 0.34417201019941024 " "
absolute error = 1.5465406733028430000000000000E-13 " "
relative error = 4.493510882555778000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3199999999998515 " "
y[1] (closed_form) = 0.34052794025352195 " "
y[1] (numeric) = 0.3405279402533669 " "
absolute error = 1.5504264538890310000000000000E-13 " "
relative error = 4.55300805195234100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3099999999998526 " "
y[1] (closed_form) = 0.336849817797226 " "
y[1] (numeric) = 0.33684981779707057 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 4.61425879532721300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2999999999998537 " "
y[1] (closed_form) = 0.33313801063985754 " "
y[1] (numeric) = 0.3331380106397017 " "
absolute error = 1.55819801506140720000000000000E-13 " "
relative error = 4.67733481408674770000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.289999999999855 " "
y[1] (closed_form) = 0.32939288995903926 " "
y[1] (numeric) = 0.329392889958883 " "
absolute error = 1.56263890715990780000000000000E-13 " "
relative error = 4.74399707702927500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.279999999999856 " "
y[1] (closed_form) = 0.3256148302637182 " "
y[1] (numeric) = 0.3256148302635616 " "
absolute error = 1.56596957623378330000000000000E-13 " "
relative error = 4.809269820313440400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.269999999999857 " "
y[1] (closed_form) = 0.32180420935671555 " "
y[1] (numeric) = 0.32180420935655857 " "
absolute error = 1.56985535681997130000000000000E-13 " "
relative error = 4.878293419337495500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.259999999999858 " "
y[1] (closed_form) = 0.3179614082969465 " "
y[1] (numeric) = 0.3179614082967891 " "
absolute error = 1.5742962489184720000000000000E-13 " "
relative error = 4.95121800268359900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2499999999998592 " "
y[1] (closed_form) = 0.3140868113613148 " "
y[1] (numeric) = 0.314086811361157 " "
absolute error = 1.57762691799234740000000000000E-13 " "
relative error = 5.02290086984104300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2399999999998603 " "
y[1] (closed_form) = 0.31018080600628506 " "
y[1] (numeric) = 0.31018080600612674 " "
absolute error = 1.58317803311547320000000000000E-13 " "
relative error = 5.10404900128924800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2299999999998614 " "
y[1] (closed_form) = 0.30624378282913783 " "
y[1] (numeric) = 0.30624378282897907 " "
absolute error = 1.58761892521397390000000000000E-13 " "
relative error = 5.18416704021629600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2199999999998625 " "
y[1] (closed_form) = 0.30227613552891003 " "
y[1] (numeric) = 0.3022761355287509 " "
absolute error = 1.5915047058001620000000000000E-13 " "
relative error = 5.265068984077801000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2099999999998636 " "
y[1] (closed_form) = 0.29827826086702525 " "
y[1] (numeric) = 0.2982782608668657 " "
absolute error = 1.595390486386350000000000000E-13 " "
relative error = 5.348664973937164000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1999999999998647 " "
y[1] (closed_form) = 0.2942505586276182 " "
y[1] (numeric) = 0.2942505586274582 " "
absolute error = 1.59983137848485060000000000000E-13 " "
relative error = 5.43696972385183900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.189999999999866 " "
y[1] (closed_form) = 0.29019343157755634 " "
y[1] (numeric) = 0.2901934315773959 " "
absolute error = 1.60427227058335120000000000000E-13 " "
relative error = 5.528285950037424000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.179999999999867 " "
y[1] (closed_form) = 0.28610728542616376 " "
y[1] (numeric) = 0.2861072854260029 " "
absolute error = 1.60871316268185180000000000000E-13 " "
relative error = 5.622761965972430000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.169999999999868 " "
y[1] (closed_form) = 0.2819925287846506 " "
y[1] (numeric) = 0.2819925287844892 " "
absolute error = 1.6137091662926650000000000000E-13 " "
relative error = 5.722524540800893000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.159999999999869 " "
y[1] (closed_form) = 0.2778495731252519 " "
y[1] (numeric) = 0.2778495731250902 " "
absolute error = 1.61703983536654050000000000000E-13 " "
relative error = 5.8198391927620300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1499999999998702 " "
y[1] (closed_form) = 0.27367883274008126 " "
y[1] (numeric) = 0.27367883273991916 " "
absolute error = 1.62092561595272850000000000000E-13 " "
relative error = 5.92272920680042900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1399999999998713 " "
y[1] (closed_form) = 0.2694807246997015 " "
y[1] (numeric) = 0.26948072469953904 " "
absolute error = 1.62481139653891660000000000000E-13 " "
relative error = 6.02941601240512100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1299999999998724 " "
y[1] (closed_form) = 0.2652556688114184 " "
y[1] (numeric) = 0.2652556688112555 " "
absolute error = 1.62869717712510460000000000000E-13 " "
relative error = 6.1401031858173600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1199999999998735 " "
y[1] (closed_form) = 0.2610040875772997 " "
y[1] (numeric) = 0.2610040875771364 " "
absolute error = 1.63313806922360530000000000000E-13 " "
relative error = 6.25713598734322800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1099999999998746 " "
y[1] (closed_form) = 0.256726406151926 " "
y[1] (numeric) = 0.25672640615176223 " "
absolute error = 1.6375789613221060000000000000E-13 " "
relative error = 6.37869312264285100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0999999999998757 " "
y[1] (closed_form) = 0.2524230522998751 " "
y[1] (numeric) = 0.25242305229971085 " "
absolute error = 1.6425749649329190000000000000E-13 " "
relative error = 6.50723042118024300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.089999999999877 " "
y[1] (closed_form) = 0.24809445635294602 " "
y[1] (numeric) = 0.24809445635278124 " "
absolute error = 1.64784852429988860000000000000E-13 " "
relative error = 6.64202073888992400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.079999999999878 " "
y[1] (closed_form) = 0.24374105116712638 " "
y[1] (numeric) = 0.24374105116696113 " "
absolute error = 1.65256697215454550000000000000E-13 " "
relative error = 6.78001085267096300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.069999999999879 " "
y[1] (closed_form) = 0.23936327207930688 " "
y[1] (numeric) = 0.23936327207914113 " "
absolute error = 1.65756297576535870000000000000E-13 " "
relative error = 6.9248843457327390000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.05999999999988 " "
y[1] (closed_form) = 0.23496155686374817 " "
y[1] (numeric) = 0.23496155686358194 " "
absolute error = 1.66228142362001560000000000000E-13 " "
relative error = 7.07469530678993700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0499999999998813 " "
y[1] (closed_form) = 0.23053634568830375 " "
y[1] (numeric) = 0.23053634568813705 " "
absolute error = 1.66699987147467250000000000000E-13 " "
relative error = 7.23096337151338800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0399999999998824 " "
y[1] (closed_form) = 0.2260880810704035 " "
y[1] (numeric) = 0.22608808107023629 " "
absolute error = 1.6722734308416420000000000000E-13 " "
relative error = 7.39655723081173100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0299999999998835 " "
y[1] (closed_form) = 0.2216172078328023 " "
y[1] (numeric) = 0.22161720783263458 " "
absolute error = 1.67726943445245520000000000000E-13 " "
relative error = 7.56831769001376600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0199999999998846 " "
y[1] (closed_form) = 0.21712417305909823 " "
y[1] (numeric) = 0.21712417305893 " "
absolute error = 1.68226543806326840000000000000E-13 " "
relative error = 7.74794171630709500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0099999999998857 " "
y[1] (closed_form) = 0.21260942604902444 " "
y[1] (numeric) = 0.21260942604885577 " "
absolute error = 1.6867063301617690000000000000E-13 " "
relative error = 7.93335630271087200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9999999999998868 " "
y[1] (closed_form) = 0.20807341827351972 " "
y[1] (numeric) = 0.20807341827335052 " "
absolute error = 1.69197988952873860000000000000E-13 " "
relative error = 8.13164845162764800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9899999999998879 " "
y[1] (closed_form) = 0.20351660332958155 " "
y[1] (numeric) = 0.20351660332941188 " "
absolute error = 1.69669833738339550000000000000E-13 " "
relative error = 8.33690376915197300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.979999999999889 " "
y[1] (closed_form) = 0.19893943689490706 " "
y[1] (numeric) = 0.1989394368947369 " "
absolute error = 1.70169434099420870000000000000E-13 " "
relative error = 8.55383109329476900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.96999999999989 " "
y[1] (closed_form) = 0.19434237668232537 " "
y[1] (numeric) = 0.19434237668215468 " "
absolute error = 1.70696790036117820000000000000E-13 " "
relative error = 8.78330258948829500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9599999999998912 " "
y[1] (closed_form) = 0.1897258823940269 " "
y[1] (numeric) = 0.1897258823938557 " "
absolute error = 1.71196390397199140000000000000E-13 " "
relative error = 9.02335454904643400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9499999999998923 " "
y[1] (closed_form) = 0.18509041567559342 " "
y[1] (numeric) = 0.1850904156754217 " "
absolute error = 1.7172374633389610000000000000E-13 " "
relative error = 9.2778302813299110000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9399999999998934 " "
y[1] (closed_form) = 0.1804364400698339 " "
y[1] (numeric) = 0.18043644006966164 " "
absolute error = 1.72251102270593040000000000000E-13 " "
relative error = 9.54635893968685500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9299999999998945 " "
y[1] (closed_form) = 0.17576442097043055 " "
y[1] (numeric) = 0.1757644209702578 " "
absolute error = 1.72750702631674360000000000000E-13 " "
relative error = 9.82853649662901900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9199999999998956 " "
y[1] (closed_form) = 0.17107482557540005 " "
y[1] (numeric) = 0.1710748255752268 " "
absolute error = 1.73250302992755680000000000000E-13 " "
relative error = 1.01271652570761680000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9099999999998967 " "
y[1] (closed_form) = 0.1663681228403739 " "
y[1] (numeric) = 0.16636812284020008 " "
absolute error = 1.73805414505068260000000000000E-13 " "
relative error = 1.04470382629628070000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8999999999998978 " "
y[1] (closed_form) = 0.16164478343170335 " "
y[1] (numeric) = 0.16164478343152902 " "
absolute error = 1.7433277044176520000000000000E-13 " "
relative error = 1.07849301870865920000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8899999999998989 " "
y[1] (closed_form) = 0.15690527967939316 " "
y[1] (numeric) = 0.15690527967921838 " "
absolute error = 1.74776859651615270000000000000E-13 " "
relative error = 1.11390043731313160000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8799999999999 " "
y[1] (closed_form) = 0.152150085529869 " "
y[1] (numeric) = 0.15215008552969375 " "
absolute error = 1.75248704437080960000000000000E-13 " "
relative error = 1.15181469551443270000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.869999999999901 " "
y[1] (closed_form) = 0.1473796764985832 " "
y[1] (numeric) = 0.14737967649840744 " "
absolute error = 1.75748304798162280000000000000E-13 " "
relative error = 1.19248670490772720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8599999999999022 " "
y[1] (closed_form) = 0.1425945296224635 " "
y[1] (numeric) = 0.1425945296222872 " "
absolute error = 1.76303416310474860000000000000E-13 " "
relative error = 1.23639677326514390000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8499999999999033 " "
y[1] (closed_form) = 0.13779512341220995 " "
y[1] (numeric) = 0.13779512341203312 " "
absolute error = 1.7683077224717180000000000000E-13 " "
relative error = 1.28328759297372140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8399999999999044 " "
y[1] (closed_form) = 0.13298193780444406 " "
y[1] (numeric) = 0.13298193780426676 " "
absolute error = 1.7730261703263750000000000000E-13 " "
relative error = 1.33328345157196470000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8299999999999055 " "
y[1] (closed_form) = 0.12815545411371565 " "
y[1] (numeric) = 0.12815545411353782 " "
absolute error = 1.77829972969334450000000000000E-13 " "
relative error = 1.38761143018962970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8199999999999066 " "
y[1] (closed_form) = 0.12331615498437172 " "
y[1] (numeric) = 0.12331615498419336 " "
absolute error = 1.7835732890603140000000000000E-13 " "
relative error = 1.44634195680716140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8099999999999077 " "
y[1] (closed_form) = 0.11846452434229247 " "
y[1] (numeric) = 0.11846452434211359 " "
absolute error = 1.78884684842728350000000000000E-13 " "
relative error = 1.5100274604223060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7999999999999088 " "
y[1] (closed_form) = 0.11360104734649912 " "
y[1] (numeric) = 0.1136010473463197 " "
absolute error = 1.7941204077942530000000000000E-13 " "
relative error = 1.57931678422112980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7899999999999099 " "
y[1] (closed_form) = 0.10872621034063833 " "
y[1] (numeric) = 0.10872621034045837 " "
absolute error = 1.79953274503930060000000000000E-13 " "
relative error = 1.65510481732176560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.779999999999911 " "
y[1] (closed_form) = 0.10384050080434835 " "
y[1] (numeric) = 0.10384050080416787 " "
absolute error = 1.804806304406270000000000000E-13 " "
relative error = 1.73805624050947680000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.769999999999912 " "
y[1] (closed_form) = 9.89444073045114200E-2 " "
y[1] (numeric) = 9.89444073043303800E-2 " "
absolute error = 1.8103574195293960000000000000E-13 " "
relative error = 1.8296712960822920000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7599999999999132 " "
y[1] (closed_form) = 9.40384194463974100E-2 " "
y[1] (numeric) = 9.40384194462158500E-2 " "
absolute error = 1.81563097889636540000000000000E-13 " "
relative error = 1.9307331935021390000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7499999999999143 " "
y[1] (closed_form) = 8.91230278247038800E-2 " "
y[1] (numeric) = 8.91230278245217600E-2 " "
absolute error = 1.82118209401949120000000000000E-13 " "
relative error = 2.04344728682420320000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7399999999999154 " "
y[1] (closed_form) = 8.4198723974496800E-2 " "
y[1] (numeric) = 8.41987239743141700E-2 " "
absolute error = 1.82631687550838250000000000000E-13 " "
relative error = 2.16905528884447340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7299999999999165 " "
y[1] (closed_form) = 7.92660003220576600E-2 " "
y[1] (numeric) = 7.92660003218744900E-2 " "
absolute error = 1.83172921275343010000000000000E-13 " "
relative error = 2.31086368091125650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7199999999999176 " "
y[1] (closed_form) = 7.4325350135641100E-2 " "
y[1] (numeric) = 7.43253501354573800E-2 " "
absolute error = 1.83714154999847780000000000000E-13 " "
relative error = 2.47175633434051830000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7099999999999187 " "
y[1] (closed_form) = 6.93772674761485400E-2 " "
y[1] (numeric) = 6.93772674759642900E-2 " "
absolute error = 1.84255388724352540000000000000E-13 " "
relative error = 2.6558467265621030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6999999999999198 " "
y[1] (closed_form) = 6.44222471477225800E-2 " "
y[1] (numeric) = 6.44222471475377700E-2 " "
absolute error = 1.8479662244885730000000000000E-13 " "
relative error = 2.8685218326071720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.689999999999921 " "
y[1] (closed_form) = 5.946078464826686000E-2 " "
y[1] (numeric) = 5.94607846480815300E-2 " "
absolute error = 1.85337856173362070000000000000E-13 " "
relative error = 3.11697629403489940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.679999999999922 " "
y[1] (closed_form) = 5.44933761198968200E-2 " "
y[1] (numeric) = 5.44933761197109300E-2 " "
absolute error = 1.85886028791770740000000000000E-13 " "
relative error = 3.4111674120315580000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.669999999999923 " "
y[1] (closed_form) = 4.95205182993257800E-2 " "
y[1] (numeric) = 4.95205182991393500E-2 " "
absolute error = 1.8642726251627550000000000000E-13 " "
relative error = 3.7646468356696040000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6599999999999242 " "
y[1] (closed_form) = 4.45427084681917700E-2 " "
y[1] (numeric) = 4.4542708468004800E-2 " "
absolute error = 1.86968496240780270000000000000E-13 " "
relative error = 4.19751071882608240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6499999999999253 " "
y[1] (closed_form) = 3.956044440332974000E-2 " "
y[1] (numeric) = 3.95604444031422250E-2 " "
absolute error = 1.87516668859188940000000000000E-13 " "
relative error = 4.7400041047922580000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6399999999999264 " "
y[1] (closed_form) = 3.457422432699431300E-2 " "
y[1] (numeric) = 3.45742243268062400E-2 " "
absolute error = 1.88071780371501520000000000000E-13 " "
relative error = 5.4396529215743480000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6299999999999275 " "
y[1] (closed_form) = 2.95845468570379400E-2 " "
y[1] (numeric) = 2.95845468568493200E-2 " "
absolute error = 1.8861995298991020000000000000E-13 " "
relative error = 6.3756242034526520000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6199999999999286 " "
y[1] (closed_form) = 2.45919109570495700E-2 " "
y[1] (numeric) = 2.459191095686039400E-2 " "
absolute error = 1.89175064502222770000000000000E-13 " "
relative error = 7.6925727664117720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6099999999999297 " "
y[1] (closed_form) = 1.959681588645868800E-2 " "
y[1] (numeric) = 1.95968158862689620E-2 " "
absolute error = 1.8972670656758340000000000000E-13 " "
relative error = 9.6815068155375040000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5999999999999308 " "
y[1] (closed_form) = 1.459976115060978300E-2 " "
y[1] (numeric) = 1.459976115041950500E-2 " "
absolute error = 1.90278348632944020000000000000E-13 " "
relative error = 1.3032976818596564000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.589999999999932 " "
y[1] (closed_form) = 9.601246450812246000E-3 " "
y[1] (numeric) = 9.601246450621415000E-3 " "
absolute error = 1.90831725421780620000000000000E-13 " "
relative error = 1.987572409472278800000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.579999999999933 " "
y[1] (closed_form) = 4.60177163437064050E-3 " "
y[1] (numeric) = 4.601771634179258600E-3 " "
absolute error = 1.91381632763665270000000000000E-13 " "
