(%i1) batch("temp/diffeq.diff.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.diff.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([30],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],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,30,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,[30],convfloat)
(%i173) completearray(array_norms,[30],convfloat)
(%i174) completearray(array_fact_1,[30],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,[30],convfloat)
(%i184) completearray(array_x,[30],convfloat)
(%i185) completearray(array_tmp0,[30],convfloat)
(%i186) completearray(array_tmp1,[30],convfloat)
(%i187) completearray(array_tmp2,[30],convfloat)
(%i188) completearray(array_m1,[30],convfloat)
(%i189) completearray(array_y_higher,[3,30],convfloat)
(%i190) completearray(array_y_higher_work,[3,30],convfloat)
(%i191) completearray(array_y_higher_work2,[3,30],convfloat)
(%i192) completearray(array_y_set_initial,[2,30],convfloat)
(%i193) completearray(array_given_rad_poles,[2,3],convfloat)
(%i194) completearray(array_given_ord_poles,[2,3],convfloat)
(%i195) completearray(array_rad_test_poles,[2,4],convfloat)
(%i196) completearray(array_ord_test_poles,[2,4],convfloat)
(%i197) completearray(array_fact_2,[30,30],convfloat)
(%i198) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i199) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i200) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i201) 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))
(%i202) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i203) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i204) 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)
(%i205) 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)
(%i206) 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)
(%i207) 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)
(%i208) 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)
(%i209) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i210) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i211) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i212) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i213) log_revs(file,revs):=printf(file,revs)
(%i214) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i215) 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)
(%i216) logstart(file):=(printf(file,""),0)
(%i217) logend(file):=(printf(file,"
~%"),0)
(%i218) 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)
(%i219) 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)
(%i220) 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)
(%i221) 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)
(%i222) 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)
(%i223) c(in_val):=(ret:in_val,ret)
(%i224) 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)
(%i225) 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)
(%i226) 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)
(%i227) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i228) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i229) 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)
(%i230) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i231) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i232) 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)
(%i233) log10(x):=log(x)/glob_log_10
(%i234) c(x):=x
(%i235) 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
(%i236) 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)
(%i237) exact_soln_y(x):=block(exp(c(x))+c(1.0))
(%o237) exact_soln_y(x) := block(exp(c(x)) + c(1.0))
(%i238) exact_soln_yp(x):=block(exp(c(x)))
(%o238) exact_soln_yp(x) := block(exp(c(x)))
(%i239) exact_soln_ypp(x):=block(exp(c(x)))
(%o239) exact_soln_ypp(x) := block(exp(c(x)))
(%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(21)
*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:-10-2+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:-10-2+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:-10-2+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]:array_y_higher[2,1],
array_tmp2[1]:array_tmp1[1]+array_const_0D0[1],
if not array_y_set_initial[1,3]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp2[1])*expt(glob_h,c(2))
*c(factorial_3(0,2)),
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),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[3,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_y_higher[2,2],
array_tmp2[2]:array_tmp1[2],
if not array_y_set_initial[1,4]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp2[2])*expt(glob_h,c(2))
*c(factorial_3(1,3)),
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),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[3,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_y_higher[2,3],
array_tmp2[3]:array_tmp1[3],
if not array_y_set_initial[1,5]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp2[3])*expt(glob_h,c(2))
*c(factorial_3(2,4)),
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),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[3,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_y_higher[2,4],
array_tmp2[4]:array_tmp1[4],
if not array_y_set_initial[1,6]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp2[4])*expt(glob_h,c(2))
*c(factorial_3(3,5)),
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),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[3,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_y_higher[2,5],
array_tmp2[5]:array_tmp1[5],
if not array_y_set_initial[1,7]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp2[5])*expt(glob_h,c(2))
*c(factorial_3(4,6)),
if 7 <= ats_max_terms
then (array_y[7]:temporary,
array_y_higher[1,7]:temporary),
temporary:c(temporary)*c(6)/c(glob_h),
array_y_higher[2,6]:c(temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[3,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(if kkk <= ats_max_terms
then array_tmp1[kkk]:array_y_higher[2,kkk],
array_tmp2[kkk]:array_tmp1[kkk],order_d:2,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp2[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(exp(c(x))+c(1.0))
(%o250) exact_soln_y(x) := block(exp(c(x)) + c(1.0))
(%i251) exact_soln_yp(x):=block(exp(c(x)))
(%o251) exact_soln_yp(x) := block(exp(c(x)))
(%i252) exact_soln_ypp(x):=block(exp(c(x)))
(%o252) exact_soln_ypp(x) := block(exp(c(x)))
(%i253) 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:30,
glob_html_log:true,term:1,
while term <= 30 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 30 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 <= 30 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 3 do
(term:1,
while term <= 30 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 3 do
(term:1,
while term <= 30 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 3 do
(term:1,
while term <= 30 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 <= 30 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 <= 30 do
(term:1,
while term <= 30 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),
zero_ats_ar(array_tmp2),zero_ats_ar(array_m1),
zero_ats_ar(array_const_2),array_const_2[1]:c(2),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
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]:true,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,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/diffpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start: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,
"array_y_init[1 + 1] : exact_soln_yp(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," (c(1.0) + exp(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_yp (x) := (block("),
omniout_str(always," (exp(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_ypp (x) := (block("),
omniout_str(always," (exp(c(x))) "),
omniout_str(always,"));"),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),
array_y_init[1+1]:exact_soln_yp(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:2,
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:2,
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:3,ord:3,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[3,iii]
:array_y_higher[3,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:3,
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:2,
calc_term:2,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: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: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:3,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:3,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 , 2 ) = diff ( y , x , 1 ) ; "),
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,
"2015-04-24T20:38:52-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"diff"),
logitem_str(html_log_file,
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "),
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,
"diff diffeq.max"),
logitem_str(html_log_file,
"diff maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i254) main():=(glob_iolevel:2,compile(all),main_prog())
(%i255) 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_const_0D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable 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_2 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/diffpostode.ode#################"
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* 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),"
"array_y_init[1 + 1] : exact_soln_yp(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("
" (c(1.0) + exp(c(x))) "
"));"
"exact_soln_yp (x) := (block("
" (exp(c(x))) "
"));"
"exact_soln_ypp (x) := (block("
" (exp(c(x))) "
"));"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -5. " "
y[1] (closed_form) = 1.0067379469990854 " "
y[1] (numeric) = 1.0067379469990854 " "
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) = 1.0068056644922305 " "
y[1] (numeric) = 1.00680566449223 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.410873175550053500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.979999999999993 " "
y[1] (closed_form) = 1.0068740625574963 " "
y[1] (numeric) = 1.0068740625574957 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61586031010760300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.96999999999999 " "
y[1] (closed_form) = 1.0069431480347462 " "
y[1] (numeric) = 1.0069431480347457 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.41027093452885400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.959999999999987 " "
y[1] (closed_form) = 1.0070129278325854 " "
y[1] (numeric) = 1.007012927832585 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.40996532989784860000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.949999999999983 " "
y[1] (closed_form) = 1.0070834089290523 " "
y[1] (numeric) = 1.0070834089290512 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.1024141742199730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.93999999999998 " "
y[1] (closed_form) = 1.0071545983723147 " "
y[1] (numeric) = 1.0071545983723138 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81869001179690200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.929999999999977 " "
y[1] (closed_form) = 1.0072265032813765 " "
y[1] (numeric) = 1.0072265032813756 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81806045419364500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.919999999999973 " "
y[1] (closed_form) = 1.0072991308467887 " "
y[1] (numeric) = 1.007299130846788 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.61306849550348500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.90999999999997 " "
y[1] (closed_form) = 1.0073724883313682 " "
y[1] (numeric) = 1.0073724883313673 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.81678257038090900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.899999999999967 " "
y[1] (closed_form) = 1.0074465830709245 " "
y[1] (numeric) = 1.0074465830709234 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.10201676523726570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.889999999999963 " "
y[1] (closed_form) = 1.0075214224749935 " "
y[1] (numeric) = 1.0075214224749922 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.32232188798273860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.87999999999996 " "
y[1] (closed_form) = 1.0075970140275778 " "
y[1] (numeric) = 1.0075970140275763 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.54259313280644320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.869999999999957 " "
y[1] (closed_form) = 1.0076733652878958 " "
y[1] (numeric) = 1.0076733652878942 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.542476250755270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.859999999999953 " "
y[1] (closed_form) = 1.007750483891137 " "
y[1] (numeric) = 1.007750483891135 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.98303198685554820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.84999999999995 " "
y[1] (closed_form) = 1.0078283775492263 " "
y[1] (numeric) = 1.0078283775492238 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42351843685413960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.839999999999947 " "
y[1] (closed_form) = 1.0079070540515938 " "
y[1] (numeric) = 1.0079070540515913 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.42332925874166550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.829999999999943 " "
y[1] (closed_form) = 1.007986521265956 " "
y[1] (numeric) = 1.0079865212659531 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8637087928517907000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.81999999999994 " "
y[1] (closed_form) = 1.0080667871391 " "
y[1] (numeric) = 1.0080667871390971 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.8634807741434860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.8099999999999365 " "
y[1] (closed_form) = 1.0081478596976805 " "
y[1] (numeric) = 1.0081478596976776 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.86325050066666140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.799999999999933 " "
y[1] (closed_form) = 1.0082297470490207 " "
y[1] (numeric) = 1.0082297470490174 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.30348225057233000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.78999999999993 " "
y[1] (closed_form) = 1.0083124573819238 " "
y[1] (numeric) = 1.0083124573819207 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08299718623129940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7799999999999265 " "
y[1] (closed_form) = 1.008395998967492 " "
y[1] (numeric) = 1.0083959989674889 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08274177221388600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.769999999999923 " "
y[1] (closed_form) = 1.008480380159954 " "
y[1] (numeric) = 1.008480380159951 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08248383419951370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.75999999999992 " "
y[1] (closed_form) = 1.0085656093974988 " "
y[1] (numeric) = 1.0085656093974957 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 3.08222334767837450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7499999999999165 " "
y[1] (closed_form) = 1.0086516952031213 " "
y[1] (numeric) = 1.008651695203118 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.3021003084763995000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.739999999999913 " "
y[1] (closed_form) = 1.0087386461854742 " "
y[1] (numeric) = 1.0087386461854702 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9621788099072014000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.72999999999991 " "
y[1] (closed_form) = 1.0088264710397274 " "
y[1] (numeric) = 1.0088264710397237 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.74173199463645130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.7199999999999065 " "
y[1] (closed_form) = 1.0089151785484405 " "
y[1] (numeric) = 1.0089151785484365 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96148553776433000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.709999999999903 " "
y[1] (closed_form) = 1.0090047775824373 " "
y[1] (numeric) = 1.0090047775824333 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.9611337601659850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6999999999999 " "
y[1] (closed_form) = 1.0090952771016968 " "
y[1] (numeric) = 1.0090952771016926 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.1808217611451760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6899999999998965 " "
y[1] (closed_form) = 1.0091866861562455 " "
y[1] (numeric) = 1.0091866861562415 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.96041975531152170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.679999999999893 " "
y[1] (closed_form) = 1.0092790138870658 " "
y[1] (numeric) = 1.0092790138870615 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.18006065273013400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.66999999999989 " "
y[1] (closed_form) = 1.009372269527007 " "
y[1] (numeric) = 1.009372269527003 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.95969159180831250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.6599999999998865 " "
y[1] (closed_form) = 1.0094664624017113 " "
y[1] (numeric) = 1.0094664624017071 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.17928445442175440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.649999999999883 " "
y[1] (closed_form) = 1.0095616019305447 " "
y[1] (numeric) = 1.0095616019305402 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.39883221589300160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.63999999999988 " "
y[1] (closed_form) = 1.0096576976275389 " "
y[1] (numeric) = 1.0096576976275347 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.17849287287058450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.629999999999876 " "
y[1] (closed_form) = 1.0097547591023441 " "
y[1] (numeric) = 1.0097547591023395 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.6178902960268620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.619999999999873 " "
y[1] (closed_form) = 1.0098527960611885 " "
y[1] (numeric) = 1.009852796061184 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.39756379922083800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.60999999999987 " "
y[1] (closed_form) = 1.0099518183078497 " "
y[1] (numeric) = 1.009951818307845 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 4.6169892651297930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.599999999999866 " "
y[1] (closed_form) = 1.0100518357446349 " "
y[1] (numeric) = 1.01005183574463 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.8363669422464450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.589999999999863 " "
y[1] (closed_form) = 1.0101528583733712 " "