relative error = 4.158868539547585000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5699999999999341 " "
y[1] (closed_form) = -3.98163355399605230000E-4 " "
y[1] (numeric) = -3.9816335559153830000E-4 " "
absolute error = 1.9193305798859140000000000000E-13 " "
relative error = 4.820460129887223500000000E-8 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5599999999999352 " "
y[1] (closed_form) = -5.398058529166113000E-3 " "
y[1] (numeric) = -5.398058529358597000E-3 " "
absolute error = 1.92484049532648530000000000000E-13 " "
relative error = 3.565801454219935700000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5499999999999363 " "
y[1] (closed_form) = -1.03974139015780700E-2 " "
y[1] (numeric) = -1.039741390177110500E-2 " "
absolute error = 1.93034824236271160000000000000E-13 " "
relative error = 1.856565738976432000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5399999999999374 " "
y[1] (closed_form) = -1.539572954126435500E-2 " "
y[1] (numeric) = -1.539572954145793600E-2 " "
absolute error = 1.93582996854679830000000000000E-13 " "
relative error = 1.2573811220561495000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5299999999999385 " "
y[1] (closed_form) = -2.039250562082624300E-2 " "
y[1] (numeric) = -2.03925056210203800E-2 " "
absolute error = 1.94136373643516440000000000000E-13 " "
relative error = 9.519986275999889000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5199999999999396 " "
y[1] (closed_form) = -2.538724246681975000E-2 " "
y[1] (numeric) = -2.538724246701443700E-2 " "
absolute error = 1.94688015708877060000000000000E-13 " "
relative error = 7.6687342456876760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5099999999999407 " "
y[1] (closed_form) = -3.037944060972253600E-2 " "
y[1] (numeric) = -3.037944060991777400E-2 " "
absolute error = 1.95236188327285730000000000000E-13 " "
relative error = 6.4265893120100110000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4999999999999418 " "
y[1] (closed_form) = -3.53686008338804700E-2 " "
y[1] (numeric) = -3.53686008340762500E-2 " "
absolute error = 1.95780891498742450000000000000E-13 " "
relative error = 5.5354434974198640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.489999999999943 " "
y[1] (closed_form) = -4.03542242274287500E-2 " "
y[1] (numeric) = -4.03542242276250800E-2 " "
absolute error = 1.96329064117151120000000000000E-13 " "
relative error = 4.8651428165407856000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.479999999999944 " "
y[1] (closed_form) = -4.5335812232182700E-2 " "
y[1] (numeric) = -4.53358122323795630E-2 " "
absolute error = 1.96863358947751980000000000000E-13 " "
relative error = 4.342336648553610000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4699999999999451 " "
y[1] (closed_form) = -5.03128666934931500E-2 " "
y[1] (numeric) = -5.031286669369057000E-2 " "
absolute error = 1.97425409353968460000000000000E-13 " "
relative error = 3.9239546924783170000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4599999999999462 " "
y[1] (closed_form) = -5.528488991006150000E-2 " "
y[1] (numeric) = -5.52848899102594700E-2 " "
absolute error = 1.97973581972377130000000000000E-13 " "
relative error = 3.58097089990491670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4499999999999473 " "
y[1] (closed_form) = -6.02513846837094300E-2 " "
y[1] (numeric) = -6.02513846839079400E-2 " "
absolute error = 1.9851481569688190000000000000E-13 " "
relative error = 3.2947759912737020000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4399999999999484 " "
y[1] (closed_form) = -6.52118543690983100E-2 " "
y[1] (numeric) = -6.52118543692973700E-2 " "
absolute error = 1.99062988315290570000000000000E-13 " "
relative error = 3.05255831537309840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4299999999999495 " "
y[1] (closed_form) = -7.01658029233933200E-2 " "
y[1] (numeric) = -7.01658029235929300E-2 " "
absolute error = 1.99618099827603150000000000000E-13 " "
relative error = 2.844948557711870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4199999999999506 " "
y[1] (closed_form) = -7.51127349558672900E-2 " "
y[1] (numeric) = -7.51127349560674500E-2 " "
absolute error = 2.0015933355210790000000000000E-13 " "
relative error = 2.6647855875533240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4099999999999517 " "
y[1] (closed_form) = -8.00521557774394200E-2 " "
y[1] (numeric) = -8.00521557776401200E-2 " "
absolute error = 2.00700567276612670000000000000E-13 " "
relative error = 2.50712257936687330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3999999999999528 " "
y[1] (closed_form) = -8.49835714501437000E-2 " "
y[1] (numeric) = -8.49835714503449600E-2 " "
absolute error = 2.01255678788925250000000000000E-13 " "
relative error = 2.36817158133902940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.389999999999954 " "
y[1] (closed_form) = -8.9906488836522400E-2 " "
y[1] (numeric) = -8.9906488836724200E-2 " "
absolute error = 2.01796912513430020000000000000E-13 " "
relative error = 2.2445200021141828000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.379999999999955 " "
y[1] (closed_form) = -9.48204156489392600E-2 " "
y[1] (numeric) = -9.48204156491415900E-2 " "
absolute error = 2.02338146237934780000000000000E-13 " "
relative error = 2.13390908332511950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3699999999999561 " "
y[1] (closed_form) = -9.97248604988079700E-2 " "
y[1] (numeric) = -9.97248604990108600E-2 " "
absolute error = 2.02893257750247360000000000000E-13 " "
relative error = 2.03453037422571840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3599999999999572 " "
y[1] (closed_form) = -0.10461933294573059 " "
y[1] (numeric) = -0.10461933294593401 " "
absolute error = 2.0342061368694430000000000000E-13 " "
relative error = 1.94438836455270770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3499999999999583 " "
y[1] (closed_form) = -0.10950334354654111 " "
y[1] (numeric) = -0.10950334354674505 " "
absolute error = 2.03947969623641260000000000000E-13 " "
relative error = 1.86248166510969840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3399999999999594 " "
y[1] (closed_form) = -0.11437640390424947 " "
y[1] (numeric) = -0.11437640390445396 " "
absolute error = 2.04489203348146020000000000000E-13 " "
relative error = 1.78786179988081050000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3299999999999605 " "
y[1] (closed_form) = -0.11923802671688076 " "
y[1] (numeric) = -0.11923802671708579 " "
absolute error = 2.05030437072650780000000000000E-13 " "
relative error = 1.71950545239628850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3199999999999616 " "
y[1] (closed_form) = -0.12408772582620506 " "
y[1] (numeric) = -0.12408772582641062 " "
absolute error = 2.05557793009347730000000000000E-13 " "
relative error = 1.65655218226215320000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3099999999999627 " "
y[1] (closed_form) = -0.12892501626635283 " "
y[1] (numeric) = -0.12892501626655894 " "
absolute error = 2.0611290452166030000000000000E-13 " "
relative error = 1.59870373097988240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2999999999999639 " "
y[1] (closed_form) = -0.13374941431231113 " "
y[1] (numeric) = -0.13374941431251777 " "
absolute error = 2.06640260458357260000000000000E-13 " "
relative error = 1.54498067539826840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.289999999999965 " "
y[1] (closed_form) = -0.13856043752829567 " "
y[1] (numeric) = -0.13856043752850283 " "
absolute error = 2.0716761639505420000000000000E-13 " "
relative error = 1.49514262577835870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.279999999999966 " "
y[1] (closed_form) = -0.14335760481599402 " "
y[1] (numeric) = -0.14335760481620174 " "
absolute error = 2.0772272790736680000000000000E-13 " "
relative error = 1.4489829693652340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2699999999999672 " "
y[1] (closed_form) = -0.14814043646267505 " "
y[1] (numeric) = -0.1481404364628833 " "
absolute error = 2.08250083844063740000000000000E-13 " "
relative error = 1.4057612412700950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2599999999999683 " "
y[1] (closed_form) = -0.15290845418915977 " "
y[1] (numeric) = -0.15290845418936858 " "
absolute error = 2.08805195356376320000000000000E-13 " "
relative error = 1.36555690438193770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2499999999999694 " "
y[1] (closed_form) = -0.15766118119764888 " "
y[1] (numeric) = -0.15766118119785819 " "
absolute error = 2.09304795717457640000000000000E-13 " "
relative error = 1.32756074848295570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2399999999999705 " "
y[1] (closed_form) = -0.16239814221940208 " "
y[1] (numeric) = -0.16239814221961188 " "
absolute error = 2.09804396078538960000000000000E-13 " "
relative error = 1.29191376952508740000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2299999999999716 " "
y[1] (closed_form) = -0.1671188635622647 " "
y[1] (numeric) = -0.16711886356247502 " "
absolute error = 2.10303996439620280000000000000E-13 " "
relative error = 1.2584096849202530000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2199999999999727 " "
y[1] (closed_form) = -0.17182287315803635 " "
y[1] (numeric) = -0.17182287315824718 " "
absolute error = 2.10831352376317230000000000000E-13 " "
relative error = 1.22702727815756110000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2099999999999738 " "
y[1] (closed_form) = -0.17650970060967744 " "
y[1] (numeric) = -0.17650970060988877 " "
absolute error = 2.11330952737398550000000000000E-13 " "
relative error = 1.1972767049484870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1999999999999749 " "
y[1] (closed_form) = -0.1811788772383485 " "
y[1] (numeric) = -0.18117887723856033 " "
absolute error = 2.11830553098479870000000000000E-13 " "
relative error = 1.16917908051614520000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.189999999999976 " "
y[1] (closed_form) = -0.18582993613027762 " "
y[1] (numeric) = -0.18582993613048995 " "
absolute error = 2.1233015345956120000000000000E-13 " "
relative error = 1.14260467328958980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.179999999999977 " "
y[1] (closed_form) = -0.1904624121834515 " "
y[1] (numeric) = -0.1904624121836643 " "
absolute error = 2.12801998245026880000000000000E-13 " "
relative error = 1.11729131121188420000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1699999999999782 " "
y[1] (closed_form) = -0.19507584215412516 " "
y[1] (numeric) = -0.19507584215433849 " "
absolute error = 2.13329354181723830000000000000E-13 " "
relative error = 1.09357136089243180000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1599999999999793 " "
y[1] (closed_form) = -0.19966976470314607 " "
y[1] (numeric) = -0.19966976470335993 " "
absolute error = 2.13856710118420780000000000000E-13 " "
relative error = 1.07105204654478760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1499999999999804 " "
y[1] (closed_form) = -0.2042437204420876 " "
y[1] (numeric) = -0.20424372044230193 " "
absolute error = 2.14328554903886470000000000000E-13 " "
relative error = 1.04937647257879030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1399999999999815 " "
y[1] (closed_form) = -0.20879725197918747 " "
y[1] (numeric) = -0.2087972519794023 " "
absolute error = 2.1482815526496780000000000000E-13 " "
relative error = 1.0288840165692480000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1299999999999826 " "
y[1] (closed_form) = -0.21332990396508653 " "
y[1] (numeric) = -0.21332990396530188 " "
absolute error = 2.15355511201664740000000000000E-13 " "
relative error = 1.00949518655813820000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1199999999999837 " "
y[1] (closed_form) = -0.21784122313836343 " "
y[1] (numeric) = -0.21784122313857932 " "
absolute error = 2.1588286713836170000000000000E-13 " "
relative error = 9.9101016799397100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1099999999999848 " "
y[1] (closed_form) = -0.22233075837086025 " "
y[1] (numeric) = -0.22233075837107663 " "
absolute error = 2.163824674994430000000000000E-13 " "
relative error = 9.73245758189269000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0999999999999859 " "
y[1] (closed_form) = -0.22679806071279499 " "
y[1] (numeric) = -0.2267980607130119 " "
absolute error = 2.16909823436139960000000000000E-13 " "
relative error = 9.56400697406416600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.089999999999987 " "
y[1] (closed_form) = -0.23124268343765622 " "
y[1] (numeric) = -0.2312426834378736 " "
absolute error = 2.17381668221605650000000000000E-13 " "
relative error = 9.40058578243460200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.079999999999988 " "
y[1] (closed_form) = -0.23566418208687526 " "
y[1] (numeric) = -0.23566418208709314 " "
absolute error = 2.17881268582686970000000000000E-13 " "
relative error = 9.24541297083352300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0699999999999892 " "
y[1] (closed_form) = -0.2400621145142718 " "
y[1] (numeric) = -0.24006211451449022 " "
absolute error = 2.18408624519383920000000000000E-13 " "
relative error = 9.0980046960470900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0599999999999903 " "
y[1] (closed_form) = -0.24443604093026802 " "
y[1] (numeric) = -0.24443604093048696 " "
absolute error = 2.18935980456080870000000000000E-13 " "
relative error = 8.95677984403855800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0499999999999914 " "
y[1] (closed_form) = -0.24878552394586723 " "
y[1] (numeric) = -0.24878552394608663 " "
absolute error = 2.19407825241546560000000000000E-13 " "
relative error = 8.8191556229488300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0399999999999925 " "
y[1] (closed_form) = -0.2531101286163924 " "
y[1] (numeric) = -0.2531101286166123 " "
absolute error = 2.19879670027012250000000000000E-13 " "
relative error = 8.68711462591276100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0299999999999936 " "
y[1] (closed_form) = -0.25740942248498044 " "
y[1] (numeric) = -0.2574094224852008 " "
absolute error = 2.20379270388093570000000000000E-13 " "
relative error = 8.56142981327548200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0199999999999947 " "
y[1] (closed_form) = -0.26168297562582704 " "
y[1] (numeric) = -0.2616829756260479 " "
absolute error = 2.2087887074917490000000000000E-13 " "
relative error = 8.44070464350738700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0099999999999958 " "
y[1] (closed_form) = -0.2659303606871795 " "
y[1] (numeric) = -0.26593036068740084 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 8.32259089887719300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9999999999999968 " "
y[1] (closed_form) = -0.2701511529340712 " "
y[1] (numeric) = -0.2701511529342929 " "
absolute error = 2.21711538017643760000000000000E-13 " "
relative error = 8.20694398708530200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9899999999999968 " "
y[1] (closed_form) = -0.27434493029079515 " "
y[1] (numeric) = -0.27434493029101675 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 8.07744161630007700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9799999999999968 " "
y[1] (closed_form) = -0.27851127338311 " "
y[1] (numeric) = -0.2785112733833316 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 7.95660847129716100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9699999999999968 " "
y[1] (closed_form) = -0.2826497655801785 " "
y[1] (numeric) = -0.2826497655804 " "
absolute error = 2.21489493412718730000000000000E-13 " "
relative error = 7.83618174804002800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9599999999999967 " "
y[1] (closed_form) = -0.2867599930362297 " "
y[1] (numeric) = -0.2867599930364512 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 7.72579892397889900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9499999999999967 " "
y[1] (closed_form) = -0.29084154473194307 " "
y[1] (numeric) = -0.2908415447321646 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 7.61737821081025700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9399999999999967 " "
y[1] (closed_form) = -0.2948940125155504 " "
y[1] (numeric) = -0.29489401251577196 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 7.51269931437714100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9299999999999967 " "
y[1] (closed_form) = -0.29891699114365045 " "
y[1] (numeric) = -0.29891699114387205 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 7.4134466183184200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9199999999999967 " "
y[1] (closed_form) = -0.3029100783217327 " "
y[1] (numeric) = -0.3029100783219544 " "
absolute error = 2.2165602686641250000000000000E-13 " "
relative error = 7.31755206345372600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9099999999999967 " "
y[1] (closed_form) = -0.30687287474440705 " "
y[1] (numeric) = -0.30687287474462877 " "
absolute error = 2.21711538017643760000000000000E-13 " "
relative error = 7.2248659384543600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8999999999999967 " "
y[1] (closed_form) = -0.31080498413533353 " "
y[1] (numeric) = -0.31080498413555513 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 7.1298893848719600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8899999999999967 " "
y[1] (closed_form) = -0.3147060132868497 " "
y[1] (numeric) = -0.31470601328707126 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 7.03974487967648400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799999999999967 " "
y[1] (closed_form) = -0.3185755720992914 " "
y[1] (numeric) = -0.3185755720995129 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.95423704661512500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8699999999999967 " "
y[1] (closed_form) = -0.3224132736200019 " "
y[1] (numeric) = -0.32241327362022343 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.87146041093407900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8599999999999967 " "
y[1] (closed_form) = -0.3262187340820272 " "
y[1] (numeric) = -0.3262187340822488 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 6.79300397442717500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8499999999999966 " "
y[1] (closed_form) = -0.3299915729424923 " "
y[1] (numeric) = -0.329991572942714 " "
absolute error = 2.2165602686641250000000000000E-13 " "
relative error = 6.71702082843917200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8399999999999966 " "
y[1] (closed_form) = -0.33373141292065533 " "
y[1] (numeric) = -0.333731412920877 " "
absolute error = 2.2165602686641250000000000000E-13 " "
relative error = 6.64174897192285700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8299999999999966 " "
y[1] (closed_form) = -0.3374378800356348 " "
y[1] (numeric) = -0.3374378800358564 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 6.56714995043767400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8199999999999966 " "
y[1] (closed_form) = -0.341110603643808 " "