y[1] (numeric) = 1.010152858373366 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 5.0556961463233010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.57999999999986 " "
y[1] (closed_form) = 1.0102548962964055 " "
y[1] (numeric) = 1.0102548962964006 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.8353948357578175000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.569999999999856 " "
y[1] (closed_form) = 1.010357959717615 " "
y[1] (numeric) = 1.0103579597176102 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.8349015924177920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.559999999999853 " "
y[1] (closed_form) = 1.0104620589434283 " "
y[1] (numeric) = 1.0104620589434234 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.834403494039729600000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.54999999999985 " "
y[1] (closed_form) = 1.0105672043838543 " "
y[1] (numeric) = 1.0105672043838487 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.493068743023690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.539999999999846 " "
y[1] (closed_form) = 1.0106734065535246 " "
y[1] (numeric) = 1.010673406553519 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.4924915280550610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.529999999999843 " "
y[1] (closed_form) = 1.0107806760727447 " "
y[1] (numeric) = 1.0107806760727391 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.4919086351095580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.51999999999984 " "
y[1] (closed_form) = 1.0108890236685562 " "
y[1] (numeric) = 1.0108890236685504 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.7109728099527570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.509999999999836 " "
y[1] (closed_form) = 1.0109984601758086 " "
y[1] (numeric) = 1.0109984601758029 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 5.7103546201711160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.499999999999833 " "
y[1] (closed_form) = 1.0111089965382443 " "
y[1] (numeric) = 1.0111089965382383 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.9293353669107450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.48999999999983 " "
y[1] (closed_form) = 1.011220643809591 " "
y[1] (numeric) = 1.011220643809585 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.9286807183741790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.479999999999826 " "
y[1] (closed_form) = 1.0113334131546694 " "
y[1] (numeric) = 1.0113334131546632 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.1475759200987010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.469999999999823 " "
y[1] (closed_form) = 1.0114473158505077 " "
y[1] (numeric) = 1.0114473158505013 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.3664151774541240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.45999999999982 " "
y[1] (closed_form) = 1.0115623632874706 " "
y[1] (numeric) = 1.0115623632874642 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.3656911096404230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.449999999999816 " "
y[1] (closed_form) = 1.0116785669703976 " "
y[1] (numeric) = 1.0116785669703912 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.3649599319961940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.439999999999813 " "
y[1] (closed_form) = 1.0117959385197537 " "
y[1] (numeric) = 1.0117959385197475 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.1447656599577220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.42999999999981 " "
y[1] (closed_form) = 1.0119144896727919 " "
y[1] (numeric) = 1.0119144896727854 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.363475974050030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.419999999999806 " "
y[1] (closed_form) = 1.012034232284726 " "
y[1] (numeric) = 1.0120342322847196 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.36272305561130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.409999999999803 " "
y[1] (closed_form) = 1.0121551783299174 " "
y[1] (numeric) = 1.0121551783299103 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0200968287542060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.3999999999998 " "
y[1] (closed_form) = 1.012277339903071 " "
y[1] (numeric) = 1.0122773399030638 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0192496438588380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.389999999999796 " "
y[1] (closed_form) = 1.012400729220446 " "
y[1] (numeric) = 1.0124007292204389 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0183941521577320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.379999999999793 " "
y[1] (closed_form) = 1.012525358621077 " "
y[1] (numeric) = 1.0125253586210698 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 7.0175302742813630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.36999999999979 " "
y[1] (closed_form) = 1.012651240568008 " "
y[1] (numeric) = 1.0126512405680006 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 7.2359284904603170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.359999999999786 " "
y[1] (closed_form) = 1.0127783876495384 " "
y[1] (numeric) = 1.0127783876495307 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.6735061363348970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.349999999999783 " "
y[1] (closed_form) = 1.0129068125804828 " "
y[1] (numeric) = 1.0129068125804748 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.8917484590083920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.33999999999978 " "
y[1] (closed_form) = 1.0130365282034406 " "
y[1] (numeric) = 1.0130365282034328 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.6715507842135690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.329999999999776 " "
y[1] (closed_form) = 1.0131675474900828 " "
y[1] (numeric) = 1.013167547490075 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.6705587260750340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.319999999999773 " "
y[1] (closed_form) = 1.0132998835424467 " "
y[1] (numeric) = 1.0132998835424392 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 7.4504267592120170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.30999999999977 " "
y[1] (closed_form) = 1.0134335495942484 " "
y[1] (numeric) = 1.0134335495942406 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.668545387596080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.299999999999766 " "
y[1] (closed_form) = 1.013568559012204 " "
y[1] (numeric) = 1.0135685590121961 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.8865960336136250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.289999999999763 " "
y[1] (closed_form) = 1.0137049252973682 " "
y[1] (numeric) = 1.0137049252973602 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.885535107720050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.2799999999997596 " "
y[1] (closed_form) = 1.0138426620864829 " "
y[1] (numeric) = 1.0138426620864744 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3224895762291730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.269999999999756 " "
y[1] (closed_form) = 1.0139817831533418 " "
y[1] (numeric) = 1.0139817831533333 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3213477079550050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.259999999999753 " "
y[1] (closed_form) = 1.0141223024101675 " "
y[1] (numeric) = 1.014122302410159 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3201946817441310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.2499999999997495 " "
y[1] (closed_form) = 1.0142642339090029 " "
y[1] (numeric) = 1.0142642339089947 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 8.1001085393328030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.239999999999746 " "
y[1] (closed_form) = 1.014407591843116 " "
y[1] (numeric) = 1.0144075918431077 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 8.0989638171958370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.229999999999743 " "
y[1] (closed_form) = 1.01455239054842 " "
y[1] (numeric) = 1.0145523905484113 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5355272657680780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.2199999999997395 " "
y[1] (closed_form) = 1.0146986445049055 " "
y[1] (numeric) = 1.0146986445048969 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5342969944554370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.209999999999736 " "
y[1] (closed_form) = 1.0148463683380908 " "
y[1] (numeric) = 1.0148463683380824 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3142584438359190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.199999999999733 " "
y[1] (closed_form) = 1.0149955768204817 " "
y[1] (numeric) = 1.0149955768204733 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3130362139928140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.1899999999997295 " "
y[1] (closed_form) = 1.015146284873051 " "
y[1] (numeric) = 1.0151462848730426 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3118020652623130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.179999999999726 " "
y[1] (closed_form) = 1.0152985075667298 " "
y[1] (numeric) = 1.0152985075667214 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.310555885059870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.169999999999723 " "
y[1] (closed_form) = 1.0154522601239138 " "
y[1] (numeric) = 1.015452260123905 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5279632850681620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.1599999999997195 " "
y[1] (closed_form) = 1.0156075579199872 " "
y[1] (numeric) = 1.0156075579199786 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5266592637531980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.149999999999716 " "
y[1] (closed_form) = 1.015764416484859 " "
y[1] (numeric) = 1.0157644164848507 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 8.0881454881606610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.139999999999713 " "
y[1] (closed_form) = 1.0159228515045162 " "
y[1] (numeric) = 1.0159228515045078 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3054485630040790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.1299999999997095 " "
y[1] (closed_form) = 1.016082878822593 " "
y[1] (numeric) = 1.0160828788225846 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.3041405017359820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.119999999999706 " "
y[1] (closed_form) = 1.0162445144419547 " "
y[1] (numeric) = 1.016244514441946 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5213149680138740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.109999999999703 " "
y[1] (closed_form) = 1.0164077745262976 " "
y[1] (numeric) = 1.0164077745262887 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7384063951504680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.099999999999700 " "
y[1] (closed_form) = 1.0165726754017663 " "
y[1] (numeric) = 1.0165726754017574 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7369889157123200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.089999999999696 " "
y[1] (closed_form) = 1.0167392335585856 " "
y[1] (numeric) = 1.0167392335585772 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.2987797742586090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.079999999999693 " "
y[1] (closed_form) = 1.0169074656527104 " "
y[1] (numeric) = 1.0169074656527017 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5157596778167980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.069999999999690 " "
y[1] (closed_form) = 1.0170773885074902 " "
y[1] (numeric) = 1.0170773885074815 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5143369520621750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.059999999999686 " "
y[1] (closed_form) = 1.0172490191153516 " "
y[1] (numeric) = 1.017249019115343 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5129004101740450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.049999999999683 " "
y[1] (closed_form) = 1.017422374639499 " "
y[1] (numeric) = 1.0174223746394904 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5114499227959350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.039999999999680 " "
y[1] (closed_form) = 1.0175974724156291 " "
y[1] (numeric) = 1.01759747241562 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.9463948650689070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.029999999999676 " "
y[1] (closed_form) = 1.0177743299536652 " "
y[1] (numeric) = 1.0177743299536561 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.9448402597663680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.019999999999673 " "
y[1] (closed_form) = 1.0179529649395087 " "
y[1] (numeric) = 1.0179529649394996 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.9432705787808910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.009999999999670 " "
y[1] (closed_form) = 1.018133395236807 " "
y[1] (numeric) = 1.0181333952367981 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7235957867146120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9999999999996665 " "
y[1] (closed_form) = 1.0183156388887402 " "
y[1] (numeric) = 1.0183156388887311 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.9400854256358480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9899999999996676 " "
y[1] (closed_form) = 1.0184997141198253 " "
y[1] (numeric) = 1.0184997141198167 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.5024467577390140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9799999999996687 " "
y[1] (closed_form) = 1.018685639337739 " "
y[1] (numeric) = 1.0186856393377302 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7188666002746610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.96999999999967 " "
y[1] (closed_form) = 1.0188734331351577 " "
y[1] (numeric) = 1.018873433135149 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.4993280916447960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.959999999999671 " "
y[1] (closed_form) = 1.019063114291618 " "
y[1] (numeric) = 1.019063114291609 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.9335279378202540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.949999999999672 " "
y[1] (closed_form) = 1.0192547017753932 " "
y[1] (numeric) = 1.0192547017753844 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7139987498026530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.939999999999673 " "
y[1] (closed_form) = 1.0194482147453918 " "
y[1] (numeric) = 1.019448214745383 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7123446473634620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.929999999999674 " "
y[1] (closed_form) = 1.0196436725530718 " "
y[1] (numeric) = 1.0196436725530629 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7106745582623730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9199999999996753 " "
y[1] (closed_form) = 1.0198410947443768 " "
y[1] (numeric) = 1.019841094744368 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7089883343320960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.9099999999996764 " "
y[1] (closed_form) = 1.0200405010616904 " "
y[1] (numeric) = 1.0200405010616815 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7072858261576970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8999999999996775 " "
y[1] (closed_form) = 1.020241911445811 " "
y[1] (numeric) = 1.020241911445802 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.9232060551453070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8899999999996786 " "
y[1] (closed_form) = 1.0204453460379441 " "
y[1] (numeric) = 1.0204453460379352 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.703831353130590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8799999999996797 " "
y[1] (closed_form) = 1.0206508251817192 " "
y[1] (numeric) = 1.0206508251817104 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7020790831378770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.869999999999681 " "
y[1] (closed_form) = 1.0208583694252213 " "
y[1] (numeric) = 1.0208583694252125 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.700309918605070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.859999999999682 " "
y[1] (closed_form) = 1.021067999523048 " "
y[1] (numeric) = 1.0210679995230394 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 8.481060611165250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.849999999999683 " "
y[1] (closed_form) = 1.0212797364383839 " "
y[1] (numeric) = 1.0212797364383746 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 9.1315562956085020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.839999999999684 " "
y[1] (closed_form) = 1.0214936013450968 " "
y[1] (numeric) = 1.0214936013450873 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.3470169555675160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.829999999999685 " "
y[1] (closed_form) = 1.0217096156298555 " "
y[1] (numeric) = 1.0217096156298457 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.5623672981471030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8199999999996863 " "
y[1] (closed_form) = 1.0219278008942685 " "
y[1] (numeric) = 1.0219278008942585 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.777605827811519000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.8099999999996874 " "
y[1] (closed_form) = 1.0221481789570444 " "
y[1] (numeric) = 1.0221481789570344 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.7754977481071470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7999999999996885 " "
y[1] (closed_form) = 1.0223707718561725 " "
y[1] (numeric) = 1.0223707718561628 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.5561834176494040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7899999999996896 " "
y[1] (closed_form) = 1.0225956018511289 " "
y[1] (numeric) = 1.0225956018511189 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 9.7712206110984840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7799999999996907 " "
y[1] (closed_form) = 1.0228226914251 " "
y[1] (numeric) = 1.0228226914250897 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 9.9861412072508780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.769999999999692 " "
y[1] (closed_form) = 1.0230520632872326 " "
y[1] (numeric) = 1.0230520632872222 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 1.0200943633253225000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.759999999999693 " "
y[1] (closed_form) = 1.0232837403749042 " "
y[1] (numeric) = 1.0232837403748933 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0632618512378902000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.749999999999694 " "
y[1] (closed_form) = 1.0235177458560163 " "
y[1] (numeric) = 1.0235177458560054 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.063018759115594800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.739999999999695 " "
y[1] (closed_form) = 1.0237541031313122 " "
y[1] (numeric) = 1.023754103131301 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.0844625884569015000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7299999999996962 " "
y[1] (closed_form) = 1.0239928358367165 " "
y[1] (numeric) = 1.023992835836705 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.1275781482071597000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7199999999996973 " "
y[1] (closed_form) = 1.0242339678456984 " "
y[1] (numeric) = 1.024233967845687 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.105633596100633000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.7099999999996984 " "
y[1] (closed_form) = 1.02447752327166 " "
y[1] (numeric) = 1.0244775232716488 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.105370746935728000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6999999999996995 " "
y[1] (closed_form) = 1.024723526470347 " "
y[1] (numeric) = 1.0247235264703358 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.083436649931628000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6899999999997006 " "
y[1] (closed_form) = 1.0249720020422837 " "
y[1] (numeric) = 1.0249720020422726 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.0831740012537004000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6799999999997017 " "
y[1] (closed_form) = 1.0252229748352348 " "
y[1] (numeric) = 1.0252229748352235 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.10456701899375000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.669999999999703 " "
y[1] (closed_form) = 1.0254764699466885 " "
y[1] (numeric) = 1.0254764699466774 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.0826411499065149000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.659999999999704 " "
y[1] (closed_form) = 1.0257325127263677 " "
y[1] (numeric) = 1.0257325127263561 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.1256657376894334000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.649999999999705 " "
y[1] (closed_form) = 1.025991128778763 " "
y[1] (numeric) = 1.0259911287787513 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.1470239586802802000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.639999999999706 " "
y[1] (closed_form) = 1.0262523439656956 " "
y[1] (numeric) = 1.026252343965684 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.1250955502312193000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6299999999997072 " "
y[1] (closed_form) = 1.026516184408902 " "
y[1] (numeric) = 1.0265161844088901 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.146437264192111000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6199999999997083 " "
y[1] (closed_form) = 1.026782676492646 " "
y[1] (numeric) = 1.0267826764926342 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.1461397168508762000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.6099999999997094 " "
y[1] (closed_form) = 1.0270518468663583 " "
y[1] (numeric) = 1.0270518468663463 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1674589459661332000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5999999999997105 " "
y[1] (closed_form) = 1.0273237224473004 " "
y[1] (numeric) = 1.0273237224472884 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1671499843679288000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5899999999997116 " "
y[1] (closed_form) = 1.0275983304232572 " "
y[1] (numeric) = 1.0275983304232452 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1668380836131727000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5799999999997127 " "
y[1] (closed_form) = 1.027875698255255 " "
y[1] (numeric) = 1.027875698255243 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.166523217379742000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.569999999999714 " "
y[1] (closed_form) = 1.0281558536803082 " "
y[1] (numeric) = 1.0281558536802962 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1662053591419763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.559999999999715 " "
y[1] (closed_form) = 1.0284388247141927 " "
y[1] (numeric) = 1.0284388247141805 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1874749355432603000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.549999999999716 " "
y[1] (closed_form) = 1.0287246396542475 " "
y[1] (numeric) = 1.0287246396542353 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.187145014333602900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.539999999999717 " "
y[1] (closed_form) = 1.0290133270822053 " "
y[1] (numeric) = 1.029013327082193 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1868119634082348000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5299999999997183 " "
y[1] (closed_form) = 1.029304915867049 " "
y[1] (numeric) = 1.0293049158670369 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1864757549116914000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5199999999997194 " "
y[1] (closed_form) = 1.0295994351679003 " "
y[1] (numeric) = 1.0295994351678885 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.1430041294756102000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.5099999999997205 " "
y[1] (closed_form) = 1.0298969144369348 " "
y[1] (numeric) = 1.0298969144369228 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1642338663095313000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4999999999997216 " "
y[1] (closed_form) = 1.0301973834223268 " "
y[1] (numeric) = 1.0301973834223146 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.185447902256053100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4899999999997227 " "
y[1] (closed_form) = 1.0305008721712259 " "
y[1] (numeric) = 1.0305008721712139 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1635515301106306000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4799999999997238 " "
y[1] (closed_form) = 1.0308074110327596 " "
y[1] (numeric) = 1.0308074110327474 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.184746359035306000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.469999999999725 " "
y[1] (closed_form) = 1.0311170306610695 " "
y[1] (numeric) = 1.0311170306610573 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.184390608217098000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.459999999999726 " "
y[1] (closed_form) = 1.0314297620183763 " "
y[1] (numeric) = 1.031429762018364 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.2055593442901073000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.449999999999727 " "
y[1] (closed_form) = 1.0317456363780766 " "
y[1] (numeric) = 1.0317456363780644 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1836690013779276000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.439999999999728 " "
y[1] (closed_form) = 1.0320646853278694 " "
y[1] (numeric) = 1.032064685327857 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.2048176875513888000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4299999999997293 " "
y[1] (closed_form) = 1.0323869407729158 " "
y[1] (numeric) = 1.0323869407729034 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.2044416085399565000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4199999999997304 " "
y[1] (closed_form) = 1.0327124349390286 " "
y[1] (numeric) = 1.0327124349390162 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.2040619881308862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.4099999999997315 " "
y[1] (closed_form) = 1.0330412003758958 " "
y[1] (numeric) = 1.033041200375883 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.2251730595179952000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3999999999997326 " "
y[1] (closed_form) = 1.033373269960335 " "
y[1] (numeric) = 1.033373269960322 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.267754070228631000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3899999999997337 " "
y[1] (closed_form) = 1.0337086768995813 " "
y[1] (numeric) = 1.0337086768995682 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2673427226972475000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3799999999997348 " "
y[1] (closed_form) = 1.0340474547346084 " "
y[1] (numeric) = 1.0340474547345953 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.266927511942782800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.369999999999736 " "
y[1] (closed_form) = 1.0343896373434818 " "
y[1] (numeric) = 1.0343896373434687 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2665084043399616000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.359999999999737 " "
y[1] (closed_form) = 1.0347352589447476 " "
y[1] (numeric) = 1.0347352589447345 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2660853660227298000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.349999999999738 " "
y[1] (closed_form) = 1.0350843541008543 " "
y[1] (numeric) = 1.0350843541008412 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.26565836288357000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.339999999999739 " "
y[1] (closed_form) = 1.0354369577216078 " "
y[1] (numeric) = 1.035436957721595 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.2437828290377105000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3299999999997403 " "
y[1] (closed_form) = 1.0357931050676645 " "
y[1] (numeric) = 1.0357931050676519 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.221918008413464000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3199999999997414 " "
y[1] (closed_form) = 1.0361528317540558 " "
y[1] (numeric) = 1.036152831754043 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.2429235042334677000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.3099999999997425 " "
y[1] (closed_form) = 1.0365161737537498 " "
y[1] (numeric) = 1.0365161737537367 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2639100114697513000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2999999999997436 " "
y[1] (closed_form) = 1.0368831674012495 " "
y[1] (numeric) = 1.0368831674012364 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.2634626641120128000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2899999999997447 " "
y[1] (closed_form) = 1.0372538493962253 " "
y[1] (numeric) = 1.0372538493962122 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.263011142181115000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.279999999999746 " "
y[1] (closed_form) = 1.0376282568071857 " "
y[1] (numeric) = 1.0376282568071729 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.2411561656271415000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.269999999999747 " "
y[1] (closed_form) = 1.0380064270751839 " "
y[1] (numeric) = 1.0380064270751714 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1979210871399652000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.259999999999748 " "
y[1] (closed_form) = 1.0383883980175617 " "
y[1] (numeric) = 1.0383883980175492 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1974804321332043000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.249999999999749 " "
y[1] (closed_form) = 1.0387742078317317 " "
y[1] (numeric) = 1.0387742078317193 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1970356774410773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.23999999999975 " "
y[1] (closed_form) = 1.0391638950989968 " "
y[1] (numeric) = 1.0391638950989845 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1752191669162346000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2299999999997513 " "
y[1] (closed_form) = 1.0395574987884086 " "
y[1] (numeric) = 1.0395574987883964 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1747741981670264000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2199999999997524 " "
y[1] (closed_form) = 1.0399550582606638 " "
y[1] (numeric) = 1.0399550582606516 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1743250993270982000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.2099999999997535 " "
y[1] (closed_form) = 1.0403566132720412 " "
y[1] (numeric) = 1.040356613272029 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.173871835395668000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1999999999997546 " "
y[1] (closed_form) = 1.0407622039783762 " "
y[1] (numeric) = 1.040762203978364 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1734143711401014000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1899999999997557 " "
y[1] (closed_form) = 1.0411718709390778 " "
y[1] (numeric) = 1.0411718709390656 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1729526710956745000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.179999999999757 " "
y[1] (closed_form) = 1.0415856551211833 " "
y[1] (numeric) = 1.041585655121171 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1724866995653722000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.169999999999758 " "
y[1] (closed_form) = 1.0420035979034556 " "
y[1] (numeric) = 1.0420035979034432 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1933258100855273000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.159999999999759 " "
y[1] (closed_form) = 1.0424257410805216 " "
y[1] (numeric) = 1.0424257410805091 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1928425580620095000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.14999999999976 " "
y[1] (closed_form) = 1.0428521268670505 " "
y[1] (numeric) = 1.042852126867038 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1923548464303975000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.139999999999761 " "
y[1] (closed_form) = 1.0432827979019763 " "
y[1] (numeric) = 1.043282797901964 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1705793765061356000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1299999999997623 " "
y[1] (closed_form) = 1.0437177972527614 " "
y[1] (numeric) = 1.0437177972527494 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1488171129698505000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1199999999997634 " "
y[1] (closed_form) = 1.0441571684197033 " "
y[1] (numeric) = 1.0441571684196909 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1908645797663725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.1099999999997645 " "
y[1] (closed_form) = 1.044600955340285 " "
y[1] (numeric) = 1.0446009553402729 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.1691022498537197000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0999999999997656 " "
y[1] (closed_form) = 1.0450492023935685 " "
y[1] (numeric) = 1.0450492023935565 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1473535062740585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0899999999997667 " "
y[1] (closed_form) = 1.0455019544046322 " "
y[1] (numeric) = 1.0455019544046205 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.1256185616341798000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.079999999999768 " "
y[1] (closed_form) = 1.045959256649055 " "
y[1] (numeric) = 1.045959256649043 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.146355232264536100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.069999999999769 " "
y[1] (closed_form) = 1.046421154857442 " "
y[1] (numeric) = 1.04642115485743 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.1458492223989097000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.05999999999977 " "
y[1] (closed_form) = 1.0468876952199992 " "
y[1] (numeric) = 1.046887695219987 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.166548554027118000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.049999999999771 " "
y[1] (closed_form) = 1.0473589243911519 " "
y[1] (numeric) = 1.0473589243911392 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.2084245606714294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.039999999999772 " "
y[1] (closed_form) = 1.0478348894942093 " "
y[1] (numeric) = 1.0478348894941965 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.2290664507142265000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0299999999997733 " "
y[1] (closed_form) = 1.0483156381260788 " "
y[1] (numeric) = 1.0483156381260654 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2708649772044694000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0199999999997744 " "
y[1] (closed_form) = 1.048801218362024 " "
y[1] (numeric) = 1.0488012183620106 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2702765845665878000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.0099999999997755 " "
y[1] (closed_form) = 1.0492916787604731 " "
y[1] (numeric) = 1.0492916787604598 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2696828313019634000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9999999999997766 " "
y[1] (closed_form) = 1.0497870683678752 " "
y[1] (numeric) = 1.0497870683678616 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2902350684777590000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9899999999997777 " "
y[1] (closed_form) = 1.050287436723603 " "
y[1] (numeric) = 1.0502874367235897 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2684790686502248000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.979999999999779 " "
y[1] (closed_form) = 1.0507928338649097 " "
y[1] (numeric) = 1.0507928338648964 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.267868971517429000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.96999999999978 " "
y[1] (closed_form) = 1.0513033103319305 " "
y[1] (numeric) = 1.0513033103319172 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.267253338267857000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.959999999999781 " "
y[1] (closed_form) = 1.0518189171727372 " "
y[1] (numeric) = 1.0518189171727237 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2877426598139896000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.949999999999782 " "
y[1] (closed_form) = 1.0523397059484438 " "
y[1] (numeric) = 1.0523397059484303 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2871053732805263000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9399999999997832 " "
y[1] (closed_form) = 1.0528657287383618 " "
y[1] (numeric) = 1.0528657287383485 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2653727756402808000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9299999999997843 " "
y[1] (closed_form) = 1.0533970381452087 " "
y[1] (numeric) = 1.0533970381451954 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2647345505128876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9199999999997854 " "
y[1] (closed_form) = 1.0539336873003675 " "
y[1] (numeric) = 1.0539336873003542 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.26409056433405000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.9099999999997865 " "
y[1] (closed_form) = 1.0544757298692016 " "