y[1] (numeric) = -0.3411106036440296 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 6.49644172148278600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8099999999999966 " "
y[1] (closed_form) = -0.34474921647587475 " "
y[1] (numeric) = -0.3447492164760963 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.42626564401353900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7999999999999966 " "
y[1] (closed_form) = -0.3483533546735839 " "
y[1] (numeric) = -0.34835335467380546 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.35977812734266300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7899999999999966 " "
y[1] (closed_form) = -0.35192265782611926 " "
y[1] (numeric) = -0.3519226578263408 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.29527538614500600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7799999999999966 " "
y[1] (closed_form) = -0.35545676900613987 " "
y[1] (numeric) = -0.3554567690063615 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 6.234246609926101000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7699999999999966 " "
y[1] (closed_form) = -0.35895533480547287 " "
y[1] (numeric) = -0.35895533480569447 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 6.17348439284994200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7599999999999966 " "
y[1] (closed_form) = -0.36241800537045377 " "
y[1] (numeric) = -0.36241800537067537 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 6.11450072654826400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7499999999999966 " "
y[1] (closed_form) = -0.3658444344369116 " "
y[1] (numeric) = -0.36584443443713316 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.0557161380612600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7399999999999965 " "
y[1] (closed_form) = -0.36923427936479514 " "
y[1] (numeric) = -0.3692342793650167 " "
absolute error = 2.21545004563950000000000000E-13 " "
relative error = 6.00012016612001800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7299999999999965 " "
y[1] (closed_form) = -0.3725872011724363 " "
y[1] (numeric) = -0.3725872011726578 " "
absolute error = 2.21489493412718730000000000000E-13 " "
relative error = 5.94463504692990400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7199999999999965 " "
y[1] (closed_form) = -0.37590286457044864 " "
y[1] (numeric) = -0.37590286457067007 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 5.89072345895858700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7099999999999965 " "
y[1] (closed_form) = -0.3791809379952552 " "
y[1] (numeric) = -0.37918093799547664 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 5.83979731239175200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6999999999999965 " "
y[1] (closed_form) = -0.38242109364224536 " "
y[1] (numeric) = -0.38242109364246674 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 5.7888666391753900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6899999999999965 " "
y[1] (closed_form) = -0.38562300749855444 " "
y[1] (numeric) = -0.3856230074987757 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.73792135077996200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6799999999999965 " "
y[1] (closed_form) = -0.3887863593754651 " "
y[1] (numeric) = -0.3887863593756864 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.69266268277908700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6699999999999965 " "
y[1] (closed_form) = -0.3919108329404257 " "
y[1] (numeric) = -0.39191083294064705 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.6472784459282400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6599999999999965 " "
y[1] (closed_form) = -0.39499611574868365 " "
y[1] (numeric) = -0.39499611574890486 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 5.60035729053367600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6499999999999965 " "
y[1] (closed_form) = -0.398041899274529 " "
y[1] (numeric) = -0.3980418992747502 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 5.55750382207861100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6399999999999965 " "
y[1] (closed_form) = -0.4010478789421474 " "
y[1] (numeric) = -0.40104787894236865 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.5172327401764500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6299999999999965 " "
y[1] (closed_form) = -0.404013754156077 " "
y[1] (numeric) = -0.40401375415629825 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.47673059472907300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6199999999999964 " "
y[1] (closed_form) = -0.406939228331268 " "
y[1] (numeric) = -0.40693922833148927 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.437358539139693000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6099999999999964 " "
y[1] (closed_form) = -0.4098240089227408 " "
y[1] (numeric) = -0.40982400892296206 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.3990845824141700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5999999999999964 " "
y[1] (closed_form) = -0.41266780745484016 " "
y[1] (numeric) = -0.4126678074550615 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.36322329876059400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5899999999999964 " "
y[1] (closed_form) = -0.4154703395500827 " "
y[1] (numeric) = -0.4154703395503041 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 5.32838207776731600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5799999999999964 " "
y[1] (closed_form) = -0.41823132495759446 " "
y[1] (numeric) = -0.4182313249578158 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.29187908106752800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5699999999999964 " "
y[1] (closed_form) = -0.42095048758113535 " "
y[1] (numeric) = -0.42095048758135667 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.25769577393271200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5599999999999964 " "
y[1] (closed_form) = -0.423627555506709 " "
y[1] (numeric) = -0.4236275555069303 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.22447034150779800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5499999999999964 " "
y[1] (closed_form) = -0.42626226102975384 " "
y[1] (numeric) = -0.42626226102997516 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.19217815399276600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5399999999999964 " "
y[1] (closed_form) = -0.428854340681913 " "
y[1] (numeric) = -0.42885434068213435 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.16079561202770100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5299999999999964 " "
y[1] (closed_form) = -0.4314035352573814 " "
y[1] (numeric) = -0.43140353525760283 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 5.132873612854768000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5199999999999964 " "
y[1] (closed_form) = -0.4339095898388259 " "
y[1] (numeric) = -0.4339095898390472 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.100669935440574000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5099999999999963 " "
y[1] (closed_form) = -0.43637225382287653 " "
y[1] (numeric) = -0.43637225382309797 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 5.0744285485980400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.49999999999999634 " "
y[1] (closed_form) = -0.4387912809451872 " "
y[1] (numeric) = -0.4387912809454087 " "
absolute error = 2.21489493412718730000000000000E-13 " "
relative error = 5.04771865419966400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4899999999999963 " "
y[1] (closed_form) = -0.4411664293050616 " "
y[1] (numeric) = -0.4411664293052831 " "
absolute error = 2.21489493412718730000000000000E-13 " "
relative error = 5.0205427861230400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4799999999999963 " "
y[1] (closed_form) = -0.44349746138964297 " "
y[1] (numeric) = -0.44349746138986434 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 4.99165137082397070000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4699999999999963 " "
y[1] (closed_form) = -0.4457841440976653 " "
y[1] (numeric) = -0.4457841440978867 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 4.96604632626312440000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4599999999999963 " "
y[1] (closed_form) = -0.4480262487627634 " "
y[1] (numeric) = -0.44802624876298486 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 4.94243323628879800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4499999999999963 " "
y[1] (closed_form) = -0.4502235511763393 " "
y[1] (numeric) = -0.45022355117656065 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 4.91707887185912240000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4399999999999963 " "
y[1] (closed_form) = -0.4523758316099825 " "
y[1] (numeric) = -0.4523758316102039 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 4.89368475593361200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4299999999999963 " "
y[1] (closed_form) = -0.4544828748374433 " "
y[1] (numeric) = -0.4544828748376648 " "
absolute error = 2.21489493412718730000000000000E-13 " "
relative error = 4.87343980764819300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.41999999999999627 " "
y[1] (closed_form) = -0.4565444701561549 " "
y[1] (numeric) = -0.45654447015637634 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 4.85021715816093400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.40999999999999626 " "
y[1] (closed_form) = -0.4585604114083033 " "
y[1] (numeric) = -0.4585604114085247 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 4.82889444340458160000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.39999999999999625 " "
y[1] (closed_form) = -0.4605304970014433 " "
y[1] (numeric) = -0.4605304970016646 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.805826354607984400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.38999999999999624 " "
y[1] (closed_form) = -0.4624545299286572 " "
y[1] (numeric) = -0.46245452992887853 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.78583180908982400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.37999999999999623 " "
y[1] (closed_form) = -0.46433231778825584 " "
y[1] (numeric) = -0.4643323177884771 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.76528211221118900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3699999999999962 " "
y[1] (closed_form) = -0.4661636728030179 " "
y[1] (numeric) = -0.46616367280323917 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.74656138427355500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3599999999999962 " "
y[1] (closed_form) = -0.46794841183896807 " "
y[1] (numeric) = -0.46794841183918934 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.728458163545108400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3499999999999962 " "
y[1] (closed_form) = -0.4696863564236901 " "
y[1] (numeric) = -0.46968635642391143 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.712143687635160000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3399999999999962 " "
y[1] (closed_form) = -0.47137733276417376 " "
y[1] (numeric) = -0.4713773327643951 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.695239770253250600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3299999999999962 " "
y[1] (closed_form) = -0.4730211717641941 " "
y[1] (numeric) = -0.47302117176441544 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.67892291445586100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3199999999999962 " "
y[1] (closed_form) = -0.474617709041221 " "
y[1] (numeric) = -0.47461770904144235 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.663183773865522400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.30999999999999617 " "
y[1] (closed_form) = -0.4761667849428573 " "
y[1] (numeric) = -0.47616678494307857 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.646847613160314000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.29999999999999616 " "
y[1] (closed_form) = -0.4776682445628036 " "
y[1] (numeric) = -0.4776682445630249 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.63340325588517300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.28999999999999615 " "
y[1] (closed_form) = -0.47912193775634915 " "
y[1] (numeric) = -0.4791219377565704 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.618186548584134500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.27999999999999614 " "
y[1] (closed_form) = -0.480527719155386 " "
y[1] (numeric) = -0.4805277191556072 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.60352085505873100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.26999999999999613 " "
y[1] (closed_form) = -0.48188544818294576 " "
y[1] (numeric) = -0.481885448183167 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.590550274773607700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2599999999999961 " "
y[1] (closed_form) = -0.4831949890672571 " "
y[1] (numeric) = -0.4831949890674783 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.578109100087779000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.24999999999999611 " "
y[1] (closed_form) = -0.48445621085532287 " "
y[1] (numeric) = -0.484456210855544 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.56504471508111100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2399999999999961 " "
y[1] (closed_form) = -0.4856689874260153 " "
y[1] (numeric) = -0.4856689874262365 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.55478820727174600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2299999999999961 " "
y[1] (closed_form) = -0.4868331975026879 " "
y[1] (numeric) = -0.48683319750290904 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.542755663331897000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2199999999999961 " "
y[1] (closed_form) = -0.48794872466530315 " "
y[1] (numeric) = -0.48794872466552436 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.533507855939115600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.20999999999999608 " "
y[1] (closed_form) = -0.4890154573620745 " "
y[1] (numeric) = -0.4890154573622956 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.52134819105305730000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.19999999999999607 " "
y[1] (closed_form) = -0.4900332889206212 " "
y[1] (numeric) = -0.4900332889208423 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.51195705175685140000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.18999999999999606 " "
y[1] (closed_form) = -0.49100211755863554 " "
y[1] (numeric) = -0.49100211755885664 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.50305421193414770000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.17999999999999605 " "
y[1] (closed_form) = -0.49192184639406106 " "
y[1] (numeric) = -0.49192184639428216 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.49463501112702900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.16999999999999604 " "
y[1] (closed_form) = -0.4927923834547807 " "
y[1] (numeric) = -0.49279238345500165 " "
absolute error = 2.20934381900406150000000000000E-13 " "
relative error = 4.48331567853218150000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.15999999999999603 " "
y[1] (closed_form) = -0.4936136416878138 " "
y[1] (numeric) = -0.49361364168803484 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.47810565864929900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.14999999999999603 " "
y[1] (closed_form) = -0.49438553896802145 " "
y[1] (numeric) = -0.49438553896824255 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.472236704488265500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.13999999999999602 " "
y[1] (closed_form) = -0.49510799810631884 " "
y[1] (numeric) = -0.49510799810654005 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.467953224400541500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.129999999999996 " "
y[1] (closed_form) = -0.49578094685739427 " "
y[1] (numeric) = -0.4957809468576155 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.46188864373990400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.119999999999996 " "
y[1] (closed_form) = -0.49640431792693335 " "
y[1] (numeric) = -0.49640431792715456 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.45628552508125100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.10999999999999599 " "
y[1] (closed_form) = -0.49697804897834863 " "
y[1] (numeric) = -0.49697804897856984 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.451141013397148500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -9.99999999999959800E-2 " "
y[1] (closed_form) = -0.4975020826390131 " "
y[1] (numeric) = -0.4975020826392343 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.446452494894851400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -8.99999999999959700E-2 " "
y[1] (closed_form) = -0.4979763665059973 " "
y[1] (numeric) = -0.4979763665062184 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.43998812444520200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -7.99999999999959600E-2 " "
y[1] (closed_form) = -0.49840085315130983 " "
y[1] (numeric) = -0.49840085315153093 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.43620659868685600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -6.99999999999959500E-2 " "
y[1] (closed_form) = -0.4987755001266399 " "
y[1] (numeric) = -0.49877550012686106 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.43398736403811400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -5.999999999999595000E-2 " "
y[1] (closed_form) = -0.4991002699676022 " "
y[1] (numeric) = -0.4991002699678233 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.429989896989078300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.99999999999959370E-2 " "
y[1] (closed_form) = -0.49937513019748325 " "
y[1] (numeric) = -0.49937513019770435 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.42755159366192700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.99999999999959300E-2 " "
y[1] (closed_form) = -0.49960005333048907 " "
y[1] (numeric) = -0.4996000533307102 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.426669393468510300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.99999999999959200E-2 " "
y[1] (closed_form) = -0.4997750168744938 " "
y[1] (numeric) = -0.49977501687471493 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.424008961808988400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.99999999999959100E-2 " "
y[1] (closed_form) = -0.49990000333328893 " "
y[1] (numeric) = -0.49990000333351 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.42179241306176250000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -9.999999999995901000E-3 " "
y[1] (closed_form) = -0.49997500020833263 " "
y[1] (numeric) = -0.49997500020855373 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.42223941721026500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.100886297209172000000000000000E-15 " "
y[1] (closed_form) = -0.5 " "
y[1] (numeric) = -0.500000000000221 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.420908084057373300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000000000000410300E-2 " "