y[1] (numeric) = 1.054475729869188 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2844981175723233000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8999999999997876 " "
y[1] (closed_form) = 1.055023220056419 " "
y[1] (numeric) = 1.0550232200564054 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2838315444566790000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8899999999997887 " "
y[1] (closed_form) = 1.055576212611495 " "
y[1] (numeric) = 1.0555762126114814 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2831589740846167000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.87999999999979 " "
y[1] (closed_form) = 1.0561347628341455 " "
y[1] (numeric) = 1.056134762834132 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.282480359237447000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.869999999999791 " "
y[1] (closed_form) = 1.0566989265798588 " "
y[1] (numeric) = 1.0566989265798454 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.2607826089709795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.859999999999792 " "
y[1] (closed_form) = 1.0572687602654793 " "
y[1] (numeric) = 1.0572687602654658 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.28110480603114000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.849999999999793 " "
y[1] (closed_form) = 1.0578443208748505 " "
y[1] (numeric) = 1.057844320874837 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2804077720269139000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8399999999997942 " "
y[1] (closed_form) = 1.0584256659645128 " "
y[1] (numeric) = 1.058425665964499 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.3006832645924818000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8299999999997953 " "
y[1] (closed_form) = 1.0590128536694599 " "
y[1] (numeric) = 1.059012853669446 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.2999620786140936000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8199999999997964 " "
y[1] (closed_form) = 1.0596059427089515 " "
y[1] (numeric) = 1.0596059427089375 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.3201898504375760000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.8099999999997975 " "
y[1] (closed_form) = 1.0602049923923857 " "
y[1] (numeric) = 1.0602049923923713 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3613310089739103000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7999999999997986 " "
y[1] (closed_form) = 1.0608100626252301 " "
y[1] (numeric) = 1.0608100626252155 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3814861341704165000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7899999999997998 " "
y[1] (closed_form) = 1.0614212139150125 " "
y[1] (numeric) = 1.0614212139149979 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.380690694036334000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.779999999999801 " "
y[1] (closed_form) = 1.0620385073773706 " "
y[1] (numeric) = 1.062038507377356 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.379888188917125000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.769999999999802 " "
y[1] (closed_form) = 1.0626620047421655 " "
y[1] (numeric) = 1.0626620047421511 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3581834351580963000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.759999999999803 " "
y[1] (closed_form) = 1.0632917683596532 " "
y[1] (numeric) = 1.0632917683596388 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3573790138893635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.749999999999804 " "
y[1] (closed_form) = 1.06392786120672 " "
y[1] (numeric) = 1.0639278612067056 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.356567474768173000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7399999999998053 " "
y[1] (closed_form) = 1.064570346893181 " "
y[1] (numeric) = 1.0645703468931664 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3766064373125492000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7299999999998064 " "
y[1] (closed_form) = 1.06521928966814 " "
y[1] (numeric) = 1.0652192896681254 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3757677942180047000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7199999999998075 " "
y[1] (closed_form) = 1.0658747544264155 " "
y[1] (numeric) = 1.065874754426401 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3749217592585167000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.7099999999998086 " "
y[1] (closed_form) = 1.0665368067150296 " "
y[1] (numeric) = 1.066536806715015 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.374068277136145000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6999999999998097 " "
y[1] (closed_form) = 1.0672055127397626 " "
y[1] (numeric) = 1.0672055127397477 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.394013463422283000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6899999999998108 " "
y[1] (closed_form) = 1.0678809393717743 " "
y[1] (numeric) = 1.0678809393717594 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.393131760430999800000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.679999999999812 " "
y[1] (closed_form) = 1.0685631541542908 " "
y[1] (numeric) = 1.068563154154276 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3922423276658288000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.669999999999813 " "
y[1] (closed_form) = 1.069252225309359 " "
y[1] (numeric) = 1.0692522253093442 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3913451080892392000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.659999999999814 " "
y[1] (closed_form) = 1.0699482217446683 " "
y[1] (numeric) = 1.0699482217446536 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3696872079618552000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.649999999999815 " "
y[1] (closed_form) = 1.0706512130604426 " "
y[1] (numeric) = 1.0706512130604278 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3895270792671516000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6399999999998163 " "
y[1] (closed_form) = 1.0713612695563992 " "
y[1] (numeric) = 1.0713612695563843 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3886061548721998000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6299999999998174 " "
y[1] (closed_form) = 1.0720784622387793 " "
y[1] (numeric) = 1.0720784622387647 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3669656131743121000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6199999999998185 " "
y[1] (closed_form) = 1.0728028628274489 " "
y[1] (numeric) = 1.0728028628274342 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3660425818055622000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.6099999999998196 " "
y[1] (closed_form) = 1.0735345437630703 " "
y[1] (numeric) = 1.073534543763056 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3444280301903710000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5999999999998207 " "
y[1] (closed_form) = 1.074273578214347 " "
y[1] (numeric) = 1.074273578214333 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.3228338668463974000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.589999999999822 " "
y[1] (closed_form) = 1.0750200400853402 " "
y[1] (numeric) = 1.075020040085326 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.3219153304410844000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.579999999999823 " "
y[1] (closed_form) = 1.075774004022859 " "
y[1] (numeric) = 1.0757740040228445 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3416293074711957000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.569999999999824 " "
y[1] (closed_form) = 1.076535545423925 " "
y[1] (numeric) = 1.0765355454239103 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3613060885306070000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.559999999999825 " "
y[1] (closed_form) = 1.0773047404433134 " "
y[1] (numeric) = 1.0773047404432987 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3603341166977065000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.549999999999826 " "
y[1] (closed_form) = 1.0780816660011667 " "
y[1] (numeric) = 1.078081666001152 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3593537843390250000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5399999999998273 " "
y[1] (closed_form) = 1.0788663997906887 " "
y[1] (numeric) = 1.0788663997906738 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3789463211444336000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5299999999998284 " "
y[1] (closed_form) = 1.0796590202859118 " "
y[1] (numeric) = 1.0796590202858967 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3985001608103687000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5199999999998295 " "
y[1] (closed_form) = 1.0804596067495462 " "
y[1] (numeric) = 1.0804596067495311 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.397463916335202000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.5099999999998306 " "
y[1] (closed_form) = 1.0812682392409054 " "
y[1] (numeric) = 1.0812682392408905 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3758832443299500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4999999999998317 " "
y[1] (closed_form) = 1.0820849986239125 " "
y[1] (numeric) = 1.0820849986238978 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3543246550584068000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.489999999999833 " "
y[1] (closed_form) = 1.0829099665751865 " "
y[1] (numeric) = 1.0829099665751716 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3737973598144170000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.479999999999834 " "
y[1] (closed_form) = 1.08374322559221 " "
y[1] (numeric) = 1.0837432255921946 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.4137184323763574000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.469999999999835 " "
y[1] (closed_form) = 1.0845848590015787 " "
y[1] (numeric) = 1.0845848590015632 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.4330941664684962000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.459999999999836 " "
y[1] (closed_form) = 1.0854349509673353 " "
y[1] (numeric) = 1.0854349509673198 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.431971794431368000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.449999999999837 " "
y[1] (closed_form) = 1.0862935864993846 " "
y[1] (numeric) = 1.086293586499369 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.4308399255895815000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4399999999998383 " "
y[1] (closed_form) = 1.0871608514619955 " "
y[1] (numeric) = 1.0871608514619802 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.4092742319798984000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4299999999998394 " "
y[1] (closed_form) = 1.0880368325823868 " "
y[1] (numeric) = 1.0880368325823715 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.4081396218419875000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4199999999998405 " "
y[1] (closed_form) = 1.0889216174594005 " "
y[1] (numeric) = 1.0889216174593852 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.406995461764574000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.4099999999998416 " "
y[1] (closed_form) = 1.089815294572262 " "
y[1] (numeric) = 1.0898152945722464 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.4262162058252872000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3999999999998427 " "
y[1] (closed_form) = 1.0907179532894267 " "
y[1] (numeric) = 1.0907179532894116 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3843205834621056000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.389999999999844 " "
y[1] (closed_form) = 1.0916296838775192 " "
y[1] (numeric) = 1.0916296838775041 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.383164397038899000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.379999999999845 " "
y[1] (closed_form) = 1.0925505775103577 " "
y[1] (numeric) = 1.0925505775103428 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.361675041523289000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.369999999999846 " "
y[1] (closed_form) = 1.0934807262780728 " "
y[1] (numeric) = 1.0934807262780584 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3199043177699998000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.359999999999847 " "
y[1] (closed_form) = 1.0944202231963167 " "
y[1] (numeric) = 1.094420223196302 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3390600442535197000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.349999999999848 " "
y[1] (closed_form) = 1.0953691622155641 " "
y[1] (numeric) = 1.0953691622155495 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.337899991214837000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3399999999998493 " "
y[1] (closed_form) = 1.0963276382305076 " "
y[1] (numeric) = 1.0963276382304925 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3772372973532107000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3299999999998504 " "
y[1] (closed_form) = 1.0972957470895472 " "
y[1] (numeric) = 1.0972957470895321 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.376022205039125000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3199999999998515 " "
y[1] (closed_form) = 1.0982735856043762 " "
y[1] (numeric) = 1.0982735856043606 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.4152322835114775000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.3099999999998526 " "
y[1] (closed_form) = 1.0992612515596603 " "
y[1] (numeric) = 1.0992612515596445 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.4341601623189387000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2999999999998537 " "
y[1] (closed_form) = 1.1002588437228185 " "
y[1] (numeric) = 1.1002588437228025 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4530409499375782000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.289999999999855 " "
y[1] (closed_form) = 1.101266461853898 " "
y[1] (numeric) = 1.101266461853882 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4517114711446857000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.279999999999856 " "
y[1] (closed_form) = 1.1022842067155523 " "
y[1] (numeric) = 1.102284206715536 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.4705151412652084000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.269999999999857 " "
y[1] (closed_form) = 1.103312180083115 " "
y[1] (numeric) = 1.103312180083099 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4490197645962632000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.259999999999858 " "
y[1] (closed_form) = 1.1043504847547798 " "
y[1] (numeric) = 1.1043504847547638 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4476574036323445000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2499999999998592 " "
y[1] (closed_form) = 1.1053992245618791 " "
y[1] (numeric) = 1.1053992245618631 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4462839487641876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2399999999998603 " "
y[1] (closed_form) = 1.1064585043792676 " "
y[1] (numeric) = 1.1064585043792516 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4448993334432558000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2299999999998614 " "
y[1] (closed_form) = 1.10752843013581 " "
y[1] (numeric) = 1.1075284301357942 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.42345483156075980000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2199999999998625 " "
y[1] (closed_form) = 1.108609108824973 " "
y[1] (numeric) = 1.1086091088249572 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.4220672394065836000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.2099999999998636 " "
y[1] (closed_form) = 1.1097006485155263 " "
y[1] (numeric) = 1.1097006485155112 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.3606402010398458000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1999999999998647 " "
y[1] (closed_form) = 1.1108031583623488 " "
y[1] (numeric) = 1.110803158362334 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3393001647483757000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.189999999999866 " "
y[1] (closed_form) = 1.1119167486173438 " "
y[1] (numeric) = 1.1119167486173291 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.317989313793081000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.179999999999867 " "
y[1] (closed_form) = 1.1130415306404648 " "
y[1] (numeric) = 1.1130415306404504 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.296708067292158800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.169999999999868 " "
y[1] (closed_form) = 1.1141776169108515 " "
y[1] (numeric) = 1.1141776169108375 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2555278348762824000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.159999999999869 " "
y[1] (closed_form) = 1.1153251210380777 " "
y[1] (numeric) = 1.1153251210380635 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2741445922042350000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1499999999998702 " "
y[1] (closed_form) = 1.116484157773512 " "
y[1] (numeric) = 1.116484157773498 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2529340441492154000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1399999999998713 " "
y[1] (closed_form) = 1.1176548430217943 " "
y[1] (numeric) = 1.11765484302178 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2714886714739437000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1299999999998724 " "
y[1] (closed_form) = 1.1188372938524247 " "
y[1] (numeric) = 1.1188372938524103 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.2899909038990923000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1199999999998735 " "
y[1] (closed_form) = 1.120031628511472 " "
y[1] (numeric) = 1.120031628511457 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.328265037456906000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.1099999999998746 " "
y[1] (closed_form) = 1.121237966433397 " "
y[1] (numeric) = 1.121237966433382 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3268359594796875000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0999999999998757 " "
y[1] (closed_form) = 1.1224564282529972 " "
y[1] (numeric) = 1.1224564282529823 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.325395637239282200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.089999999999877 " "
y[1] (closed_form) = 1.12368713581747 " "
y[1] (numeric) = 1.1236871358174554 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.3041836520083283000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.079999999999878 " "
y[1] (closed_form) = 1.1249302121985978 " "
y[1] (numeric) = 1.124930212198583 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.322481018702579000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.069999999999879 " "
y[1] (closed_form) = 1.126185781705054 " "
y[1] (numeric) = 1.1261857817050391 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3210066022546674000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.05999999999988 " "
y[1] (closed_form) = 1.127453969894836 " "
y[1] (numeric) = 1.1274539698948212 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.319520701263286000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0499999999998813 " "
y[1] (closed_form) = 1.1287349035878196 " "
y[1] (numeric) = 1.1287349035878051 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.2786792783894899000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0399999999998824 " "
y[1] (closed_form) = 1.1300287108784413 " "
y[1] (numeric) = 1.1300287108784268 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.2772152761417407000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0299999999998835 " "
y[1] (closed_form) = 1.1313355211485083 " "
y[1] (numeric) = 1.1313355211484941 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.256113190963494000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0199999999998846 " "
y[1] (closed_form) = 1.132655465080137 " "
y[1] (numeric) = 1.1326554650801226 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.2742532716341845000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.0099999999998857 " "
y[1] (closed_form) = 1.1339886746688204 " "
y[1] (numeric) = 1.1339886746688062 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.2531743069966958000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9999999999998868 " "
y[1] (closed_form) = 1.135335283236628 " "
y[1] (numeric) = 1.135335283236614 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2321303069519253000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9899999999998879 " "
y[1] (closed_form) = 1.1366954254455393 " "
y[1] (numeric) = 1.1366954254455253 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2306559696757746000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.979999999999889 " "
y[1] (closed_form) = 1.138069237310908 " "
y[1] (numeric) = 1.1380692373108945 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.1901491101219039000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.96999999999989 " "
y[1] (closed_form) = 1.1394568562150662 " "
y[1] (numeric) = 1.1394568562150527 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.1886997587094617000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9599999999998912 " "
y[1] (closed_form) = 1.1408584209210604 " "
y[1] (numeric) = 1.1408584209210468 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.1872394200756056000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9499999999998923 " "
y[1] (closed_form) = 1.142274071586529 " "
y[1] (numeric) = 1.1422740715865156 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.1663292222853074000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9399999999998934 " "
y[1] (closed_form) = 1.1437039497777182 " "
y[1] (numeric) = 1.143703949777705 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 1.1454565399658703000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9299999999998945 " "
y[1] (closed_form) = 1.1451481984836391 " "
y[1] (numeric) = 1.1451481984836258 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.1634019346267364000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9199999999998956 " "
y[1] (closed_form) = 1.1466069621303654 " "
y[1] (numeric) = 1.1466069621303525 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.1231910768903533000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.9099999999998967 " "
y[1] (closed_form) = 1.1480803865954778 " "
y[1] (numeric) = 1.148080386595465 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.1217495948904788000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8999999999998978 " "
y[1] (closed_form) = 1.1495686192226504 " "
y[1] (numeric) = 1.1495686192226378 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.1009819047848805000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8899999999998989 " "
y[1] (closed_form) = 1.151071808836386 " "
y[1] (numeric) = 1.1510718088363738 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.0609636320797608000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8799999999999 " "
y[1] (closed_form) = 1.1525901057568992 " "
y[1] (numeric) = 1.152590105756887 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 1.05956603391601000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.869999999999901 " "
y[1] (closed_form) = 1.1541236618151467 " "
y[1] (numeric) = 1.1541236618151347 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.0389188838823207000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8599999999999022 " "
y[1] (closed_form) = 1.1556726303680125 " "
y[1] (numeric) = 1.1556726303680007 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.018312950552367000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8499999999999033 " "
y[1] (closed_form) = 1.1572371663136427 " "
y[1] (numeric) = 1.157237166313631 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 1.0169362342997125000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8399999999999044 " "
y[1] (closed_form) = 1.158817426106936 " "
y[1] (numeric) = 1.158817426106924 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.0347107659774883000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8299999999999055 " "
y[1] (closed_form) = 1.160413567775188 " "
y[1] (numeric) = 1.1604135677751763 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 9.9501761929920380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8199999999999066 " "
y[1] (closed_form) = 1.1620257509338958 " "
y[1] (numeric) = 1.1620257509338843 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 9.9363714158847970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.8099999999999077 " "
y[1] (closed_form) = 1.1636541368027191 " "
y[1] (numeric) = 1.1636541368027076 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 9.92246672866780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7999999999999088 " "
y[1] (closed_form) = 1.1652988882216015 " "
y[1] (numeric) = 1.1652988882215902 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 9.7179144043112590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7899999999999099 " "
y[1] (closed_form) = 1.1669601696670557 " "
y[1] (numeric) = 1.1669601696670446 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.5138039282173050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.779999999999911 " "
y[1] (closed_form) = 1.1686381472686105 " "
y[1] (numeric) = 1.1686381472685996 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.3101407537963350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.769999999999912 " "
y[1] (closed_form) = 1.1703329888254244 " "
y[1] (numeric) = 1.1703329888254133 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.4863857998175750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7599999999999132 " "
y[1] (closed_form) = 1.1720448638230654 " "
y[1] (numeric) = 1.1720448638230543 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.4725300958509930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7499999999999143 " "
y[1] (closed_form) = 1.17377394345046 " "
y[1] (numeric) = 1.1737739434504488 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.458576166391229000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7399999999999154 " "
y[1] (closed_form) = 1.1755204006170117 " "
y[1] (numeric) = 1.1755204006170006 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.4445236683465330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7299999999999165 " "
y[1] (closed_form) = 1.1772844099698927 " "
y[1] (numeric) = 1.1772844099698816 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.4303722636873190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7199999999999176 " "
y[1] (closed_form) = 1.179066147911508 " "
y[1] (numeric) = 1.179066147911497 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.4161216195690630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.7099999999999187 " "
y[1] (closed_form) = 1.1808657926171369 " "
y[1] (numeric) = 1.1808657926171258 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.401771408456030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6999999999999198 " "
y[1] (closed_form) = 1.1826835240527493 " "
y[1] (numeric) = 1.1826835240527382 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.3873213082457630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.689999999999921 " "
y[1] (closed_form) = 1.184519523993004 " "
y[1] (numeric) = 1.1845195239929929 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.3727710023943320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.679999999999922 " "
y[1] (closed_form) = 1.1863739760394245 " "
y[1] (numeric) = 1.1863739760394136 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.1709577764414580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.669999999999923 " "
y[1] (closed_form) = 1.1882470656387611 " "
y[1] (numeric) = 1.1882470656387503 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.1565011654185880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6599999999999242 " "
y[1] (closed_form) = 1.190138980101535 " "
y[1] (numeric) = 1.1901389801015239 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.32851577158190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6499999999999253 " "
y[1] (closed_form) = 1.1920499086207685 " "
y[1] (numeric) = 1.1920499086207574 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.313561593320471000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6399999999999264 " "
y[1] (closed_form) = 1.1939800422909062 " "
y[1] (numeric) = 1.1939800422908953 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.112535600218720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6299999999999275 " "
y[1] (closed_form) = 1.1959295741269236 " "
y[1] (numeric) = 1.1959295741269125 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.283347854623160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6199999999999286 " "
y[1] (closed_form) = 1.197898699083629 " "
y[1] (numeric) = 1.1978986990836178 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 9.2680877395931520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.6099999999999297 " "
y[1] (closed_form) = 1.1998876140751586 " "
y[1] (numeric) = 1.1998876140751478 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.0676705998942160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5999999999999308 " "
y[1] (closed_form) = 1.2018965179946695 " "
y[1] (numeric) = 1.2018965179946586 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.052514487253710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.589999999999932 " "
y[1] (closed_form) = 1.2039256117342274 " "
y[1] (numeric) = 1.2039256117342165 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 9.0372573980329850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.579999999999933 " "
y[1] (closed_form) = 1.2059750982048973 " "
y[1] (numeric) = 1.2059750982048867 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 8.8377787006267560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5699999999999341 " "
y[1] (closed_form) = 1.2080451823570342 " "
y[1] (numeric) = 1.2080451823570235 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 8.8226344445215630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5599999999999352 " "
y[1] (closed_form) = 1.2101360712007783 " "
y[1] (numeric) = 1.210136071200768 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 8.4404159743923450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5499999999999363 " "
y[1] (closed_form) = 1.2122479738267566 " "
y[1] (numeric) = 1.2122479738267464 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 8.425711609406360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5399999999999374 " "
y[1] (closed_form) = 1.2143811014269914 " "
y[1] (numeric) = 1.2143811014269814 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.2280654811615820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5299999999999385 " "
y[1] (closed_form) = 1.2165356673160204 " "
y[1] (numeric) = 1.2165356673160106 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 8.030970960560769000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5199999999999396 " "
y[1] (closed_form) = 1.218711886952228 " "
y[1] (numeric) = 1.2187118869522182 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 8.0166302809552790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.5099999999999407 " "
y[1] (closed_form) = 1.2209099779593913 " "
y[1] (numeric) = 1.2209099779593815 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 8.0021973716938010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4999999999999418 " "
y[1] (closed_form) = 1.2231301601484428 " "
y[1] (numeric) = 1.223130160148433 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 7.9876720687810240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.489999999999943 " "
y[1] (closed_form) = 1.2253726555394515 " "
y[1] (numeric) = 1.2253726555394415 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 8.1542599930366330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.479999999999944 " "
y[1] (closed_form) = 1.2276376883838256 " "
y[1] (numeric) = 1.2276376883838158 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 7.9583436620974460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4699999999999451 " "
y[1] (closed_form) = 1.2299254851867365 " "
y[1] (numeric) = 1.2299254851867272 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 7.5824702546393620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4599999999999462 " "
y[1] (closed_form) = 1.2322362747297713 " "
y[1] (numeric) = 1.2322362747297622 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 7.3880545384226310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4499999999999473 " "
y[1] (closed_form) = 1.23457028809381 " "
y[1] (numeric) = 1.2345702880938008 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 7.5539428550889260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4399999999999484 " "
y[1] (closed_form) = 1.236927758682134 " "
y[1] (numeric) = 1.2369277586821252 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 7.0010067534603730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4299999999999495 " "
y[1] (closed_form) = 1.2393089222437665 " "
y[1] (numeric) = 1.2393089222437579 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 6.9875552710439440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4199999999999506 " "
y[1] (closed_form) = 1.2417140168970484 " "
y[1] (numeric) = 1.2417140168970398 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 6.9740209695919110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.4099999999999517 " "
y[1] (closed_form) = 1.244143283153449 " "
y[1] (numeric) = 1.2441432831534405 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 6.7819318734452470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3999999999999528 " "
y[1] (closed_form) = 1.2465969639416181 " "
y[1] (numeric) = 1.2465969639416101 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.4123417660397020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.389999999999954 " "
y[1] (closed_form) = 1.2490753046316796 " "
y[1] (numeric) = 1.249075304631672 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 6.0440844034437340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.379999999999955 " "
y[1] (closed_form) = 1.2515785530597678 " "
y[1] (numeric) = 1.2515785530597605 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 5.8545841526385730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3699999999999561 " "
y[1] (closed_form) = 1.2541069595528114 " "
y[1] (numeric) = 1.2541069595528043 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.6657267575762840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3599999999999572 " "
y[1] (closed_form) = 1.256660776953567 " "
y[1] (numeric) = 1.2566607769535598 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.6542127262268680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3499999999999583 " "
y[1] (closed_form) = 1.2592402606459023 " "
y[1] (numeric) = 1.259240260645896 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.1136337870288550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3399999999999594 " "
y[1] (closed_form) = 1.2618456685803365 " "
y[1] (numeric) = 1.26184566858033 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.1030753626713780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3299999999999605 " "
y[1] (closed_form) = 1.2644772612998345 " "
y[1] (numeric) = 1.264477261299828 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.0924549929878200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3199999999999616 " "
y[1] (closed_form) = 1.2671353019658607 " "
y[1] (numeric) = 1.2671353019658544 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.9065391266862385000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.3099999999999627 " "
y[1] (closed_form) = 1.2698200563846969 " "
y[1] (numeric) = 1.2698200563846909 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.7213022843919983000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2999999999999639 " "
y[1] (closed_form) = 1.2725317930340225 " "
y[1] (numeric) = 1.272531793034016 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.0602221320326150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.289999999999965 " "
y[1] (closed_form) = 1.275270783089762 " "
y[1] (numeric) = 1.275270783089756 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.7011226262476550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.279999999999966 " "
y[1] (closed_form) = 1.2780373004532035 " "
y[1] (numeric) = 1.2780373004531977 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.51720753846824360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2699999999999672 " "
y[1] (closed_form) = 1.280831621778389 " "
y[1] (numeric) = 1.2808316217783833 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.5073525902139950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2599999999999683 " "
y[1] (closed_form) = 1.2836540264997793 " "
y[1] (numeric) = 1.2836540264997738 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.3244636082063010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2499999999999694 " "
y[1] (closed_form) = 1.2865047968601988 " "
y[1] (numeric) = 1.2865047968601935 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.14228577398755570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2399999999999705 " "
y[1] (closed_form) = 1.289384217939059 " "
y[1] (numeric) = 1.2893842179390538 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.13303532341871950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2299999999999716 " "
y[1] (closed_form) = 1.2922925776808678 " "