y[1] (closed_form) = -0.49997500020833263 " "
y[1] (numeric) = -0.49997500020855373 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.42223941721026500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.00000000000041120E-2 " "
y[1] (closed_form) = -0.4999000033332888 " "
y[1] (numeric) = -0.49990000333351 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.4240133032742500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00000000000041230E-2 " "
y[1] (closed_form) = -0.4997750168744937 " "
y[1] (numeric) = -0.4997750168747149 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.42511968462139400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000041300E-2 " "
y[1] (closed_form) = -0.4996000533304889 " "
y[1] (numeric) = -0.49960005333071006 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.426669393468512500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000041400E-2 " "
y[1] (closed_form) = -0.49937513019748303 " "
y[1] (numeric) = -0.49937513019770413 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.427551593661928600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.00000000000041500E-2 " "
y[1] (closed_form) = -0.499100269967602 " "
y[1] (numeric) = -0.4991002699678231 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.429989896989080500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000041600E-2 " "
y[1] (closed_form) = -0.4987755001266396 " "
y[1] (numeric) = -0.4987755001268607 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.43287441540256400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000041700E-2 " "
y[1] (closed_form) = -0.49840085315130955 " "
y[1] (numeric) = -0.4984008531515306 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.43509281344992900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000041800E-2 " "
y[1] (closed_form) = -0.4979763665059969 " "
y[1] (numeric) = -0.497976366506218 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.439988124445204400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000418 " "
y[1] (closed_form) = -0.4975020826390127 " "
y[1] (numeric) = -0.4975020826392338 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.444220900167179500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000419 " "
y[1] (closed_form) = -0.4969780489783482 " "
y[1] (numeric) = -0.49697804897856934 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.45002403949165740000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1200000000000042 " "
y[1] (closed_form) = -0.49640431792693285 " "
y[1] (numeric) = -0.496404317927154 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.45516726020670600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1300000000000042 " "
y[1] (closed_form) = -0.49578094685739377 " "
y[1] (numeric) = -0.4957809468576149 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.46076897281299800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1400000000000042 " "
y[1] (closed_form) = -0.4951079981063183 " "
y[1] (numeric) = -0.4951079981065395 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.46795322440054650000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1500000000000042 " "
y[1] (closed_form) = -0.49438553896802084 " "
y[1] (numeric) = -0.49438553896824194 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.472236704488271600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000422 " "
y[1] (closed_form) = -0.49361364168781313 " "
y[1] (numeric) = -0.49361364168803423 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.47923024570572200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000423 " "
y[1] (closed_form) = -0.49279238345478 " "
y[1] (numeric) = -0.49279238345500104 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.48556860098371260000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000424 " "
y[1] (closed_form) = -0.49192184639406034 " "
y[1] (numeric) = -0.4919218463942813 " "
absolute error = 2.2098989305163740000000000000E-13 " "
relative error = 4.49237810175664830000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000425 " "
y[1] (closed_form) = -0.49100211755863477 " "
y[1] (numeric) = -0.4910021175588557 " "
absolute error = 2.20934381900406150000000000000E-13 " "
relative error = 4.499662506527224400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000426 " "
y[1] (closed_form) = -0.49003328892062037 " "
y[1] (numeric) = -0.49003328892084136 " "
absolute error = 2.2098989305163740000000000000E-13 " "
relative error = 4.509691444399712000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000427 " "
y[1] (closed_form) = -0.4890154573620737 " "
y[1] (numeric) = -0.4890154573622946 " "
absolute error = 2.20934381900406150000000000000E-13 " "
relative error = 4.51794270660085300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000428 " "
y[1] (closed_form) = -0.48794872466530226 " "
y[1] (numeric) = -0.4879487246655233 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.53009492656200550000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000428 " "
y[1] (closed_form) = -0.48683319750268694 " "
y[1] (numeric) = -0.486833197502908 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.54047516350091660000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000043 " "
y[1] (closed_form) = -0.4856689874260143 " "
y[1] (numeric) = -0.4856689874262353 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 4.55135925755486400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000043 " "
y[1] (closed_form) = -0.48445621085532187 " "
y[1] (numeric) = -0.48445621085554286 " "
absolute error = 2.2098989305163740000000000000E-13 " "
relative error = 4.56160718141012600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000043 " "
y[1] (closed_form) = -0.48319498906725605 " "
y[1] (numeric) = -0.48319498906747715 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.57581142927218630000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000043 " "
y[1] (closed_form) = -0.4818854481829447 " "
y[1] (numeric) = -0.4818854481831658 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.58824635995566330000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000043 " "
y[1] (closed_form) = -0.4805277191553849 " "
y[1] (numeric) = -0.480527719155606 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 4.601210430539264000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000043 " "
y[1] (closed_form) = -0.479121937756348 " "
y[1] (numeric) = -0.47912193775656914 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.61586934509765200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3000000000000043 " "
y[1] (closed_form) = -0.4776682445628024 " "
y[1] (numeric) = -0.47766824456302365 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.63224112815609430000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3100000000000043 " "
y[1] (closed_form) = -0.476166784942856 " "
y[1] (numeric) = -0.4761667849430773 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.64684761316032600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32000000000000434 " "
y[1] (closed_form) = -0.47461770904121975 " "
y[1] (numeric) = -0.474617709041441 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.66201417673138300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.33000000000000435 " "
y[1] (closed_form) = -0.4730211717641928 " "
y[1] (numeric) = -0.4730211717644141 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.67892291445587360000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.34000000000000435 " "
y[1] (closed_form) = -0.4713773327641724 " "
y[1] (numeric) = -0.47137733276439375 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 4.69641740751693570000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.35000000000000436 " "
y[1] (closed_form) = -0.4696863564236887 " "
y[1] (numeric) = -0.46968635642391005 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.71214368763517400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.36000000000000437 " "
y[1] (closed_form) = -0.4679484118389667 " "
y[1] (numeric) = -0.46794841183918795 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.72845816354512200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000044 " "
y[1] (closed_form) = -0.4661636728030164 " "
y[1] (numeric) = -0.4661636728032377 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.74775219244824900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000044 " "
y[1] (closed_form) = -0.4643323177882543 " "
y[1] (numeric) = -0.4643323177884756 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.766477617006039700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3900000000000044 " "
y[1] (closed_form) = -0.4624545299286557 " "
y[1] (numeric) = -0.4624545299288769 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.78343109085101800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4000000000000044 " "
y[1] (closed_form) = -0.46053049700144166 " "
y[1] (numeric) = -0.4605304970016628 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 4.80221023244501600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4100000000000044 " "
y[1] (closed_form) = -0.45856041140830167 " "
y[1] (numeric) = -0.4585604114085229 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 4.82405223288225770000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4200000000000044 " "
y[1] (closed_form) = -0.45654447015615324 " "
y[1] (numeric) = -0.4565444701563745 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.84656946413375600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000443 " "
y[1] (closed_form) = -0.45448287483744165 " "
y[1] (numeric) = -0.454482874837663 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.86977556719133200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.44000000000000444 " "
y[1] (closed_form) = -0.45237583160998074 " "
y[1] (numeric) = -0.45237583161020206 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.89245765343715900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.45000000000000445 " "
y[1] (closed_form) = -0.4502235511763375 " "
y[1] (numeric) = -0.45022355117655877 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 4.91461293461146900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.46000000000000446 " "
y[1] (closed_form) = -0.44802624876276165 " "
y[1] (numeric) = -0.44802624876298297 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.93995520508486200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.47000000000000447 " "
y[1] (closed_form) = -0.4457841440976635 " "
y[1] (numeric) = -0.4457841440978848 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.96480107893960850000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000045 " "
y[1] (closed_form) = -0.4434974613896411 " "
y[1] (numeric) = -0.4434974613898624 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 4.990399702977746400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000045 " "
y[1] (closed_form) = -0.44116642930505967 " "
y[1] (numeric) = -0.44116642930528105 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 5.01802622332300100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000044 " "
y[1] (closed_form) = -0.43879128094518527 " "
y[1] (numeric) = -0.43879128094540665 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 5.04518846941061400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000044 " "
y[1] (closed_form) = -0.43637225382287453 " "
y[1] (numeric) = -0.43637225382309586 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.071884337743915000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000045 " "
y[1] (closed_form) = -0.43390958983882383 " "
y[1] (numeric) = -0.4339095898390451 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.099390610149540000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000045 " "
y[1] (closed_form) = -0.4314035352573794 " "
y[1] (numeric) = -0.4314035352576007 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.130300098884948000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000045 " "
y[1] (closed_form) = -0.4288543406819109 " "
y[1] (numeric) = -0.42885434068213224 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.16079561202772700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000045 " "
y[1] (closed_form) = -0.4262622610297517 " "
y[1] (numeric) = -0.426262261029973 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.192178153992791000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000045 " "
y[1] (closed_form) = -0.4236275555067069 " "
y[1] (numeric) = -0.42362755550692816 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.223159965199444000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000045 " "
y[1] (closed_form) = -0.4209504875811332 " "
y[1] (numeric) = -0.4209504875813545 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.257695773932738000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000045 " "
y[1] (closed_form) = -0.41823132495759224 " "
y[1] (numeric) = -0.41823132495781357 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.29187908106755500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000045 " "
y[1] (closed_form) = -0.4154703395500805 " "
y[1] (numeric) = -0.4154703395503019 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 5.32838207776734400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000045 " "
y[1] (closed_form) = -0.4126678074548379 " "
y[1] (numeric) = -0.41266780745505927 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 5.364568476412682000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000045 " "
y[1] (closed_form) = -0.40982400892273846 " "
y[1] (numeric) = -0.4098240089229598 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.40043909435158600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000045 " "
y[1] (closed_form) = -0.40693922833126567 " "
y[1] (numeric) = -0.406939228331487 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.438722653173628000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000046 " "
y[1] (closed_form) = -0.4040137541560746 " "
y[1] (numeric) = -0.4040137541562959 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.47810458634845500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000046 " "
y[1] (closed_form) = -0.40104787894214494 " "
y[1] (numeric) = -0.4010478789423662 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.51723274017648300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000046 " "
y[1] (closed_form) = -0.39804189927452654 " "
y[1] (numeric) = -0.39804189927474776 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 5.557503822078645000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000046 " "
y[1] (closed_form) = -0.39499611574868115 " "
y[1] (numeric) = -0.3949961157489024 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.601762649954173000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000046 " "
y[1] (closed_form) = -0.3919108329404232 " "
y[1] (numeric) = -0.3919108329406445 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.64586202294208900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000046 " "
y[1] (closed_form) = -0.3887863593754625 " "
y[1] (numeric) = -0.38878635937568373 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 5.68980707069847300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000046 " "
y[1] (closed_form) = -0.38562300749855183 " "
y[1] (numeric) = -0.38562300749877304 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 5.7364818321270210000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000046 " "
y[1] (closed_form) = -0.38242109364224275 " "
y[1] (numeric) = -0.382421093642464 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.78596349642759700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000046 " "
y[1] (closed_form) = -0.3791809379952526 " "
y[1] (numeric) = -0.37918093799547387 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.83540538661160200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000046 " "
y[1] (closed_form) = -0.37590286457044597 " "
y[1] (numeric) = -0.37590286457066724 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 5.88629323324369500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000046 " "
y[1] (closed_form) = -0.37258720117243366 " "
y[1] (numeric) = -0.372587201172655 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 5.9401653965187200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000047 " "
y[1] (closed_form) = -0.36923427936479236 " "
y[1] (numeric) = -0.3692342793650138 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 5.99711334067976300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000047 " "
y[1] (closed_form) = -0.36584443443690884 " "
y[1] (numeric) = -0.3658444344371302 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 6.05116410889212800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000047 " "
y[1] (closed_form) = -0.362418005370451 " "
y[1] (numeric) = -0.36241800537067237 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 6.10837397231329200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000047 " "
y[1] (closed_form) = -0.35895533480547004 " "
y[1] (numeric) = -0.3589553348056914 " "
absolute error = 2.21378471110256210000000000000E-13 " "
relative error = 6.16729853674493100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000047 " "
y[1] (closed_form) = -0.35545676900613704 " "
y[1] (numeric) = -0.35545676900635836 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 6.22643818481351800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000047 " "
y[1] (closed_form) = -0.35192265782611637 " "
y[1] (numeric) = -0.3519226578263377 " "
absolute error = 2.21322959959024960000000000000E-13 " "
relative error = 6.28896591444759400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000047 " "
y[1] (closed_form) = -0.34835335467358103 " "
y[1] (numeric) = -0.3483533546738023 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 6.35181047747132700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000047 " "
y[1] (closed_form) = -0.3447492164758718 " "
y[1] (numeric) = -0.344749216476093 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 6.41660450799152200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000047 " "
y[1] (closed_form) = -0.341110603643805 " "
y[1] (numeric) = -0.3411106036440263 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 6.4866775305186900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000047 " "
y[1] (closed_form) = -0.3374378800356318 " "
y[1] (numeric) = -0.33743788003585307 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 6.5572794845803600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000047 " "
y[1] (closed_form) = -0.3337314129206523 " "
y[1] (numeric) = -0.33373141292087355 " "
absolute error = 2.2126744880779370000000000000E-13 " "
relative error = 6.630105535207801000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000048 " "
y[1] (closed_form) = -0.3299915729424893 " "
y[1] (numeric) = -0.32999157294271053 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 6.70356323599557800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000048 " "
y[1] (closed_form) = -0.3262187340820241 " "