y[1] (numeric) = 1.2922925776808627 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.95191151096814740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2199999999999727 " "
y[1] (closed_form) = 1.2952301669240223 " "
y[1] (numeric) = 1.2952301669240176 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.60008346199921670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.2099999999999738 " "
y[1] (closed_form) = 1.2981972794298953 " "
y[1] (numeric) = 1.2981972794298913 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.0787330646739330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1999999999999749 " "
y[1] (closed_form) = 1.3011942119122097 " "
y[1] (numeric) = 1.3011942119122062 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.7303485108341370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.189999999999976 " "
y[1] (closed_form) = 1.3042212640667112 " "
y[1] (numeric) = 1.3042212640667081 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.38351003360993460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.179999999999977 " "
y[1] (closed_form) = 1.3072787386011382 " "
y[1] (numeric) = 1.307278738601135 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.3779354602499242000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1699999999999782 " "
y[1] (closed_form) = 1.310366941265492 " "
y[1] (numeric) = 1.3103669412654888 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.37233126924605770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1599999999999793 " "
y[1] (closed_form) = 1.3134861808826117 " "
y[1] (numeric) = 1.3134861808826095 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.69049821883794720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1499999999999804 " "
y[1] (closed_form) = 1.3166367693790595 " "
y[1] (numeric) = 1.316636769379058 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.180517110431489900000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1399999999999815 " "
y[1] (closed_form) = 1.31981902181631 " "
y[1] (numeric) = 1.319819021816309 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.72954704409268900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1299999999999826 " "
y[1] (closed_form) = 1.3230332564222587 " "
y[1] (numeric) = 1.3230332564222582 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.35659899472948100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1199999999999837 " "
y[1] (closed_form) = 1.3262797946230447 " "
y[1] (numeric) = 1.3262797946230451 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.348382533236749500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.1099999999999848 " "
y[1] (closed_form) = 1.3295589610751941 " "
y[1] (numeric) = 1.3295589610751948 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.01018634206640700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0999999999999859 " "
y[1] (closed_form) = 1.3328710836980844 " "
y[1] (numeric) = 1.3328710836980855 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.32956043689397900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.089999999999987 " "
y[1] (closed_form) = 1.3362164937067378 " "
y[1] (numeric) = 1.3362164937067391 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.97044742244128800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.079999999999988 " "
y[1] (closed_form) = 1.3395955256449432 " "
y[1] (numeric) = 1.3395955256449448 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.16028473126386520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0699999999999892 " "
y[1] (closed_form) = 1.3430085174187103 " "
y[1] (numeric) = 1.3430085174187123 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.48800355202977400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0599999999999903 " "
y[1] (closed_form) = 1.3464558103300608 " "
y[1] (numeric) = 1.3464558103300632 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.81401471584619580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0499999999999914 " "
y[1] (closed_form) = 1.3499377491111584 " "
y[1] (numeric) = 1.349937749111161 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.9738208379273710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0399999999999925 " "
y[1] (closed_form) = 1.353454681958783 " "
y[1] (numeric) = 1.3534546819587863 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.46086486549750520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0299999999999936 " "
y[1] (closed_form) = 1.3570069605691497 " "
y[1] (numeric) = 1.3570069605691537 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.9453075811595270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0199999999999947 " "
y[1] (closed_form) = 1.3605949401730801 " "
y[1] (numeric) = 1.3605949401730848 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.42713071006459040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.0099999999999958 " "
y[1] (closed_form) = 1.364218979571525 " "
y[1] (numeric) = 1.36421897957153 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.7435528971160770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9999999999999968 " "
y[1] (closed_form) = 1.3678794411714434 " "
y[1] (numeric) = 1.3678794411714492 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.22051794499281000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9899999999999968 " "
y[1] (closed_form) = 1.3715766910220468 " "
y[1] (numeric) = 1.3715766910220526 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.2091410315152517000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9799999999999968 " "
y[1] (closed_form) = 1.3753110988514008 " "
y[1] (numeric) = 1.3753110988514063 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.0362614158802540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9699999999999968 " "
y[1] (closed_form) = 1.3790830381034 " "
y[1] (numeric) = 1.379083038103406 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.34723955507481300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9599999999999967 " "
y[1] (closed_form) = 1.3828928859751133 " "
y[1] (numeric) = 1.3828928859751195 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.49582827488257340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9499999999999967 " "
y[1] (closed_form) = 1.3867410234545026 " "
y[1] (numeric) = 1.3867410234545086 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.3232328398573130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9399999999999967 " "
y[1] (closed_form) = 1.3906278353585224 " "
y[1] (numeric) = 1.3906278353585286 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.47082158131689300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9299999999999967 " "
y[1] (closed_form) = 1.3945537103716024 " "
y[1] (numeric) = 1.3945537103716088 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.6174582555949384000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9199999999999967 " "
y[1] (closed_form) = 1.3985190410845154 " "
y[1] (numeric) = 1.3985190410845216 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.4455947722238810000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9099999999999967 " "
y[1] (closed_form) = 1.4025242240336373 " "
y[1] (numeric) = 1.4025242240336435 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.4328995045947710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8999999999999967 " "
y[1] (closed_form) = 1.4065696597406006 " "
y[1] (numeric) = 1.4065696597406065 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.26228753866444150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8899999999999967 " "
y[1] (closed_form) = 1.410655752752347 " "
y[1] (numeric) = 1.4106557527523529 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.24994143417239230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799999999999967 " "
y[1] (closed_form) = 1.4147829116815829 " "
y[1] (numeric) = 1.4147829116815884 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.92365152087385400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8699999999999967 " "
y[1] (closed_form) = 1.4189515492476403 " "
y[1] (numeric) = 1.4189515492476463 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.2250944622842385000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8599999999999967 " "
y[1] (closed_form) = 1.4231620823177502 " "
y[1] (numeric) = 1.423162082317756 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.0565721921488330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8499999999999966 " "
y[1] (closed_form) = 1.4274149319487281 " "
y[1] (numeric) = 1.427414931948734 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.0444860137263733000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8399999999999966 " "
y[1] (closed_form) = 1.4317105234290812 " "
y[1] (numeric) = 1.431710523429087 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.03235125647016600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8299999999999966 " "
y[1] (closed_form) = 1.436049286321537 " "
y[1] (numeric) = 1.4360492863215428 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.02016823728860550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8199999999999966 " "
y[1] (closed_form) = 1.4404316545060007 " "
y[1] (numeric) = 1.4404316545060065 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.00793728046106600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8099999999999966 " "
y[1] (closed_form) = 1.4448580662229427 " "
y[1] (numeric) = 1.4448580662229484 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.99565871763629070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7999999999999966 " "
y[1] (closed_form) = 1.4493289641172231 " "
y[1] (numeric) = 1.4493289641172287 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.83012777675835100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7899999999999966 " "
y[1] (closed_form) = 1.4538447952823574 " "
y[1] (numeric) = 1.4538447952823628 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.66550166530380600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7799999999999966 " "
y[1] (closed_form) = 1.458406011305225 " "
y[1] (numeric) = 1.4584060113052306 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.80628925010924660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7699999999999966 " "
y[1] (closed_form) = 1.4630130683112297 " "
y[1] (numeric) = 1.4630130683112357 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.0978474238074770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7599999999999966 " "
y[1] (closed_form) = 1.467666427009911 " "
y[1] (numeric) = 1.4676664270099171 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.2361457777346107000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7499999999999966 " "
y[1] (closed_form) = 1.4723665527410164 " "
y[1] (numeric) = 1.4723665527410228 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.3734310120250030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7399999999999965 " "
y[1] (closed_form) = 1.477113915521036 " "
y[1] (numeric) = 1.4771139155210424 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.35937504559661240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7299999999999965 " "
y[1] (closed_form) = 1.481908990090204 " "
y[1] (numeric) = 1.4819089900902103 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.1954323642522960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7199999999999965 " "
y[1] (closed_form) = 1.4867522559599733 " "
y[1] (numeric) = 1.4867522559599797 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.33111402186382060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7099999999999965 " "
y[1] (closed_form) = 1.4916441974609669 " "
y[1] (numeric) = 1.4916441974609733 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 4.3169098594602423000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6999999999999965 " "
y[1] (closed_form) = 1.4965853037914112 " "
y[1] (numeric) = 1.4965853037914179 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.45102469660451360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6899999999999965 " "
y[1] (closed_form) = 1.5015760690660573 " "
y[1] (numeric) = 1.501576069066064 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 4.43623089431235000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6799999999999965 " "
y[1] (closed_form) = 1.5066169923655914 " "
y[1] (numeric) = 1.5066169923655985 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.7161470988353343000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6699999999999965 " "
y[1] (closed_form) = 1.5117085777865444 " "
y[1] (numeric) = 1.5117085777865518 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 4.8471458521820227000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6599999999999965 " "
y[1] (closed_form) = 1.516851334491701 " "
y[1] (numeric) = 1.5168513344917085 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.9770972248779527000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6499999999999965 " "
y[1] (closed_form) = 1.522045776761018 " "
y[1] (numeric) = 1.5220457767610256 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.9601113729422620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6399999999999965 " "
y[1] (closed_form) = 1.5272924240430505 " "
y[1] (numeric) = 1.527292424043058 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 4.9430720984433185000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6299999999999965 " "
y[1] (closed_form) = 1.532591801006899 " "
y[1] (numeric) = 1.5325918010069068 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 5.0708617697616860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6199999999999964 " "
y[1] (closed_form) = 1.5379444375946765 " "
y[1] (numeric) = 1.5379444375946842 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 5.0532132256550890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6099999999999964 " "
y[1] (closed_form) = 1.5433508690745017 " "
y[1] (numeric) = 1.5433508690745097 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.1793833388610060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5999999999999964 " "
y[1] (closed_form) = 1.5488116360940283 " "
y[1] (numeric) = 1.5488116360940363 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.1611219795974180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5899999999999964 " "
y[1] (closed_form) = 1.554327284734509 " "
y[1] (numeric) = 1.554327284734517 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.1428073455369450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5799999999999964 " "
y[1] (closed_form) = 1.559898366565404 " "
y[1] (numeric) = 1.559898366565412 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.1244401229174360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5699999999999964 " "
y[1] (closed_form) = 1.565525438699539 " "
y[1] (numeric) = 1.5655254386995474 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 5.3896888409301550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5599999999999964 " "
y[1] (closed_form) = 1.571209063848817 " "
y[1] (numeric) = 1.571209063848825 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.08755070297270100000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5499999999999964 " "
y[1] (closed_form) = 1.5769498103804889 " "
y[1] (numeric) = 1.5769498103804969 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.0690299238961940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5399999999999964 " "
y[1] (closed_form) = 1.5827482523739917 " "
y[1] (numeric) = 1.5827482523740002 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 5.3310404699517720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5299999999999964 " "
y[1] (closed_form) = 1.5886049696783573 " "
y[1] (numeric) = 1.588604969678366 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 5.4511598272473920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5199999999999964 " "
y[1] (closed_form) = 1.5945205479701965 " "
y[1] (numeric) = 1.5945205479702051 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 5.4309363420245380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5099999999999963 " "
y[1] (closed_form) = 1.6004955788122681 " "
y[1] (numeric) = 1.6004955788122768 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 5.410661364339810000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.49999999999999634 " "
y[1] (closed_form) = 1.6065306597126356 " "
y[1] (numeric) = 1.6065306597126443 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 5.3903357148659780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4899999999999963 " "
y[1] (closed_form) = 1.6126263941844183 " "
y[1] (numeric) = 1.612626394184427 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 5.3699602234625840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4799999999999963 " "
y[1] (closed_form) = 1.6187833918061432 " "
y[1] (numeric) = 1.6187833918061523 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 5.6238708946530320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4699999999999963 " "
y[1] (closed_form) = 1.625002268282703 " "
y[1] (numeric) = 1.6250022682827123 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 5.7389910087367860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4599999999999963 " "
y[1] (closed_form) = 1.6312836455069282 " "
y[1] (numeric) = 1.6312836455069375 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 5.7168926032806880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4499999999999963 " "
y[1] (closed_form) = 1.6376281516217757 " "
y[1] (numeric) = 1.637628151621785 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 5.69474419306710100000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4399999999999963 " "
y[1] (closed_form) = 1.6440364210831437 " "
y[1] (numeric) = 1.644036421083153 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 5.6725467193160670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4299999999999963 " "
y[1] (closed_form) = 1.650509094723319 " "
y[1] (numeric) = 1.6505090947233285 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 5.7848321116806080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.41999999999999627 " "
y[1] (closed_form) = 1.6570468198150592 " "
y[1] (numeric) = 1.657046819815069 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 5.8960087909838240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.40999999999999626 " "
y[1] (closed_form) = 1.663650250136322 " "
y[1] (numeric) = 1.6636502501363315 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 5.7391377851167780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.39999999999999625 " "
y[1] (closed_form) = 1.6703200460356418 " "
y[1] (numeric) = 1.6703200460356513 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 5.7162206934159070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.38999999999999624 " "
y[1] (closed_form) = 1.677056874498167 " "
y[1] (numeric) = 1.677056874498177 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.9580610375043840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.37999999999999623 " "
y[1] (closed_form) = 1.6838614092123585 " "
y[1] (numeric) = 1.6838614092123687 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 6.0658506517642420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3699999999999962 " "
y[1] (closed_form) = 1.6907343306373572 " "
y[1] (numeric) = 1.6907343306373672 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.9098623837961080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3599999999999962 " "
y[1] (closed_form) = 1.6976763260710337 " "
y[1] (numeric) = 1.697676326071044 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 6.0164895214095520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3499999999999962 " "
y[1] (closed_form) = 1.704688089718716 " "
y[1] (numeric) = 1.7046880897187262 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.9917423534277290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3399999999999962 " "
y[1] (closed_form) = 1.7117703227626124 " "
y[1] (numeric) = 1.7117703227626224 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.8372359239762880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3299999999999962 " "
y[1] (closed_form) = 1.718923733431929 " "
y[1] (numeric) = 1.718923733431939 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.8129438946524980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3199999999999962 " "
y[1] (closed_form) = 1.7261490370736938 " "
y[1] (numeric) = 1.7261490370737038 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.7886121111336140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.30999999999999617 " "
y[1] (closed_form) = 1.733446956224292 " "
y[1] (numeric) = 1.7334469562243022 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.8923359551763730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.29999999999999616 " "
y[1] (closed_form) = 1.7408182206817209 " "
y[1] (numeric) = 1.740818220681731 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.8673856380889220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.28999999999999615 " "
y[1] (closed_form) = 1.748263567578568 " "
y[1] (numeric) = 1.7482635675785785 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 5.9694068017049540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.27999999999999614 " "
y[1] (closed_form) = 1.7557837414557285 " "
y[1] (numeric) = 1.755783741455739 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 5.9438393152130780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.26999999999999613 " "
y[1] (closed_form) = 1.7633794943368561 " "
y[1] (numeric) = 1.763379494336867 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 6.1700760819032780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2599999999999961 " "
y[1] (closed_form) = 1.7710515858035691 " "
y[1] (numeric) = 1.7710515858035805 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 6.3940965593266430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.24999999999999611 " "
y[1] (closed_form) = 1.7788007830714079 " "
y[1] (numeric) = 1.7788007830714192 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 6.366241210903490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2399999999999961 " "
y[1] (closed_form) = 1.7866278610665565 " "
y[1] (numeric) = 1.786627861066568 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 6.4626325983794220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2299999999999961 " "
y[1] (closed_form) = 1.7945336025033372 " "
y[1] (numeric) = 1.7945336025033487 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 6.4341617454221820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2199999999999961 " "
y[1] (closed_form) = 1.8025187979624815 " "
y[1] (numeric) = 1.8025187979624935 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 6.6520297483195870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.20999999999999608 " "
y[1] (closed_form) = 1.8105842459701904 " "
y[1] (numeric) = 1.8105842459702024 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 6.622397545233640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.19999999999999607 " "
y[1] (closed_form) = 1.818730753077985 " "
y[1] (numeric) = 1.818730753077997 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 6.5927343262103830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.18999999999999606 " "
y[1] (closed_form) = 1.8269591339433657 " "
y[1] (numeric) = 1.8269591339433775 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 6.4415037218842740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.17999999999999605 " "
y[1] (closed_form) = 1.8352702114112753 " "
y[1] (numeric) = 1.8352702114112873 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 6.5333205930103210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.16999999999999604 " "
y[1] (closed_form) = 1.843664816596387 " "
y[1] (numeric) = 1.8436648165963994 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 6.74444604239790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.15999999999999603 " "
y[1] (closed_form) = 1.8521437889662147 " "
y[1] (numeric) = 1.8521437889662273 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 6.8334556723542030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.14999999999999603 " "
y[1] (closed_form) = 1.8607079764250614 " "
y[1] (numeric) = 1.8607079764250742 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 6.9213370656878530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.13999999999999602 " "
y[1] (closed_form) = 1.8693582353988094 " "
y[1] (numeric) = 1.8693582353988225 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 7.0080904999902040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.129999999999996 " "
y[1] (closed_form) = 1.8780954309205649 " "
y[1] (numeric) = 1.8780954309205784 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 7.2119449722466160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.119999999999996 " "
y[1] (closed_form) = 1.886920436717161 " "
y[1] (numeric) = 1.8869204367171748 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 7.2958908269090430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.10999999999999599 " "
y[1] (closed_form) = 1.895834135296532 " "
y[1] (numeric) = 1.895834135296546 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 7.3787099039067300000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -9.99999999999959800E-2 " "
y[1] (closed_form) = 1.9048374180359633 " "
y[1] (numeric) = 1.9048374180359777 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.5769717580456220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -8.99999999999959700E-2 " "
y[1] (closed_form) = 1.913931185271232 " "
y[1] (numeric) = 1.9139311852712462 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.4249559360140320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -7.99999999999959600E-2 " "
y[1] (closed_form) = 1.9231163463866396 " "
y[1] (numeric) = 1.923116346386654 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.5049537940047870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -6.99999999999959500E-2 " "
y[1] (closed_form) = 1.932393819905952 " "
y[1] (numeric) = 1.932393819905967 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.6987353078479370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -5.999999999999595000E-2 " "
y[1] (closed_form) = 1.9417645335842524 " "
y[1] (numeric) = 1.9417645335842677 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 7.8902861159722500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.99999999999959370E-2 " "
y[1] (closed_form) = 1.9512294245007178 " "
y[1] (numeric) = 1.951229424500733 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.7382151710661510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.99999999999959300E-2 " "
y[1] (closed_form) = 1.960789439152327 " "
y[1] (numeric) = 1.9607894391523426 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 7.9269716749758050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.99999999999959200E-2 " "
y[1] (closed_form) = 1.9704455335485123 " "
y[1] (numeric) = 1.9704455335485276 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 7.7754383356315980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.99999999999959100E-2 " "
y[1] (closed_form) = 1.9801986733067594 " "
y[1] (numeric) = 1.9801986733067751 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 7.9614066821642530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -9.999999999995901000E-3 " "
y[1] (closed_form) = 1.990049833749172 " "
y[1] (numeric) = 1.9900498337491883 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 8.1451508824729850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.100886297209172000000000000000E-15 " "
y[1] (closed_form) = 2.000000000000004 " "
y[1] (numeric) = 2.000000000000021 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 8.4376949871511730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000000000000410300E-2 " "
y[1] (closed_form) = 2.010050167084172 " "
y[1] (numeric) = 2.0100501670841897 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 8.837375646086870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.00000000000041120E-2 " "
y[1] (closed_form) = 2.0202013400267598 " "
y[1] (numeric) = 2.020201340026778 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 9.0127935483952250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.00000000000041230E-2 " "
y[1] (closed_form) = 2.030454533953521 " "
y[1] (numeric) = 2.030454533953539 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 8.7485674251542380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000041300E-2 " "
y[1] (closed_form) = 2.0408107741923924 " "
y[1] (numeric) = 2.040810774192411 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 9.1393808037316260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000041400E-2 " "
y[1] (closed_form) = 2.0512710963760283 " "
y[1] (numeric) = 2.0512710963760465 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 8.8762804858021720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.00000000000041500E-2 " "
y[1] (closed_form) = 2.061836546545364 " "
y[1] (numeric) = 2.0618365465453823 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 8.830795842842030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000041600E-2 " "
y[1] (closed_form) = 2.072508181254221 " "
y[1] (numeric) = 2.0725081812542387 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 8.5710486234377690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000041700E-2 " "
y[1] (closed_form) = 2.083287067674963 " "
y[1] (numeric) = 2.0832870676749806 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 8.5267021859965760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000041800E-2 " "
y[1] (closed_form) = 2.0941742837052146 " "
y[1] (numeric) = 2.094174283705232 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 8.2703141371353070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000418 " "
y[1] (closed_form) = 2.105170918075652 " "
y[1] (numeric) = 2.1051709180756695 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 8.2271130744976610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000419 " "
y[1] (closed_form) = 2.116278070458876 " "
y[1] (numeric) = 2.1162780704588937 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 8.3937780398351910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1200000000000042 " "
y[1] (closed_form) = 2.12749685157938 " "
y[1] (numeric) = 2.127496851579399 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 8.7669914998258250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1300000000000042 " "
y[1] (closed_form) = 2.1388283833246264 " "
y[1] (numeric) = 2.1388283833246455 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 8.9281758987459490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1400000000000042 " "
y[1] (closed_form) = 2.1502737988572322 " "
y[1] (numeric) = 2.150273798857252 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 9.0871800808749530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1500000000000042 " "
y[1] (closed_form) = 2.161834242728288 " "
y[1] (numeric) = 2.1618342427283075 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 9.0385862371866630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000422 " "
y[1] (closed_form) = 2.173510870991815 " "
y[1] (numeric) = 2.1735108709918354 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 9.3986664275486880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000423 " "
y[1] (closed_form) = 2.1853048513203706 " "
y[1] (numeric) = 2.18530485132039 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 8.9415100239203000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000424 " "
y[1] (closed_form) = 2.1972173631218155 " "
y[1] (numeric) = 2.1972173631218355 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 9.0951467882355740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000425 " "
y[1] (closed_form) = 2.209249597657257 " "
y[1] (numeric) = 2.2092495976572772 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 9.2466254943603250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000426 " "
y[1] (closed_form) = 2.221402758160175 " "
y[1] (numeric) = 2.2214027581601963 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 9.5958654928733940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000427 " "
y[1] (closed_form) = 2.2336780599567483 " "
y[1] (numeric) = 2.23367805995677 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 9.741946107969750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000428 " "
y[1] (closed_form) = 2.246076730587386 " "
y[1] (numeric) = 2.2460767305874074 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 9.4904514091236970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000428 " "
y[1] (closed_form) = 2.2586000099294834 " "
y[1] (numeric) = 2.2586000099295043 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 9.241208169305110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2400000000000043 " "
y[1] (closed_form) = 2.27124915032141 " "
y[1] (numeric) = 2.271249150321431 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 9.189741627420871000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000043 " "
y[1] (closed_form) = 2.284025416687747 " "
y[1] (numeric) = 2.2840254166877676 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 8.9439038216690910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000043 " "
y[1] (closed_form) = 2.2969300866657774 " "
y[1] (numeric) = 2.296930086665798 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 8.8936549578469350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000043 " "
y[1] (closed_form) = 2.3099644507332533 " "
y[1] (numeric) = 2.3099644507332737 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 8.8434710095293360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000043 " "
y[1] (closed_form) = 2.3231298123374424 " "
y[1] (numeric) = 2.323129812337464 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 9.3668339871023530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000043 " "
y[1] (closed_form) = 2.336427488025478 " "
y[1] (numeric) = 2.3364274880254996 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 9.3135230578214210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3000000000000043 " "
y[1] (closed_form) = 2.349858807576009 " "
y[1] (numeric) = 2.349858807576031 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 9.449274322744560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3100000000000043 " "
y[1] (closed_form) = 2.3634251141321836 " "
y[1] (numeric) = 2.363425114132206 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 9.3950345029892330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32000000000000434 " "
y[1] (closed_form) = 2.377127764335963 " "
y[1] (numeric) = 2.377127764335986 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 9.5276955837836230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.33000000000000435 " "
y[1] (closed_form) = 2.3909681284637863 " "
y[1] (numeric) = 2.3909681284638094 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 9.6582796890063270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.34000000000000435 " "
y[1] (closed_form) = 2.4049475905635997 " "
y[1] (numeric) = 2.404947590563623 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 9.6021381101246750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.35000000000000436 " "
y[1] (closed_form) = 2.4190675485932633 " "
y[1] (numeric) = 2.4190675485932864 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 9.5460909827144310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.36000000000000437 " "
y[1] (closed_form) = 2.4333294145603466 " "
y[1] (numeric) = 2.43332941456037 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 9.6726435727182170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000044 " "
y[1] (closed_form) = 2.4477346146633305 " "
y[1] (numeric) = 2.447734614663355 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 9.97857627025180100000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000044 " "
y[1] (closed_form) = 2.4622845894342307 " "
y[1] (numeric) = 2.4622845894342555 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.0099968077742694000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3900000000000044 " "
y[1] (closed_form) = 2.476980793882649 " "
y[1] (numeric) = 2.476980793882674 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 1.0040043836036992000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4000000000000044 " "
y[1] (closed_form) = 2.4918246976412766 " "
y[1] (numeric) = 2.4918246976413014 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 9.9802348757294680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4100000000000044 " "
y[1] (closed_form) = 2.50681778511286 " "
y[1] (numeric) = 2.506817785112885 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 1.009769641486485000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4200000000000044 " "
y[1] (closed_form) = 2.5219615556186405 " "
y[1] (numeric) = 2.521961555618666 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 1.0037062184813612000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000443 " "
y[1] (closed_form) = 2.537257523548288 " "
y[1] (numeric) = 2.5372575235483144 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 1.0326607818867324000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.44000000000000444 " "
y[1] (closed_form) = 2.552707218511343 " "
y[1] (numeric) = 2.5527072185113693 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 1.0264108312598978000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.45000000000000445 " "
y[1] (closed_form) = 2.568312185490176 " "