y[1] (numeric) = -0.32621873408224533 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 6.78109239431176100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000048 " "
y[1] (closed_form) = -0.3224132736199988 " "
y[1] (numeric) = -0.32241327362021993 " "
absolute error = 2.21156426505331180000000000000E-13 " "
relative error = 6.85940823782551600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000048 " "
y[1] (closed_form) = -0.3185755720992883 " "
y[1] (numeric) = -0.3185755720995093 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 6.93855472804352200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000048 " "
y[1] (closed_form) = -0.31470601328684655 " "
y[1] (numeric) = -0.31470601328706754 " "
absolute error = 2.2098989305163740000000000000E-13 " "
relative error = 7.02210582961472500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000048 " "
y[1] (closed_form) = -0.31080498413533036 " "
y[1] (numeric) = -0.31080498413555135 " "
absolute error = 2.2098989305163740000000000000E-13 " "
relative error = 7.11024289608606200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000048 " "
y[1] (closed_form) = -0.3068728747444039 " "
y[1] (numeric) = -0.306872874744625 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 7.20496770978067300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000048 " "
y[1] (closed_form) = -0.3029100783217295 " "
y[1] (numeric) = -0.3029100783219506 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 7.29922611288166800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000048 " "
y[1] (closed_form) = -0.29891699114364717 " "
y[1] (numeric) = -0.29891699114386827 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 7.39673293606277200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000048 " "
y[1] (closed_form) = -0.29489401251554714 " "
y[1] (numeric) = -0.2948940125157682 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 7.4957576221122800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000048 " "
y[1] (closed_form) = -0.2908415447319398 " "
y[1] (numeric) = -0.29084154473216084 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 7.60020045989646300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000048 " "
y[1] (closed_form) = -0.28675999303622635 " "
y[1] (numeric) = -0.28675999303644745 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 7.71031248163575900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000049 " "
y[1] (closed_form) = -0.2826497655801751 " "
y[1] (numeric) = -0.28264976558039623 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 7.82243406076285700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000049 " "
y[1] (closed_form) = -0.2785112733831066 " "
y[1] (numeric) = -0.2785112733833277 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 7.93867022574573400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000049 " "
y[1] (closed_form) = -0.27434493029079177 " "
y[1] (numeric) = -0.27434493029101287 " "
absolute error = 2.21100915354099930000000000000E-13 " "
relative error = 8.05923095133356800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000049 " "
y[1] (closed_form) = -0.27015115293406783 " "
y[1] (numeric) = -0.27015115293428904 " "
absolute error = 2.21211937656562440000000000000E-13 " "
relative error = 8.18845062306843700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000038 " "
y[1] (closed_form) = -0.2659303606871761 " "
y[1] (numeric) = -0.26593036068739695 " "
absolute error = 2.20823359597943640000000000000E-13 " "
relative error = 8.30380401197238400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000027 " "
y[1] (closed_form) = -0.26168297562582366 " "
y[1] (numeric) = -0.261682975626044 " "
absolute error = 2.20323759236862320000000000000E-13 " "
relative error = 8.41949151296337300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000016 " "
y[1] (closed_form) = -0.257409422484977 " "
y[1] (numeric) = -0.2574094224851969 " "
absolute error = 2.19879670027012250000000000000E-13 " "
relative error = 8.54202103032358700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000005 " "
y[1] (closed_form) = -0.253110128616389 " "
y[1] (numeric) = -0.25311012861660837 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 8.66737616804031700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999994 " "
y[1] (closed_form) = -0.24878552394586376 " "
y[1] (numeric) = -0.2487855239460827 " "
absolute error = 2.18935980456080870000000000000E-13 " "
relative error = 8.80018969687809500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0599999999999983 " "
y[1] (closed_form) = -0.24443604093026453 " "
y[1] (numeric) = -0.244436040930483 " "
absolute error = 2.18464135670615180000000000000E-13 " "
relative error = 8.93747643920239500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0699999999999972 " "
y[1] (closed_form) = -0.2400621145142683 " "
y[1] (numeric) = -0.24006211451448622 " "
absolute error = 2.17936779733918230000000000000E-13 " "
relative error = 9.0783495836018300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.079999999999996 " "
y[1] (closed_form) = -0.23566418208687173 " "
y[1] (numeric) = -0.23566418208708914 " "
absolute error = 2.17409423797221280000000000000E-13 " "
relative error = 9.2253910573936400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.089999999999995 " "
y[1] (closed_form) = -0.23124268343765267 " "
y[1] (numeric) = -0.2312426834378696 " "
absolute error = 2.1693757901175560000000000000E-13 " "
relative error = 9.38138131709780200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999939 " "
y[1] (closed_form) = -0.22679806071279143 " "
y[1] (numeric) = -0.22679806071300787 " "
absolute error = 2.16437978650674270000000000000E-13 " "
relative error = 9.54320235236769600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999928 " "
y[1] (closed_form) = -0.22233075837085667 " "
y[1] (numeric) = -0.2223307583710726 " "
absolute error = 2.15938378289592950000000000000E-13 " "
relative error = 9.71248332313062200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999917 " "
y[1] (closed_form) = -0.21784122313835982 " "
y[1] (numeric) = -0.2178412231385753 " "
absolute error = 2.15466533504127260000000000000E-13 " "
relative error = 9.89098988703693200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999906 " "
y[1] (closed_form) = -0.21332990396508292 " "
y[1] (numeric) = -0.21332990396529786 " "
absolute error = 2.1493917756743030000000000000E-13 " "
relative error = 1.00754359127546780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999895 " "
y[1] (closed_form) = -0.20879725197918383 " "
y[1] (numeric) = -0.20879725197939827 " "
absolute error = 2.14439577206348990000000000000E-13 " "
relative error = 1.02702298604833960000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999884 " "
y[1] (closed_form) = -0.20424372044208397 " "
y[1] (numeric) = -0.2042437204422979 " "
absolute error = 2.13939976845267670000000000000E-13 " "
relative error = 1.04747395113150220000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999873 " "
y[1] (closed_form) = -0.1996697647031424 " "
y[1] (numeric) = -0.19966976470335587 " "
absolute error = 2.13468132059801970000000000000E-13 " "
relative error = 1.06910594289112430000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999862 " "
y[1] (closed_form) = -0.19507584215412146 " "
y[1] (numeric) = -0.19507584215433443 " "
absolute error = 2.12968531698720650000000000000E-13 " "
relative error = 1.09172170857764600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.179999999999985 " "
y[1] (closed_form) = -0.19046241218344778 " "
y[1] (numeric) = -0.19046241218366025 " "
absolute error = 2.12468931337639330000000000000E-13 " "
relative error = 1.11554258345208570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999984 " "
y[1] (closed_form) = -0.1858299361302739 " "
y[1] (numeric) = -0.18582993613048585 " "
absolute error = 2.11941575400942380000000000000E-13 " "
relative error = 1.14051363205744850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999829 " "
y[1] (closed_form) = -0.18117887723834478 " "
y[1] (numeric) = -0.18117887723855622 " "
absolute error = 2.11441975039861060000000000000E-13 " "
relative error = 1.16703435998063140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999818 " "
y[1] (closed_form) = -0.1765097006096737 " "
y[1] (numeric) = -0.17650970060988463 " "
absolute error = 2.10942374678779740000000000000E-13 " "
relative error = 1.19507525053962370000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999807 " "
y[1] (closed_form) = -0.1718228731580326 " "
y[1] (numeric) = -0.17182287315824302 " "
absolute error = 2.1041501874208280000000000000E-13 " "
relative error = 1.22460423850877760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999796 " "
y[1] (closed_form) = -0.16711886356226094 " "
y[1] (numeric) = -0.16711886356247085 " "
absolute error = 2.09915418381001470000000000000E-13 " "
relative error = 1.2560845251487512000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999785 " "
y[1] (closed_form) = -0.1623981422193983 " "
y[1] (numeric) = -0.16239814221960772 " "
absolute error = 2.09415818019920150000000000000E-13 " "
relative error = 1.28952102011734500000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999774 " "
y[1] (closed_form) = -0.15766118119764508 " "
y[1] (numeric) = -0.15766118119785397 " "
absolute error = 2.0888846208322320000000000000E-13 " "
relative error = 1.32492006273477850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999763 " "
y[1] (closed_form) = -0.15290845418915597 " "
y[1] (numeric) = -0.15290845418936433 " "
absolute error = 2.08361106146526250000000000000E-13 " "
relative error = 1.36265262278286060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999751 " "
y[1] (closed_form) = -0.14814043646267122 " "
y[1] (numeric) = -0.14814043646287905 " "
absolute error = 2.0783375020982930000000000000E-13 " "
relative error = 1.40295084294692040000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.279999999999974 " "
y[1] (closed_form) = -0.1433576048159902 " "
y[1] (numeric) = -0.1433576048161975 " "
absolute error = 2.07306394273132360000000000000E-13 " "
relative error = 1.44607880788204440000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999973 " "
y[1] (closed_form) = -0.1385604375282918 " "
y[1] (numeric) = -0.1385604375284986 " "
absolute error = 2.0677903833643540000000000000E-13 " "
relative error = 1.49233823178578280000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999718 " "
y[1] (closed_form) = -0.13374941431230727 " "
y[1] (numeric) = -0.13374941431251353 " "
absolute error = 2.06251682399738460000000000000E-13 " "
relative error = 1.54207540616317830000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999707 " "
y[1] (closed_form) = -0.12892501626634897 " "
y[1] (numeric) = -0.1289250162665547 " "
absolute error = 2.0572432646304150000000000000E-13 " "
relative error = 1.5956897460306010000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999696 " "
y[1] (closed_form) = -0.12408772582620119 " "
y[1] (numeric) = -0.12408772582640637 " "
absolute error = 2.05183092738536740000000000000E-13 " "
relative error = 1.6535325421784158000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999685 " "
y[1] (closed_form) = -0.11923802671687687 " "
y[1] (numeric) = -0.11923802671708153 " "
absolute error = 2.0465573680183980000000000000E-13 " "
relative error = 1.71636299624264850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999674 " "
y[1] (closed_form) = -0.11437640390424558 " "
y[1] (numeric) = -0.11437640390444968 " "
absolute error = 2.04100625289527220000000000000E-13 " "
relative error = 1.78446443779083640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999663 " "
y[1] (closed_form) = -0.10950334354653721 " "
y[1] (numeric) = -0.10950334354674077 " "
absolute error = 2.03559391565022450000000000000E-13 " "
relative error = 1.85893311539398670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3599999999999652 " "
y[1] (closed_form) = -0.10461933294572667 " "
y[1] (numeric) = -0.1046193329459297 " "
absolute error = 2.0303203562832550000000000000E-13 " "
relative error = 1.940674155642460000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3699999999999641 " "
y[1] (closed_form) = -9.97248604988040500E-2 " "
y[1] (numeric) = -9.97248604990065400E-2 " "
absolute error = 2.02490801903820740000000000000E-13 " "
relative error = 2.03049471206078160000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.379999999999963 " "
y[1] (closed_form) = -9.48204156489353300E-2 " "
y[1] (numeric) = -9.48204156491372800E-2 " "
absolute error = 2.01949568179315970000000000000E-13 " "
relative error = 2.12981104118987820000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.389999999999962 " "
y[1] (closed_form) = -8.99064888365184600E-2 " "
y[1] (numeric) = -8.99064888367198800E-2 " "
absolute error = 2.01422212242619030000000000000E-13 " "
relative error = 2.24035233551245970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999608 " "
y[1] (closed_form) = -8.49835714501397700E-2 " "
y[1] (numeric) = -8.49835714503406200E-2 " "
absolute error = 2.00853222942498630000000000000E-13 " "
relative error = 2.3634358913750772000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999597 " "
y[1] (closed_form) = -8.00521557774354700E-2 " "
y[1] (numeric) = -8.00521557776357600E-2 " "
absolute error = 2.00284233642378240000000000000E-13 " "
relative error = 2.50192179957298400000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999586 " "
y[1] (closed_form) = -7.51127349558633400E-2 " "
y[1] (numeric) = -7.51127349560630800E-2 " "
absolute error = 1.99742999917873480000000000000E-13 " "
relative error = 2.65924280396984070000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999575 " "
y[1] (closed_form) = -7.01658029233893600E-2 " "
y[1] (numeric) = -7.01658029235885400E-2 " "
absolute error = 1.99174010617753080000000000000E-13 " "
relative error = 2.83861941742791060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999564 " "
y[1] (closed_form) = -6.52118543690943600E-2 " "
y[1] (numeric) = -6.52118543692929800E-2 " "
absolute error = 1.9861889910544050000000000000E-13 " "
relative error = 3.04574836932671800000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4499999999999553 " "
y[1] (closed_form) = -6.02513846837054600E-2 " "
y[1] (numeric) = -6.025138468390354000E-2 " "
absolute error = 1.98077665380935740000000000000E-13 " "
relative error = 3.28752055111696640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4599999999999542 " "
y[1] (closed_form) = -5.528488991005752000E-2 " "
y[1] (numeric) = -5.52848899102550400E-2 " "
absolute error = 1.97515614974719260000000000000E-13 " "
relative error = 3.57268713559990000000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4699999999999531 " "
y[1] (closed_form) = -5.031286669348918000E-2 " "
y[1] (numeric) = -5.03128666936861400E-2 " "
absolute error = 1.96967442356310580000000000000E-13 " "
relative error = 3.91485230917679950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.479999999999952 " "
y[1] (closed_form) = -4.53358122321787200E-2 " "
y[1] (numeric) = -4.53358122323751300E-2 " "
absolute error = 1.964123308439980000000000000E-13 " "
relative error = 4.3323880432120570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.489999999999951 " "
y[1] (closed_form) = -4.03542242274247700E-2 " "
y[1] (numeric) = -4.03542242276206400E-2 " "
absolute error = 1.95871097119493240000000000000E-13 " "
relative error = 4.8537941409955065000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999498 " "
y[1] (closed_form) = -3.53686008338764850E-2 " "
y[1] (numeric) = -3.53686008340718100E-2 " "
absolute error = 1.95329863394988480000000000000E-13 " "
relative error = 5.5226912795458720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999487 " "
y[1] (closed_form) = -3.037944060971854400E-2 " "
y[1] (numeric) = -3.037944060991333300E-2 " "
absolute error = 1.94785160223531760000000000000E-13 " "
relative error = 6.4117428206106910000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999476 " "
y[1] (closed_form) = -2.538724246681575700E-2 " "
y[1] (numeric) = -2.538724246700999600E-2 " "
absolute error = 1.9423698760512310000000000000E-13 " "
relative error = 7.6509683105211080000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999465 " "
y[1] (closed_form) = -2.03925056208222500E-2 " "
y[1] (numeric) = -2.03925056210159380E-2 " "
absolute error = 1.93688814986714420000000000000E-13 " "
relative error = 9.4980390633774740000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999454 " "
y[1] (closed_form) = -1.53957295412603600E-2 " "
y[1] (numeric) = -1.539572954145349600E-2 " "
absolute error = 1.93135438197877820000000000000E-13 " "
relative error = 1.2544740908852503000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5499999999999443 " "
y[1] (closed_form) = -1.039741390157407500E-2 " "
y[1] (numeric) = -1.03974139017666610E-2 " "
absolute error = 1.92585530855993170000000000000E-13 " "
relative error = 1.852244535795939000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5599999999999432 " "
y[1] (closed_form) = -5.398058529162116000E-3 " "
y[1] (numeric) = -5.3980585293541520000E-3 " "
absolute error = 1.92034756152370530000000000000E-13 " "
relative error = 3.55747821397146000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999942 " "
y[1] (closed_form) = -3.9816335539560850000E-4 " "
y[1] (numeric) = -3.98163355587092760000E-4 " "
absolute error = 1.91484252499291020000000000000E-13 " "
relative error = 4.80918823654767100000000E-8 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.579999999999941 " "
y[1] (closed_form) = 4.601771634374637300E-3 " "
y[1] (numeric) = 4.601771634183704000E-3 " "
absolute error = 1.90933206745125260000000000000E-13 " "
relative error = 4.1491239008663305000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.58999999999994 " "
y[1] (closed_form) = 9.601246450816243000E-3 " "
y[1] (numeric) = 9.601246450625859000E-3 " "
absolute error = 1.9038416676497860000000000000E-13 " "
relative error = 1.9829109453678614000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999388 " "
y[1] (closed_form) = 1.459976115061377700E-2 " "
y[1] (numeric) = 1.459976115042394600E-2 " "
absolute error = 1.898307899761420000000000000E-13 " "
relative error = 1.300232161456706000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999377 " "
y[1] (closed_form) = 1.95968158864626820E-2 " "
y[1] (numeric) = 1.9596815886273400E-2 " "
absolute error = 1.89282617357733330000000000000E-13 " "
relative error = 9.6588455213526910000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999366 " "
y[1] (closed_form) = 2.459191095705356400E-2 " "
y[1] (numeric) = 2.459191095686483200E-2 " "
absolute error = 1.8873097529237270000000000000E-13 " "
relative error = 7.6745144215089980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999355 " "
y[1] (closed_form) = 2.95845468570419300E-2 " "
y[1] (numeric) = 2.95845468568537500E-2 " "
absolute error = 1.88179333227012080000000000000E-13 " "
relative error = 6.3607306252257250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999344 " "
y[1] (closed_form) = 3.4574224326998300E-2 " "
y[1] (numeric) = 3.45742243268106700E-2 " "
absolute error = 1.87627691161651460000000000000E-13 " "
relative error = 5.4268084046396630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6499999999999333 " "
y[1] (closed_form) = 3.95604444033337300E-2 " "
y[1] (numeric) = 3.956044440314665500E-2 " "
absolute error = 1.87072579649338880000000000000E-13 " "
relative error = 4.7287785178058930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6599999999999322 " "
y[1] (closed_form) = 4.45427084681957500E-2 " "
y[1] (numeric) = 4.45427084680092230E-2 " "
absolute error = 1.86531345924834100000000000000E-13 " "
relative error = 4.1876965352931030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.669999999999931 " "
y[1] (closed_form) = 4.95205182993297630E-2 " "
y[1] (numeric) = 4.95205182991437730E-2 " "
absolute error = 1.85990112200329350000000000000E-13 " "
relative error = 3.75581917531841900000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.67999999999993 " "
y[1] (closed_form) = 5.449337611990079000E-2 " "
y[1] (numeric) = 5.449337611971534000E-2 " "
absolute error = 1.85448878475824590000000000000E-13 " "
relative error = 3.4031453303202350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.689999999999929 " "
y[1] (closed_form) = 5.946078464827084000E-2 " "
y[1] (numeric) = 5.94607846480859400E-2 " "
absolute error = 1.848937669635120000000000000E-13 " "
relative error = 3.1095076874147650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999278 " "
y[1] (closed_form) = 6.44222471477265400E-2 " "
y[1] (numeric) = 6.44222471475421900E-2 " "
absolute error = 1.84352533239007240000000000000E-13 " "
relative error = 2.8616284187707514000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999267 " "
y[1] (closed_form) = 6.9377267476152490E-2 " "
y[1] (numeric) = 6.9377267475968710E-2 " "
absolute error = 1.83797421726694670000000000000E-13 " "
relative error = 2.6492456162225260000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999256 " "
y[1] (closed_form) = 7.43253501356450300E-2 " "
y[1] (numeric) = 7.43253501354618000E-2 " "
absolute error = 1.83242310214382100000000000000E-13 " "
relative error = 2.4654079648459340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999245 " "
y[1] (closed_form) = 7.9266000322061600E-2 " "
y[1] (numeric) = 7.9266000321878900E-2 " "
absolute error = 1.82701076489877320000000000000E-13 " "
relative error = 2.30491100531821950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999234 " "
y[1] (closed_form) = 8.41987239745007400E-2 " "
y[1] (numeric) = 8.41987239743185900E-2 " "
absolute error = 1.82159842765372560000000000000E-13 " "
relative error = 2.1634513466087560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7499999999999223 " "
y[1] (closed_form) = 8.91230278247078100E-2 " "
y[1] (numeric) = 8.91230278245261800E-2 " "
absolute error = 1.8163248682867560000000000000E-13 " "
relative error = 2.03799726357951630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7599999999999212 " "
y[1] (closed_form) = 9.40384194464013400E-2 " "
y[1] (numeric) = 9.40384194462202700E-2 " "
absolute error = 1.81077375316363030000000000000E-13 " "
relative error = 1.92556804317166200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.76999999999992 " "
y[1] (closed_form) = 9.89444073045153200E-2 " "
y[1] (numeric) = 9.89444073043347900E-2 " "
absolute error = 1.80536141591858270000000000000E-13 " "
relative error = 1.82462199239046330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.779999999999919 " "
y[1] (closed_form) = 0.10384050080435227 " "
y[1] (numeric) = 0.10384050080417226 " "
absolute error = 1.80008785655161320000000000000E-13 " "
relative error = 1.73351230262572650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999179 " "
y[1] (closed_form) = 0.10872621034064223 " "
y[1] (numeric) = 0.10872621034046276 " "
absolute error = 1.79467551930656550000000000000E-13 " "
relative error = 1.65063742558836320000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999168 " "
y[1] (closed_form) = 0.113601047346503 " "
y[1] (numeric) = 0.11360104734632409 " "
absolute error = 1.78912440418343980000000000000E-13 " "
relative error = 1.57491893426501470000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999157 " "
y[1] (closed_form) = 0.11846452434229636 " "
y[1] (numeric) = 0.11846452434211797 " "
absolute error = 1.78385084481647030000000000000E-13 " "
relative error = 1.50581016107584810000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999146 " "
y[1] (closed_form) = 0.12331615498437559 " "
y[1] (numeric) = 0.12331615498419773 " "
absolute error = 1.77857728544950080000000000000E-13 " "
relative error = 1.44229057877684420000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999135 " "
y[1] (closed_form) = 0.1281554541137195 " "
y[1] (numeric) = 0.12815545411354218 " "
absolute error = 1.77330372608253130000000000000E-13 " "
relative error = 1.38371303690982940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999124 " "
y[1] (closed_form) = 0.13298193780444792 " "
y[1] (numeric) = 0.1329819378042711 " "
absolute error = 1.7683077224717180000000000000E-13 " "
relative error = 1.32973526455302780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8499999999999113 " "
y[1] (closed_form) = 0.13779512341221378 " "
y[1] (numeric) = 0.13779512341203745 " "
absolute error = 1.7633117188609050000000000000E-13 " "
relative error = 1.27966191777771580000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8599999999999102 " "
y[1] (closed_form) = 0.14259452962246733 " "
y[1] (numeric) = 0.14259452962229152 " "
absolute error = 1.75803815949393540000000000000E-13 " "
relative error = 1.2328931300159339000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.869999999999909 " "
y[1] (closed_form) = 0.147379676498587 " "
y[1] (numeric) = 0.14737967649841172 " "
absolute error = 1.7527646001269660000000000000E-13 " "
relative error = 1.1892851455293910000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.879999999999908 " "
y[1] (closed_form) = 0.1521500855298728 " "
y[1] (numeric) = 0.15215008552969803 " "
absolute error = 1.74776859651615270000000000000E-13 " "
relative error = 1.14871351562467560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999069 " "
y[1] (closed_form) = 0.15690527967939696 " "
y[1] (numeric) = 0.15690527967922266 " "
absolute error = 1.74305014866149580000000000000E-13 " "
relative error = 1.11089324223063310000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999058 " "
y[1] (closed_form) = 0.16164478343170713 " "
y[1] (numeric) = 0.1616447834315333 " "
absolute error = 1.73833170080683890000000000000E-13 " "
relative error = 1.07540228883492680000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999047 " "
y[1] (closed_form) = 0.16636812284037766 " "
y[1] (numeric) = 0.16636812284020433 " "
absolute error = 1.73333569719602560000000000000E-13 " "
relative error = 1.04186767729481390000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999999036 " "
y[1] (closed_form) = 0.1710748255754038 " "
y[1] (numeric) = 0.17107482557523104 " "
absolute error = 1.72750702631674360000000000000E-13 " "
relative error = 1.00979616405063570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999999025 " "
y[1] (closed_form) = 0.1757644209704343 " "
y[1] (numeric) = 0.17576442097026204 " "
absolute error = 1.72251102270593040000000000000E-13 " "
relative error = 9.80011206588663100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999999014 " "
y[1] (closed_form) = 0.1804364400698376 " "
y[1] (numeric) = 0.1804364400696659 " "
absolute error = 1.7172374633389610000000000000E-13 " "
relative error = 9.51713225263315600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9499999999999003 " "
y[1] (closed_form) = 0.18509041567559714 " "
y[1] (numeric) = 0.18509041567542592 " "
absolute error = 1.71224145972814770000000000000E-13 " "
relative error = 9.25083804841167900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9599999999998992 " "
y[1] (closed_form) = 0.1897258823940306 " "
y[1] (numeric) = 0.1897258823938599 " "
absolute error = 1.70696790036117820000000000000E-13 " "
relative error = 8.99702180230779700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.969999999999898 " "
y[1] (closed_form) = 0.19434237668232907 " "
y[1] (numeric) = 0.19434237668215887 " "
absolute error = 1.7019718967503650000000000000E-13 " "
relative error = 8.75759536239694300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.979999999999897 " "
y[1] (closed_form) = 0.19893943689491073 " "
y[1] (numeric) = 0.19893943689474103 " "
absolute error = 1.69697589313955180000000000000E-13 " "
relative error = 8.53011308178164400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998959 " "
y[1] (closed_form) = 0.2035166033295852 " "
y[1] (numeric) = 0.203516603329416 " "
absolute error = 1.69197988952873860000000000000E-13 " "
relative error = 8.31371918481097900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998948 " "
y[1] (closed_form) = 0.20807341827352335 " "
y[1] (numeric) = 0.20807341827335465 " "
absolute error = 1.68698388591792540000000000000E-13 " "
relative error = 8.10763767864041600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998936 " "
y[1] (closed_form) = 0.21260942604902808 " "
y[1] (numeric) = 0.2126094260488599 " "
absolute error = 1.68171032655095600000000000000E-13 " "
relative error = 7.9098577979470710000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998925 " "
y[1] (closed_form) = 0.21712417305910184 " "
y[1] (numeric) = 0.21712417305893414 " "
absolute error = 1.6769918786962990000000000000E-13 " "
relative error = 7.7236534977605500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998914 " "
y[1] (closed_form) = 0.2216172078328059 " "
y[1] (numeric) = 0.22161720783263872 " "
absolute error = 1.67171831932932950000000000000E-13 " "
relative error = 7.54326947657656400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998903 " "
y[1] (closed_form) = 0.22608808107040707 " "
y[1] (numeric) = 0.2260880810702404 " "
absolute error = 1.66672231571851630000000000000E-13 " "
relative error = 7.37200434373838200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998892 " "
y[1] (closed_form) = 0.2305363456883073 " "
y[1] (numeric) = 0.2305363456881411 " "
absolute error = 1.66200386786385930000000000000E-13 " "
relative error = 7.20929215261763100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999888 " "
y[1] (closed_form) = 0.23496155686375172 " "
y[1] (numeric) = 0.23496155686358597 " "
absolute error = 1.65756297576535870000000000000E-13 " "
relative error = 7.05461352014507400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999887 " "
y[1] (closed_form) = 0.23936327207931038 " "
y[1] (numeric) = 0.23936327207914515 " "
absolute error = 1.65228941639838920000000000000E-13 " "
relative error = 6.90285273110287900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999886 " "
y[1] (closed_form) = 0.24374105116712988 " "
y[1] (numeric) = 0.24374105116696512 " "
absolute error = 1.64757096854373230000000000000E-13 " "
relative error = 6.75951367508469300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999885 " "
y[1] (closed_form) = 0.2480944563529495 " "
y[1] (numeric) = 0.24809445635278518 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 6.62300198319484600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998837 " "
y[1] (closed_form) = 0.25242305229987855 " "
y[1] (numeric) = 0.2524230522997148 " "
absolute error = 1.6375789613221060000000000000E-13 " "
relative error = 6.48743823672911700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998826 " "
y[1] (closed_form) = 0.25672640615192943 " "
y[1] (numeric) = 0.2567264061517662 " "
absolute error = 1.63258295771129270000000000000E-13 " "
relative error = 6.35923270294656900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998815 " "
y[1] (closed_form) = 0.2610040875773031 " "
y[1] (numeric) = 0.2610040875771403 " "
absolute error = 1.6281420656127920000000000000E-13 " "
relative error = 6.23799451083529700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998804 " "
y[1] (closed_form) = 0.26525566881142176 " "
y[1] (numeric) = 0.2652556688112594 " "
absolute error = 1.62370117351429140000000000000E-13 " "
relative error = 6.1212685134681500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998793 " "
y[1] (closed_form) = 0.2694807246997049 " "
y[1] (numeric) = 0.26948072469954293 " "
absolute error = 1.61981539292810340000000000000E-13 " "
relative error = 6.01087663963031300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998782 " "
y[1] (closed_form) = 0.2736788327400846 " "
y[1] (numeric) = 0.27367883273992305 " "
absolute error = 1.61537450082960280000000000000E-13 " "
relative error = 5.90244588759898600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999877 " "
y[1] (closed_form) = 0.2778495731252552 " "
y[1] (numeric) = 0.27784957312509406 " "
absolute error = 1.61148872024341470000000000000E-13 " "
relative error = 5.799860342117394000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999876 " "
y[1] (closed_form) = 0.28199252878465386 " "
y[1] (numeric) = 0.2819925287844931 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 5.700870681169312000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999875 " "
y[1] (closed_form) = 0.2861072854261671 " "
y[1] (numeric) = 0.2861072854260067 " "
absolute error = 1.60371715907103860000000000000E-13 " "
relative error = 5.60529997228922000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999874 " "
y[1] (closed_form) = 0.29019343157755956 " "
y[1] (numeric) = 0.29019343157739974 " "
absolute error = 1.59816604394791280000000000000E-13 " "
relative error = 5.5072440311963900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998727 " "
y[1] (closed_form) = 0.2942505586276214 " "
y[1] (numeric) = 0.29425055862746197 " "
absolute error = 1.59428026336172480000000000000E-13 " "
relative error = 5.4181044576343900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998716 " "
y[1] (closed_form) = 0.29827826086702847 " "
y[1] (numeric) = 0.29827826086686937 " "
absolute error = 1.59094959428784930000000000000E-13 " "
relative error = 5.33377655368954200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998705 " "
y[1] (closed_form) = 0.3022761355289132 " "
y[1] (numeric) = 0.30227613552875454 " "
absolute error = 1.58650870218934870000000000000E-13 " "
relative error = 5.24854103819120900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998694 " "
y[1] (closed_form) = 0.306243782829141 " "
y[1] (numeric) = 0.30624378282898274 " "
absolute error = 1.58262292160316060000000000000E-13 " "
relative error = 5.16785322785192600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998683 " "
y[1] (closed_form) = 0.31018080600628817 " "
y[1] (numeric) = 0.3101808060061304 " "
absolute error = 1.57762691799234740000000000000E-13 " "
relative error = 5.08615261629168900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999867 " "
y[1] (closed_form) = 0.3140868113613179 " "
y[1] (numeric) = 0.3140868113611607 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 5.00522704552768900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999866 " "
y[1] (closed_form) = 0.31796140829694963 " "
y[1] (numeric) = 0.31796140829679276 " "
absolute error = 1.56874513379534620000000000000E-13 " "
relative error = 4.93375954710286170000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999865 " "
y[1] (closed_form) = 0.3218042093567186 " "
y[1] (numeric) = 0.32180420935656223 " "
absolute error = 1.5637491301845330000000000000E-13 " "
relative error = 4.859318444934086500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999864 " "
y[1] (closed_form) = 0.32561483026372123 " "
y[1] (numeric) = 0.3256148302635652 " "
absolute error = 1.56041846111065750000000000000E-13 " "
relative error = 4.79222171744096200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999863 " "
y[1] (closed_form) = 0.32939288995904226 " "
y[1] (numeric) = 0.32939288995888655 " "
absolute error = 1.5570877920367820000000000000E-13 " "
relative error = 4.72714451192433200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998617 " "
y[1] (closed_form) = 0.33313801063986054 " "
y[1] (numeric) = 0.3331380106397053 " "
absolute error = 1.55264689993828140000000000000E-13 " "
relative error = 4.660671704667088700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998606 " "
y[1] (closed_form) = 0.33684981779722895 " "
y[1] (numeric) = 0.3368498177970741 " "
absolute error = 1.54820600783978080000000000000E-13 " "
relative error = 4.59613135005981600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998595 " "
y[1] (closed_form) = 0.34052794025352484 " "
y[1] (numeric) = 0.34052794025337046 " "
absolute error = 1.54376511574128020000000000000E-13 " "
relative error = 4.53344625581072400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998584 " "
y[1] (closed_form) = 0.3441720101995678 " "
y[1] (numeric) = 0.3441720101994137 " "
absolute error = 1.54098955817971730000000000000E-13 " "
relative error = 4.47738198491555440000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998573 " "
y[1] (closed_form) = 0.3477816632313998 " "
y[1] (numeric) = 0.34778166323124615 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 4.418141692130730400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999856 " "
y[1] (closed_form) = 0.3513565383867258 " "
y[1] (numeric) = 0.3513565383865726 " "
absolute error = 1.5321077739827160000000000000E-13 " "
relative error = 4.360550058403578000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999855 " "
y[1] (closed_form) = 0.3548962781810092 " "
y[1] (numeric) = 0.35489627818085645 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 4.304544667850963600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.369999999999854 " "
y[1] (closed_form) = 0.35840052864322053 " "
y[1] (numeric) = 0.3584005286430681 " "
absolute error = 1.524336212810340000000000000E-13 " "
relative error = 4.253163963180928700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999853 " "
y[1] (closed_form) = 0.3618689393512336 " "
y[1] (numeric) = 0.36186893935108155 " "
absolute error = 1.5204504322241520000000000000E-13 " "
relative error = 4.2016605098797600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999852 " "
y[1] (closed_form) = 0.365301163466868 " "
y[1] (numeric) = 0.3653011634667163 " "
absolute error = 1.51656465163796380000000000000E-13 " "
relative error = 4.15154618519443400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998507 " "
y[1] (closed_form) = 0.3686968577705723 " "
y[1] (numeric) = 0.36869685777042105 " "
absolute error = 1.51267887105177580000000000000E-13 " "
relative error = 4.10277125820547500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998496 " "
y[1] (closed_form) = 0.37205568269574596 " "
y[1] (numeric) = 0.3720556826955951 " "
absolute error = 1.50879309046558770000000000000E-13 " "
relative error = 4.05528838998926300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998485 " "
y[1] (closed_form) = 0.37537730236269545 " "
y[1] (numeric) = 0.3753773023625449 " "
absolute error = 1.50546242139171230000000000000E-13 " "
relative error = 4.01053130254825800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998474 " "
y[1] (closed_form) = 0.378661384612222 " "
y[1] (numeric) = 0.3786613846120718 " "
absolute error = 1.50157664080552420000000000000E-13 " "
relative error = 3.965486584652017600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998463 " "
y[1] (closed_form) = 0.3819076010388375 " "
y[1] (numeric) = 0.38190760103868765 " "
absolute error = 1.49824597173164880000000000000E-13 " "
relative error = 3.92305879133127600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999845 " "
y[1] (closed_form) = 0.3851156270236043 " "
y[1] (numeric) = 0.3851156270234548 " "
absolute error = 1.49491530265777330000000000000E-13 " "
relative error = 3.88173108998806700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.459999999999844 " "
y[1] (closed_form) = 0.38828514176659745 " "
y[1] (numeric) = 0.3882851417664482 " "
absolute error = 1.4926948566085230000000000000E-13 " "
relative error = 3.8443264911377900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999843 " "
y[1] (closed_form) = 0.39141582831898375 " "
y[1] (numeric) = 0.39141582831883476 " "
absolute error = 1.489919299046960000000000000E-13 " "
relative error = 3.80648709441753200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999842 " "
y[1] (closed_form) = 0.394507373614717 " "
y[1] (numeric) = 0.3945073736145683 " "
absolute error = 1.48714374148539720000000000000E-13 " "
relative error = 3.76962216918604100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999841 " "
y[1] (closed_form) = 0.3975594685018438 " "
y[1] (numeric) = 0.3975594685016953 " "
absolute error = 1.48492329543614700000000000000E-13 " "
relative error = 3.73509729508369140000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998397 " "
y[1] (closed_form) = 0.4005718077734189 " "
y[1] (numeric) = 0.40057180777327067 " "
absolute error = 1.4821477378745840000000000000E-13 " "
relative error = 3.7000800084087600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998386 " "
y[1] (closed_form) = 0.40354409019802534 " "
y[1] (numeric) = 0.40354409019787746 " "
absolute error = 1.47881706880070850000000000000E-13 " "
relative error = 3.66457372247733800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998375 " "
y[1] (closed_form) = 0.4064760185498977 " "
y[1] (numeric) = 0.4064760185497501 " "
absolute error = 1.47604151123914560000000000000E-13 " "
relative error = 3.63131265776741430000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998364 " "
y[1] (closed_form) = 0.4093672996386439 " "
y[1] (numeric) = 0.40936729963849655 " "
absolute error = 1.47326595367758270000000000000E-13 " "
relative error = 3.59888529195678760000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998353 " "
y[1] (closed_form) = 0.4122176443385645 " "
y[1] (numeric) = 0.41221764433841745 " "
absolute error = 1.47049039611601980000000000000E-13 " "
relative error = 3.5672669918715800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.549999999999834 " "
y[1] (closed_form) = 0.41502676761756485 " "
y[1] (numeric) = 0.41502676761741814 " "
absolute error = 1.46715972704214440000000000000E-13 " "
relative error = 3.5350966287410400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999833 " "
y[1] (closed_form) = 0.417794388565658 " "
y[1] (numeric) = 0.4177943885655115 " "
absolute error = 1.4649392809928940000000000000E-13 " "
relative error = 3.50636418555600900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999832 " "
y[1] (closed_form) = 0.4205202304230553 " "
y[1] (numeric) = 0.4205202304229091 " "
absolute error = 1.46216372343133120000000000000E-13 " "
relative error = 3.47703539009372450000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999831 " "
y[1] (closed_form) = 0.42320402060784273 " "
y[1] (numeric) = 0.4232040206076968 " "
absolute error = 1.45938816586976830000000000000E-13 " "
relative error = 3.448426987469700400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998298 " "
y[1] (closed_form) = 0.42584549074323824 " "
y[1] (numeric) = 0.42584549074309247 " "
absolute error = 1.45772283133283050000000000000E-13 " "
relative error = 3.42312614086539300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998287 " "
y[1] (closed_form) = 0.4284443766844295 " "
y[1] (numeric) = 0.42844437668428403 " "
absolute error = 1.4543921622589550000000000000E-13 " "
relative error = 3.39458805251209300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998276 " "
y[1] (closed_form) = 0.43100041854498805 " "
y[1] (numeric) = 0.43100041854484283 " "
absolute error = 1.45217171620970480000000000000E-13 " "
relative error = 3.36930465430192200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998265 " "
y[1] (closed_form) = 0.43351336072285795 " "
y[1] (numeric) = 0.433513360722713 " "
absolute error = 1.44939615864814200000000000000E-13 " "
relative error = 3.343371369757461000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998254 " "
y[1] (closed_form) = 0.4359829519259155 " "
y[1] (numeric) = 0.4359829519257709 " "
absolute error = 1.44606548957426640000000000000E-13 " "
relative error = 3.31679365715196400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998243 " "
y[1] (closed_form) = 0.43840894519709844 " "
y[1] (numeric) = 0.438408945196954 " "
absolute error = 1.44440015503732870000000000000E-13 " "
relative error = 3.294641158354923400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999823 " "
y[1] (closed_form) = 0.4407910979391012 " "
y[1] (numeric) = 0.44079109793895704 " "
absolute error = 1.44162459747576580000000000000E-13 " "
relative error = 3.270539274082476000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999822 " "
y[1] (closed_form) = 0.44312917193863477 " "
y[1] (numeric) = 0.44312917193849083 " "
absolute error = 1.43940415142651550000000000000E-13 " "
relative error = 3.248272157595272000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999821 " "
y[1] (closed_form) = 0.4454229333902476 " "
y[1] (numeric) = 0.44542293339010386 " "
absolute error = 1.43718370537726510000000000000E-13 " "
relative error = 3.226559742756011700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.67999999999982 " "
y[1] (closed_form) = 0.4476721529197059 " "
y[1] (numeric) = 0.44767215291956236 " "
absolute error = 1.43551837084032740000000000000E-13 " "
relative error = 3.20662869351581200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998188 " "
y[1] (closed_form) = 0.44987660560693116 " "
y[1] (numeric) = 0.4498766056067878 " "
absolute error = 1.4332979247910770000000000000E-13 " "
relative error = 3.18598012638911700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998177 " "
y[1] (closed_form) = 0.45203607100849164 " "
y[1] (numeric) = 0.4520360710083486 " "
absolute error = 1.43052236722951420000000000000E-13 " "
relative error = 3.16461994733743600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998166 " "
y[1] (closed_form) = 0.4541503331796467 " "
y[1] (numeric) = 0.454150333179504 " "
absolute error = 1.42719169815563870000000000000E-13 " "
relative error = 3.142553453970690600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998155 " "
y[1] (closed_form) = 0.4562191806959412 " "
y[1] (numeric) = 0.45621918069579864 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 3.124652412562151600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998144 " "
y[1] (closed_form) = 0.4582424066743475 " "
y[1] (numeric) = 0.4582424066742052 " "
absolute error = 1.42330591756945070000000000000E-13 " "
relative error = 3.10601091657789500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998133 " "
y[1] (closed_form) = 0.4602198087939538 " "
y[1] (numeric) = 0.4602198087938116 " "
absolute error = 1.42219569454482550000000000000E-13 " "
relative error = 3.09025310812199360000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999812 " "
y[1] (closed_form) = 0.4621511893161959 " "
y[1] (numeric) = 0.46215118931605387 " "
absolute error = 1.42053036000788780000000000000E-13 " "
relative error = 3.073735160369749400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999811 " "
y[1] (closed_form) = 0.46403635510463115 " "
y[1] (numeric) = 0.4640363551044892 " "
absolute error = 1.41942013698326260000000000000E-13 " "
relative error = 3.05885545683852960000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.76999999999981 " "
y[1] (closed_form) = 0.4658751176442516 " "
y[1] (numeric) = 0.46587511764410977 " "
absolute error = 1.41830991395863750000000000000E-13 " "
relative error = 3.044399368505612500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999809 " "
y[1] (closed_form) = 0.46766729306033555 " "
y[1] (numeric) = 0.46766729306019394 " "
absolute error = 1.41608946790938720000000000000E-13 " "
relative error = 3.02798482793769360000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998077 " "
y[1] (closed_form) = 0.469412702136835 " "
y[1] (numeric) = 0.46941270213669356 " "
absolute error = 1.41442413337244940000000000000E-13 " "
relative error = 3.0131782266090900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998066 " "
y[1] (closed_form) = 0.47111117033429667 " "
y[1] (numeric) = 0.4711111703341554 " "
absolute error = 1.41275879883551170000000000000E-13 " "
relative error = 2.998780092250900600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998055 " "
y[1] (closed_form) = 0.4727625278073163 " "
y[1] (numeric) = 0.4727625278071752 " "
absolute error = 1.4110934642985740000000000000E-13 " "
relative error = 2.98478280595388700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998044 " "
y[1] (closed_form) = 0.47436660942152264 " "
y[1] (numeric) = 0.4743666094213817 " "
absolute error = 1.40942812976163620000000000000E-13 " "
relative error = 2.971179045423108500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999998033 " "
y[1] (closed_form) = 0.475923254770091 " "
y[1] (numeric) = 0.4759232547699503 " "
absolute error = 1.4072076837123860000000000000E-13 " "
relative error = 2.95679538582786840000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999998022 " "
y[1] (closed_form) = 0.4774323081897838 " "
y[1] (numeric) = 0.47743230818964333 " "
absolute error = 1.40498723766313560000000000000E-13 " "
relative error = 2.94279882940942500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999801 " "
y[1] (closed_form) = 0.4788936187765166 " "
y[1] (numeric) = 0.47889361877637615 " "
absolute error = 1.4044321261508230000000000000E-13 " "
relative error = 2.932659929232057000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8599999999998 " "
y[1] (closed_form) = 0.48030704040044836 " "
y[1] (numeric) = 0.48030704040030797 " "
absolute error = 1.40387701463851040000000000000E-13 " "
relative error = 2.922874112917542000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999799 " "
y[1] (closed_form) = 0.48167243172059465 " "
y[1] (numeric) = 0.48167243172045443 " "
absolute error = 1.40221168010157270000000000000E-13 " "
relative error = 2.91113127461477440000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999798 " "
y[1] (closed_form) = 0.4829896561989612 " "
y[1] (numeric) = 0.48298965619882106 " "
absolute error = 1.40165656858926000000000000000E-13 " "
relative error = 2.902042622651666600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997967 " "
y[1] (closed_form) = 0.484258582114198 " "
y[1] (numeric) = 0.4842585821140579 " "
absolute error = 1.4005463455646350000000000000E-13 " "
relative error = 2.89214563725451500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997956 " "
y[1] (closed_form) = 0.4854790825747708 " "
y[1] (numeric) = 0.48547908257463085 " "
absolute error = 1.39943612254000980000000000000E-13 " "
relative error = 2.88258788641934200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997945 " "
y[1] (closed_form) = 0.48665103553165073 " "
y[1] (numeric) = 0.4866510355315109 " "
absolute error = 1.39832589951538470000000000000E-13 " "
relative error = 2.873364685205608000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997934 " "
y[1] (closed_form) = 0.48777432379051866 " "
y[1] (numeric) = 0.487774323790379 " "
absolute error = 1.3966605649784470000000000000E-13 " "
relative error = 2.863333506620291000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997923 " "
y[1] (closed_form) = 0.48884883502348475 " "
y[1] (numeric) = 0.48884883502334525 " "
absolute error = 1.39499523044150920000000000000E-13 " "
relative error = 2.853633128479261000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997912 " "
y[1] (closed_form) = 0.48987446178032124 " "
y[1] (numeric) = 0.4898744617801819 " "
absolute error = 1.39332989590457150000000000000E-13 " "
relative error = 2.844259100261884400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.94999999999979 " "
y[1] (closed_form) = 0.490851101499207 " "
y[1] (numeric) = 0.4908511014990679 " "
absolute error = 1.39110944985532110000000000000E-13 " "
relative error = 2.834076251650356500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999789 " "
y[1] (closed_form) = 0.49177865651698416 " "
y[1] (numeric) = 0.4917786565168451 " "
absolute error = 1.39055433834300860000000000000E-13 " "
relative error = 2.827602052093093000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999788 " "
y[1] (closed_form) = 0.49265703407892375 " "
y[1] (numeric) = 0.4926570340787848 " "
absolute error = 1.38944411531838340000000000000E-13 " "
relative error = 2.82030706801152500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999787 " "
y[1] (closed_form) = 0.49348614634800164 " "
y[1] (numeric) = 0.49348614634786275 " "
absolute error = 1.38888900380607080000000000000E-13 " "
relative error = 2.814443757103243000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997857 " "
y[1] (closed_form) = 0.49426591041368184 " "
y[1] (numeric) = 0.49426591041354306 " "
absolute error = 1.38777878078144570000000000000E-13 " "
relative error = 2.80775742680681230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997846 " "
y[1] (closed_form) = 0.49499624830020755 " "
y[1] (numeric) = 0.49499624830006883 " "
absolute error = 1.3872236692691330000000000000E-13 " "
relative error = 2.80249329976295800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997835 " "
y[1] (closed_form) = 0.4956770869743987 " "
y[1] (numeric) = 0.49567708697426005 " "
absolute error = 1.38666855775682050000000000000E-13 " "
relative error = 2.797524021578267000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997824 " "
y[1] (closed_form) = 0.49630835835295534 " "
y[1] (numeric) = 0.4963083583528168 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 2.79172879403098760000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997813 " "
y[1] (closed_form) = 0.49688999930926564 " "
y[1] (numeric) = 0.49688999930912714 " "
absolute error = 1.38500322321988280000000000000E-13 " "
relative error = 2.78734372828029700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.03999999999978 " "
y[1] (closed_form) = 0.4974219516797186 " "
y[1] (numeric) = 0.49742195167958025 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 2.781014959254658500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999779 " "
y[1] (closed_form) = 0.4979041622695205 " "
y[1] (numeric) = 0.49790416226938217 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 2.77832159983858600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999778 " "
y[1] (closed_form) = 0.49833658285801424 " "
y[1] (numeric) = 0.4983365828578759 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 2.77591077249306600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999777 " "
y[1] (closed_form) = 0.49871917020350126 " "
y[1] (numeric) = 0.49871917020336304 " "
absolute error = 1.382227665658320000000000000E-13 " "
relative error = 2.771555112056961500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999776 " "
y[1] (closed_form) = 0.4990518860475659 " "
y[1] (numeric) = 0.4990518860474277 " "
absolute error = 1.382227665658320000000000000E-13 " "
relative error = 2.769707327639628300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997747 " "
y[1] (closed_form) = 0.499334697118901 " "
y[1] (numeric) = 0.49933469711876277 " "
absolute error = 1.382227665658320000000000000E-13 " "
relative error = 2.76813863253164900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997736 " "
y[1] (closed_form) = 0.499567575136635 " "
y[1] (numeric) = 0.49956757513649686 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.76573705522843600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997725 " "
y[1] (closed_form) = 0.49975049681316036 " "
y[1] (numeric) = 0.4997504968130222 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.764724723550534600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997714 " "
y[1] (closed_form) = 0.4998834438564617 " "
y[1] (numeric) = 0.4998834438563236 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.762878946297476000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997703 " "
y[1] (closed_form) = 0.4999664029719456 " "
y[1] (numeric) = 0.49996640297180756 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.761310205875671700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999769 " "
y[1] (closed_form) = 0.4999993658637696 " "
y[1] (numeric) = 0.49999936586363153 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.761128164105575700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999768 " "
y[1] (closed_form) = 0.49998232923567193 " "
y[1] (numeric) = 0.4999823292355338 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.76233251032096100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999767 " "
y[1] (closed_form) = 0.4999152947913013 " "
y[1] (numeric) = 0.49991529479116315 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.763813327061361000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999766 " "
y[1] (closed_form) = 0.49979826923404624 " "
y[1] (numeric) = 0.4997982692339081 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.76446046174480760000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999765 " "
y[1] (closed_form) = 0.49963126426636495 " "
y[1] (numeric) = 0.4996312642662268 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.765384500457132600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997637 " "
y[1] (closed_form) = 0.499414296588615 " "
y[1] (numeric) = 0.49941429658847686 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.76658590589796300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997626 " "
y[1] (closed_form) = 0.4991473878973835 " "
y[1] (numeric) = 0.4991473878972454 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.766953160771884000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997615 " "
y[1] (closed_form) = 0.49883056488331695 " "
y[1] (numeric) = 0.4988305648831789 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.76759771415433200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997604 " "
y[1] (closed_form) = 0.4984638592284528 " "
y[1] (numeric) = 0.49846385922831477 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.769633756915266000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997593 " "
y[1] (closed_form) = 0.49804730760305105 " "
y[1] (numeric) = 0.498047307602913 " "
absolute error = 1.38056233112138220000000000000E-13 " "
relative error = 2.771950194381343500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999758 " "
y[1] (closed_form) = 0.49758095166192706 " "
y[1] (numeric) = 0.49758095166178895 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 2.775663815145543000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999757 " "
y[1] (closed_form) = 0.4970648380402862 " "
y[1] (numeric) = 0.49706483804014806 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.779662628306903000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999756 " "
y[1] (closed_form) = 0.49649901834906074 " "
y[1] (numeric) = 0.49649901834892257 " "
absolute error = 1.38167255414600730000000000000E-13 " "
relative error = 2.782830384519774400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999755 " "
y[1] (closed_form) = 0.4958835491697482 " "
y[1] (numeric) = 0.49588354916960997 " "
absolute error = 1.382227665658320000000000000E-13 " "
relative error = 2.78740375229742300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999754 " "
y[1] (closed_form) = 0.4952184920487535 " "
y[1] (numeric) = 0.49521849204861523 " "
absolute error = 1.38278277717063250000000000000E-13 " "
relative error = 2.79226805818571800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997527 " "
y[1] (closed_form) = 0.49450391349123474 " "
y[1] (numeric) = 0.4945039134910963 " "
absolute error = 1.38444811170757020000000000000E-13 " "
relative error = 2.799670688009853000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997516 " "
y[1] (closed_form) = 0.49373988495445204 " "
y[1] (numeric) = 0.49373988495431353 " "
absolute error = 1.38500322321988280000000000000E-13 " "
relative error = 2.80512728548889800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997505 " "
y[1] (closed_form) = 0.49292648284062246 " "
y[1] (numeric) = 0.49292648284048385 " "
absolute error = 1.3861134462445080000000000000E-13 " "
relative error = 2.812008472859185000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997494 " "
y[1] (closed_form) = 0.4920637884892795 " "
y[1] (numeric) = 0.49206378848914084 " "
absolute error = 1.38666855775682050000000000000E-13 " "
relative error = 2.81806666167029200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997483 " "
y[1] (closed_form) = 0.4911518881691394 " "
y[1] (numeric) = 0.49115188816900074 " "
absolute error = 1.38666855775682050000000000000E-13 " "
relative error = 2.82329884330871100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999747 " "
y[1] (closed_form) = 0.49019087306947434 " "
y[1] (numeric) = 0.4901908730693355 " "
absolute error = 1.38833389229375830000000000000E-13 " "
relative error = 2.83223121556771800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999746 " "
y[1] (closed_form) = 0.4891808392909933 " "
y[1] (numeric) = 0.4891808392908544 " "
absolute error = 1.38944411531838340000000000000E-13 " "
relative error = 2.840348606728361000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999745 " "
y[1] (closed_form) = 0.48812188783623256 " "
y[1] (numeric) = 0.48812188783609356 " "
absolute error = 1.3899992268306960000000000000E-13 " "
relative error = 2.847647813935047500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999744 " "
y[1] (closed_form) = 0.4870141245994551 " "
y[1] (numeric) = 0.487014124599316 " "
absolute error = 1.39110944985532110000000000000E-13 " "
relative error = 2.856404731586459400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997428 " "
y[1] (closed_form) = 0.4858576603560614 " "
y[1] (numeric) = 0.4858576603559222 " "
absolute error = 1.39221967287994630000000000000E-13 " "
relative error = 2.865488776815119400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997417 " "
y[1] (closed_form) = 0.48465261075151217 " "
y[1] (numeric) = 0.4846526107513729 " "
absolute error = 1.3927747843922590000000000000E-13 " "
relative error = 2.873758963626739000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997406 " "
y[1] (closed_form) = 0.48339909628976363 " "
y[1] (numeric) = 0.4833990962896243 " "
absolute error = 1.39332989590457150000000000000E-13 " "
relative error = 2.882359331241630700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997395 " "
y[1] (closed_form) = 0.48209724232121737 " "
y[1] (numeric) = 0.4820972423210778 " "
absolute error = 1.39555034195382180000000000000E-13 " "
relative error = 2.89474865119427100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997384 " "
y[1] (closed_form) = 0.4807471790301854 " "
y[1] (numeric) = 0.48074717903004566 " "
absolute error = 1.39721567649075950000000000000E-13 " "
relative error = 2.90634191407918900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997373 " "
y[1] (closed_form) = 0.4793490414218717 " "
y[1] (numeric) = 0.47934904142173174 " "
absolute error = 1.39943612254000980000000000000E-13 " "
relative error = 2.919451175679677600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999736 " "
y[1] (closed_form) = 0.477902969308872 " "
y[1] (numeric) = 0.4779029693087319 " "
absolute error = 1.40110145707694760000000000000E-13 " "
relative error = 2.931769725354868600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999735 " "
y[1] (closed_form) = 0.4764091072971926 " "
y[1] (numeric) = 0.4764091072970524 " "
absolute error = 1.40221168010157270000000000000E-13 " "
relative error = 2.94329318777453160000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.459999999999734 " "
y[1] (closed_form) = 0.47486760477178974 " "
y[1] (numeric) = 0.47486760477164935 " "
absolute error = 1.40387701463851040000000000000E-13 " "
relative error = 2.95635457237218900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999733 " "
y[1] (closed_form) = 0.4732786158816314 " "
y[1] (numeric) = 0.4732786158814908 " "
absolute error = 1.40609746068776080000000000000E-13 " "
relative error = 2.970971883165392500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997318 " "
y[1] (closed_form) = 0.47164229952428244 " "
y[1] (numeric) = 0.4716422995241416 " "
absolute error = 1.4083179067370110000000000000E-13 " "
relative error = 2.985987279252725300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997307 " "
y[1] (closed_form) = 0.469958819330015 " "
y[1] (numeric) = 0.46995881932987404 " "
absolute error = 1.40942812976163620000000000000E-13 " "
relative error = 2.999046026566651300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997295 " "
y[1] (closed_form) = 0.4682283436454456 " "
y[1] (numeric) = 0.46822834364530447 " "
absolute error = 1.4110934642985740000000000000E-13 " "
relative error = 3.013686555820913600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997284 " "
y[1] (closed_form) = 0.4664510455167007 " "
y[1] (numeric) = 0.4664510455165593 " "
absolute error = 1.41386902186013690000000000000E-13 " "
relative error = 3.0311198473013495000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997273 " "
y[1] (closed_form) = 0.464627102672112 " "
y[1] (numeric) = 0.4646271026719704 " "
absolute error = 1.41608946790938720000000000000E-13 " "
relative error = 3.047797814129503700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997262 " "
y[1] (closed_form) = 0.4627566975044441 " "
y[1] (numeric) = 0.4627566975043022 " "
absolute error = 1.418865025470950000000000000E-13 " "
relative error = 3.06611451141087800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999725 " "
y[1] (closed_form) = 0.460840017052655 " "
y[1] (numeric) = 0.46084001705251293 " "
absolute error = 1.42053036000788780000000000000E-13 " "
relative error = 3.08248048659710900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.549999999999724 " "
y[1] (closed_form) = 0.45887725298319276 " "
y[1] (numeric) = 0.45887725298305043 " "
absolute error = 1.42330591756945070000000000000E-13 " "
relative error = 3.10171382067086700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999723 " "
y[1] (closed_form) = 0.45686860157082865 " "
y[1] (numeric) = 0.4568686015706861 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 3.12021084118581200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999722 " "
y[1] (closed_form) = 0.45481426367903 " "
y[1] (numeric) = 0.4548142636788872 " "
absolute error = 1.42774680966795130000000000000E-13 " "
relative error = 3.139186528845401300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997207 " "
y[1] (closed_form) = 0.4527144447398741 " "
y[1] (numeric) = 0.45271444473973116 " "
absolute error = 1.4294121442048890000000000000E-13 " "
relative error = 3.15742552687095500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997196 " "
y[1] (closed_form) = 0.450569354733505 " "
y[1] (numeric) = 0.4505693547333618 " "
absolute error = 1.4321877017664520000000000000E-13 " "
relative error = 3.17861764614137500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997185 " "
y[1] (closed_form) = 0.4483792081671358 " "
y[1] (numeric) = 0.44837920816699234 " "
absolute error = 1.43440814781570230000000000000E-13 " "
relative error = 3.19909603676586830000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997174 " "
y[1] (closed_form) = 0.44614422405359794 " "
y[1] (numeric) = 0.4461442240534542 " "
absolute error = 1.43718370537726510000000000000E-13 " "
relative error = 3.221343296387958500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997163 " "
y[1] (closed_form) = 0.44386462588944037 " "
y[1] (numeric) = 0.4438646258892964 " "
absolute error = 1.43940415142651550000000000000E-13 " "
relative error = 3.24288998823043900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997152 " "
y[1] (closed_form) = 0.44154064163257983 " "
y[1] (numeric) = 0.4415406416324356 " "
absolute error = 1.44217970898807830000000000000E-13 " "
relative error = 3.2662445378882304000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.639999999999714 " "
y[1] (closed_form) = 0.43917250367950533 " "
y[1] (numeric) = 0.4391725036793609 " "
absolute error = 1.44440015503732870000000000000E-13 " "
relative error = 3.28891299645527800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999713 " "
y[1] (closed_form) = 0.43676044884203874 " "
y[1] (numeric) = 0.436760448841894 " "
absolute error = 1.44717571259889160000000000000E-13 " "
relative error = 3.313431233152444600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999712 " "
y[1] (closed_form) = 0.43430471832365386 " "
y[1] (numeric) = 0.43430471832350886 " "
absolute error = 1.44995127016045440000000000000E-13 " "
relative error = 3.338557489674605600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999711 " "
y[1] (closed_form) = 0.43180555769535595 " "
y[1] (numeric) = 0.4318055576952108 " "
absolute error = 1.45161660469739220000000000000E-13 " "
relative error = 3.36173673272062270000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997097 " "
y[1] (closed_form) = 0.4292632168711253 " "
y[1] (numeric) = 0.4292632168709799 " "
absolute error = 1.45383705074664250000000000000E-13 " "
relative error = 3.386819540103101500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997086 " "
y[1] (closed_form) = 0.4266779500829257 " "
y[1] (numeric) = 0.42667795008278003 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 3.413845519847252000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997075 " "
y[1] (closed_form) = 0.42405001585528157 " "
y[1] (numeric) = 0.4240500158551357 " "
absolute error = 1.45883305435745570000000000000E-13 " "
relative error = 3.44023817901547100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997064 " "
y[1] (closed_form) = 0.42137967697942574 " "
y[1] (numeric) = 0.42137967697927964 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 3.467308890832063000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997053 " "
y[1] (closed_form) = 0.4186672004870206 " "
y[1] (numeric) = 0.41866720048687417 " "
absolute error = 1.46438416948058150000000000000E-13 " "
relative error = 3.49772842911294600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.729999999999704 " "
y[1] (closed_form) = 0.4159128576234549 " "
y[1] (numeric) = 0.4159128576233082 " "
absolute error = 1.46715972704214440000000000000E-13 " "
relative error = 3.52756521023553370000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999703 " "
y[1] (closed_form) = 0.41311692382071974 " "
y[1] (numeric) = 0.41311692382057286 " "
absolute error = 1.4688250615790820000000000000E-13 " "
relative error = 3.55547056265481800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999702 " "
y[1] (closed_form) = 0.41027967866986553 " "
y[1] (numeric) = 0.4102796786697183 " "
absolute error = 1.47215573065295760000000000000E-13 " "
relative error = 3.588176083752707700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999701 " "
y[1] (closed_form) = 0.4074014058930429 " "
y[1] (numeric) = 0.4074014058928954 " "
absolute error = 1.47493128821452050000000000000E-13 " "
relative error = 3.620339220433965700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7699999999997 " "
y[1] (closed_form) = 0.40448239331513103 " "
y[1] (numeric) = 0.4044823933149832 " "
absolute error = 1.4782619572883960000000000000E-13 " "
relative error = 3.65470038182029500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996987 " "
y[1] (closed_form) = 0.40152293283495516 " "
y[1] (numeric) = 0.401522932834807 " "
absolute error = 1.48159262636227140000000000000E-13 " "
relative error = 3.68993276648354200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996976 " "
y[1] (closed_form) = 0.39852332039609717 " "
y[1] (numeric) = 0.3985233203959486 " "
absolute error = 1.48547840694845950000000000000E-13 " "
relative error = 3.727456665451910000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996965 " "
y[1] (closed_form) = 0.3954838559573012 " "
y[1] (numeric) = 0.39548385595715235 " "
absolute error = 1.48825396451002230000000000000E-13 " "
relative error = 3.76312191279611460000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996954 " "
y[1] (closed_form) = 0.3924048434624783 " "
y[1] (numeric) = 0.3924048434623292 " "
absolute error = 1.49102952207158520000000000000E-13 " "
relative error = 3.79972252359356330000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996943 " "
y[1] (closed_form) = 0.38928659081031214 " "
y[1] (numeric) = 0.38928659081016265 " "
absolute error = 1.49491530265777330000000000000E-13 " "
relative error = 3.84014075477416400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999693 " "
y[1] (closed_form) = 0.3861294098234693 " "
y[1] (numeric) = 0.3861294098233195 " "
absolute error = 1.49824597173164880000000000000E-13 " "
relative error = 3.88016538915442100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999692 " "
y[1] (closed_form) = 0.3829336162174176 " "
y[1] (numeric) = 0.3829336162172675 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 3.919795666204920000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999691 " "
y[1] (closed_form) = 0.3796995295688545 " "
y[1] (numeric) = 0.3796995295687039 " "
absolute error = 1.50601753290402480000000000000E-13 " "
relative error = 3.96634026545699070000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.85999999999969 " "
y[1] (closed_form) = 0.3764274732837497 " "
y[1] (numeric) = 0.3764274732835987 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 4.01114004862246900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999689 " "
y[1] (closed_form) = 0.373117774565005 " "
y[1] (numeric) = 0.37311777456485373 " "
absolute error = 1.51267887105177580000000000000E-13 " "
relative error = 4.054159233811133000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996877 " "
y[1] (closed_form) = 0.36977076437973433 " "
y[1] (numeric) = 0.3697707643795827 " "
absolute error = 1.51656465163796380000000000000E-13 " "
relative error = 4.101364406626087400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996866 " "
y[1] (closed_form) = 0.36638677742616693 " "
y[1] (numeric) = 0.3663867774260148 " "
absolute error = 1.5215606552487770000000000000E-13 " "
relative error = 4.15288091436486700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996855 " "
y[1] (closed_form) = 0.36296615210017824 " "
y[1] (numeric) = 0.36296615210002575 " "
absolute error = 1.52489132432265250000000000000E-13 " "
relative error = 4.201194286297484400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996844 " "
y[1] (closed_form) = 0.3595092304614503 " "
y[1] (numeric) = 0.35950923046129735 " "
absolute error = 1.52933221642115300000000000000E-13 " "
relative error = 4.25394422963262800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996833 " "
y[1] (closed_form) = 0.35601635819926625 " "
y[1] (numeric) = 0.3560163581991129 " "
absolute error = 1.53321799700734120000000000000E-13 " "
relative error = 4.30659423842873600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999682 " "
y[1] (closed_form) = 0.3524878845979416 " "
y[1] (numeric) = 0.3524878845977879 " "
absolute error = 1.53710377759352920000000000000E-13 " "
relative error = 4.36072797040044800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999681 " "
y[1] (closed_form) = 0.34892416250189606 " "
y[1] (numeric) = 0.34892416250174196 " "
absolute error = 1.54098955817971730000000000000E-13 " "
relative error = 4.41640254183125900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.94999999999968 " "
y[1] (closed_form) = 0.34532554828036954 " "
y[1] (numeric) = 0.34532554828021506 " "
absolute error = 1.54487533876590530000000000000E-13 " "
relative error = 4.47367808857172200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999679 " "
y[1] (closed_form) = 0.34169240179178534 " "
y[1] (numeric) = 0.34169240179163046 " "
absolute error = 1.54876111935209340000000000000E-13 " "
relative error = 4.53261796642423100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999678 " "
y[1] (closed_form) = 0.3380250863477646 " "
y[1] (numeric) = 0.33802508634760936 " "
absolute error = 1.55264689993828140000000000000E-13 " "
relative error = 4.59328896773329400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996767 " "
y[1] (closed_form) = 0.3343239686767958 " "
y[1] (numeric) = 0.33432396867664016 " "
absolute error = 1.55653268052446950000000000000E-13 " "
relative error = 4.65576155572988870000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996756 " "
y[1] (closed_form) = 0.3305894188875617 " "
y[1] (numeric) = 0.3305894188874056 " "
absolute error = 1.560973572622970000000000000E-13 " "
relative error = 4.72178927527586700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996745 " "
y[1] (closed_form) = 0.32682181043192915 " "
y[1] (numeric) = 0.3268218104317726 " "
absolute error = 1.56541446472147070000000000000E-13 " "
relative error = 4.78981027200299840000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = sin ( x ) / 2.0 ; "
Iterations = 9003
"Total Elapsed Time "= 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 3 Minutes 0 Seconds
"Expected Time Remaining "= 19 Seconds
"Optimized Time Remaining "= 19 Seconds
"Expected Total Time "= 3 Minutes 19 Seconds
"Time to Timeout "= 0.0 Seconds
Percent Done = 90.03999999999675 "%"
(%o253) temp/diffeq.div_sin_c.max