y[1] (numeric) = 2.568312185490203 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 1.0547565811468382000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.46000000000000446 " "
y[1] (closed_form) = 2.5840739849944887 " "
y[1] (numeric) = 2.5840739849945162 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 1.0655086181970368000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.47000000000000447 " "
y[1] (closed_form) = 2.599994193217367 " "
y[1] (numeric) = 2.599994193217395 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.0760647194343535000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000045 " "
y[1] (closed_form) = 2.6160744021929005 " "
y[1] (numeric) = 2.6160744021929285 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.069450478820554900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000045 " "
y[1] (closed_form) = 2.6323162199553862 " "
y[1] (numeric) = 2.632316219955414 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.0628517960136312000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000044 " "
y[1] (closed_form) = 2.6487212707001353 " "
y[1] (numeric) = 2.6487212707001637 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.0730351186741256000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000044 " "
y[1] (closed_form) = 2.665291194945894 " "
y[1] (numeric) = 2.665291194945922 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.0497021966532966000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000045 " "
y[1] (closed_form) = 2.682027649698894 " "
y[1] (numeric) = 2.682027649698922 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.0431518192474613000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000045 " "
y[1] (closed_form) = 2.6989323086185584 " "
y[1] (numeric) = 2.698932308618586 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 1.0201638226635203000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000045 " "
y[1] (closed_form) = 2.716006862184866 " "
y[1] (numeric) = 2.716006862184895 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.0791536743955822000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000045 " "
y[1] (closed_form) = 2.733253017867403 " "
y[1] (numeric) = 2.7332530178674324 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.0723444795818031000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000045 " "
y[1] (closed_form) = 2.750672500296109 " "
y[1] (numeric) = 2.7506725002961385 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.065553527253751000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000045 " "
y[1] (closed_form) = 2.7682670514337433 " "
y[1] (numeric) = 2.768267051433773 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.0748232199832015000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000045 " "
y[1] (closed_form) = 2.7860384307500814 " "
y[1] (numeric) = 2.786038430750112 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 1.0998468341804093000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000045 " "
y[1] (closed_form) = 2.803988415397865 " "
y[1] (numeric) = 2.803988415397896 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 1.108643834574954000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000045 " "
y[1] (closed_form) = 2.822118800390517 " "
y[1] (numeric) = 2.8221188003905486 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 1.117257497983124000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000045 " "
y[1] (closed_form) = 2.8404313987816456 " "
y[1] (numeric) = 2.8404313987816785 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 1.1569581135809329000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000045 " "
y[1] (closed_form) = 2.8589280418463505 " "
y[1] (numeric) = 2.858928041846384 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.1650062628804254000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000046 " "
y[1] (closed_form) = 2.877610579264352 " "
y[1] (numeric) = 2.877610579264385 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.1574426011204547000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000046 " "
y[1] (closed_form) = 2.89648087930496 " "
y[1] (numeric) = 2.8964808793049945 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.1958980504859006000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000046 " "
y[1] (closed_form) = 2.9155408290139047 " "
y[1] (numeric) = 2.9155408290139397 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.203311825683496000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000046 " "
y[1] (closed_form) = 2.93479233440204 " "
y[1] (numeric) = 2.9347923344020757 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.2105502788579287000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000046 " "
y[1] (closed_form) = 2.9542373206359485 " "
y[1] (numeric) = 2.954237320635984 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.2025823565304228000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000046 " "
y[1] (closed_form) = 2.9738777322304566 " "
y[1] (numeric) = 2.9738777322304926 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.2095731310001123000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000046 " "
y[1] (closed_form) = 2.9937155332430914 " "
y[1] (numeric) = 2.9937155332431273 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.2015579168568313000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000046 " "
y[1] (closed_form) = 3.013752707470486 " "
y[1] (numeric) = 3.013752707470522 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.1935692636190635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000046 " "
y[1] (closed_form) = 3.03399125864676 " "
y[1] (numeric) = 3.033991258646796 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.185607436914606900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000046 " "
y[1] (closed_form) = 3.0544332106438974 " "
y[1] (numeric) = 3.0544332106439334 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.177672697916746000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000046 " "
y[1] (closed_form) = 3.075080607674132 " "
y[1] (numeric) = 3.075080607674169 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.1986483972345092000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000047 " "
y[1] (closed_form) = 3.095935514494374 " "
y[1] (numeric) = 3.095935514494411 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.1905740363450383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000047 " "
y[1] (closed_form) = 3.1170000166126846 " "
y[1] (numeric) = 3.1170000166127214 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.1825282072860288000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000047 " "
y[1] (closed_form) = 3.1382762204968286 " "
y[1] (numeric) = 3.1382762204968655 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.1745111592414222000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000047 " "
y[1] (closed_form) = 3.159766253784925 " "
y[1] (numeric) = 3.1597662537849622 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 1.1805776323714225000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000047 " "
y[1] (closed_form) = 3.1814722654982113 " "
y[1] (numeric) = 3.1814722654982486 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 1.1725229866671057000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000047 " "
y[1] (closed_form) = 3.203396426255947 " "
y[1] (numeric) = 3.203396426255985 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.1783612708019965000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000047 " "
y[1] (closed_form) = 3.225540928492478 " "
y[1] (numeric) = 3.225540928492516 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.1702713955298476000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000047 " "
y[1] (closed_form) = 3.247907986676482 " "
y[1] (numeric) = 3.2479079866765206 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 1.1895583685081744000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000047 " "
y[1] (closed_form) = 3.2704998375324164 " "
y[1] (numeric) = 3.2704998375324554 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.1949198106761308000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000047 " "
y[1] (closed_form) = 3.2933187402641937 " "
y[1] (numeric) = 3.293318740264233 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.200124943675658900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000047 " "
y[1] (closed_form) = 3.3163669767811026 " "
y[1] (numeric) = 3.3163669767811426 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 1.2051750957096728000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000048 " "
y[1] (closed_form) = 3.339646851926002 " "
y[1] (numeric) = 3.3396468519260427 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.2233690901372894000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000048 " "
y[1] (closed_form) = 3.3631606937058063 " "
y[1] (numeric) = 3.3631606937058476 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 1.2280203141452561000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000048 " "
y[1] (closed_form) = 3.386910853524288 " "
y[1] (numeric) = 3.38691085352433 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 1.245632871968161000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000048 " "
y[1] (closed_form) = 3.4108997064172213 " "
y[1] (numeric) = 3.410899706417264 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.2498920465294734000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000048 " "
y[1] (closed_form) = 3.4351296512898863 " "
y[1] (numeric) = 3.4351296512899294 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 1.2540037124735845000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000048 " "
y[1] (closed_form) = 3.4596031111569614 " "
y[1] (numeric) = 3.4596031111570054 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.2708056491616887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000048 " "
y[1] (closed_form) = 3.4843225333848284 " "
y[1] (numeric) = 3.484322533384873 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.2745353095043538000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000048 " "
y[1] (closed_form) = 3.50929038993631 " "
y[1] (numeric) = 3.5092903899363543 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.2654672611978468000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000048 " "
y[1] (closed_form) = 3.534509177617867 " "
y[1] (numeric) = 3.534509177617912 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.2690025104160474000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000048 " "
y[1] (closed_form) = 3.5599814183292837 " "
y[1] (numeric) = 3.5599814183293295 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.2848715552010664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000048 " "
y[1] (closed_form) = 3.585709659315859 " "
y[1] (numeric) = 3.585709659315904 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 1.263267350356217000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000048 " "
y[1] (closed_form) = 3.6116964734231303 " "
y[1] (numeric) = 3.611696473423176 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.2664737735063158000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000049 " "
y[1] (closed_form) = 3.6379444593541654 " "
y[1] (numeric) = 3.637944459354212 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.2817503828119070000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000049 " "
y[1] (closed_form) = 3.66445624192943 " "
y[1] (numeric) = 3.6644562419294773 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.284595943744201000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000049 " "
y[1] (closed_form) = 3.6912344723492754 " "
y[1] (numeric) = 3.6912344723493233 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 1.2993386094295364000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000049 " "
y[1] (closed_form) = 3.7182818284590584 " "
y[1] (numeric) = 3.7182818284591073 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.313773816433688200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0100000000000038 " "
y[1] (closed_form) = 3.745601015016927 " "
y[1] (numeric) = 3.745601015016979 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.3871855903537156000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0200000000000027 " "
y[1] (closed_form) = 3.7731947639643053 " "
y[1] (numeric) = 3.773194763964361 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 1.4711976111441188000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0300000000000016 " "
y[1] (closed_form) = 3.8010658346990835 " "
y[1] (numeric) = 3.8010658346991426 " "
absolute error = 5.90638649100583300000000000000E-14 " "
relative error = 1.5538763988478563000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0400000000000005 " "
y[1] (closed_form) = 3.8292170143515607 " "
y[1] (numeric) = 3.8292170143516238 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.6468293011956020000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999994 " "
y[1] (closed_form) = 3.857651118063162 " "
y[1] (numeric) = 3.857651118063229 " "
absolute error = 6.70574706873594600000000000000E-14 " "
relative error = 1.7382979599520515000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0599999999999983 " "
y[1] (closed_form) = 3.886370989267953 " "
y[1] (numeric) = 3.886370989268024 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 1.8168668035333466000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0699999999999972 " "
y[1] (closed_form) = 3.9153794999769884 " "
y[1] (numeric) = 3.9153794999770626 " "
absolute error = 7.41628980449604600000000000000E-14 " "
relative error = 1.8941432891855398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.079999999999996 " "
y[1] (closed_form) = 3.944679551065512 " "
y[1] (numeric) = 3.9446795510655908 " "
absolute error = 7.86037901434610800000000000000E-14 " "
relative error = 1.992653373383121200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.089999999999995 " "
y[1] (closed_form) = 3.9742740725630505 " "
y[1] (numeric) = 3.9742740725631327 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 2.0672078050540185000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999939 " "
y[1] (closed_form) = 4.004166023946414 " "
y[1] (numeric) = 4.004166023946501 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 2.1737731305363353000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999928 " "
y[1] (closed_form) = 4.034358394435653 " "
y[1] (numeric) = 4.034358394435745 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 2.267581813140077000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999917 " "
y[1] (closed_form) = 4.064854203292977 " "
y[1] (numeric) = 4.064854203293072 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 2.337970469664682700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999906 " "
y[1] (closed_form) = 4.095656500124682 " "
y[1] (numeric) = 4.095656500124782 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 2.4505024145227708000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999895 " "
y[1] (closed_form) = 4.126768365186123 " "
y[1] (numeric) = 4.126768365186226 " "
absolute error = 1.03028696685214530000000000000E-13 " "
relative error = 2.4965950973739176000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999884 " "
y[1] (closed_form) = 4.158192909689731 " "
y[1] (numeric) = 4.15819290968984 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 2.6058860076191254000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999873 " "
y[1] (closed_form) = 4.189933276116144 " "
y[1] (numeric) = 4.189933276116257 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 2.692134978494802000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999862 " "
y[1] (closed_form) = 4.221992638528455 " "
y[1] (numeric) = 4.221992638528572 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 2.7768772103136474000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.179999999999985 " "
y[1] (closed_form) = 4.254374202889622 " "
y[1] (numeric) = 4.254374202889745 " "
absolute error = 1.2345680033831741000000000000E-13 " "
relative error = 2.9018792059820236000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999984 " "
y[1] (closed_form) = 4.287081207383066 " "
y[1] (numeric) = 4.287081207383193 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 2.9626104072483260000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999829 " "
y[1] (closed_form) = 4.32011692273649 " "
y[1] (numeric) = 4.320116922736624 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 3.0838693798738430000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999818 " "
y[1] (closed_form) = 4.353484652548962 " "
y[1] (numeric) = 4.353484652549099 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 3.1418389531644490000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999807 " "
y[1] (closed_form) = 4.3871877336212695 " "
y[1] (numeric) = 4.387187733621410 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 3.218926959748629000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999796 " "
y[1] (closed_form) = 4.421229536289603 " "
y[1] (numeric) = 4.421229536289749 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 3.294587164842448000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999785 " "
y[1] (closed_form) = 4.455613464762601 " "
y[1] (numeric) = 4.4556134647627506 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 3.34889854538967000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999774 " "
y[1] (closed_form) = 4.490342957461762 " "
y[1] (numeric) = 4.490342957461918 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 3.461455503955134000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999763 " "
y[1] (closed_form) = 4.525421487365298 " "
y[1] (numeric) = 4.52542148736546 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 3.5720092114455090000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999751 " "
y[1] (closed_form) = 4.560852562355432 " "
y[1] (numeric) = 4.560852562355599 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 3.6611037217433917000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.279999999999974 " "
y[1] (closed_form) = 4.596639725569188 " "
y[1] (numeric) = 4.596639725569360 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 3.748534227369495500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999973 " "
y[1] (closed_form) = 4.632786555752710 " "
y[1] (numeric) = 4.632786555752890 " "
absolute error = 1.78523862359725170000000000000E-13 " "
relative error = 3.853487748923920500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999718 " "
y[1] (closed_form) = 4.669296667619141 " "
y[1] (numeric) = 4.669296667619324 " "
absolute error = 1.8296475445822580000000000000E-13 " "
relative error = 3.918464974116089300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999707 " "
y[1] (closed_form) = 4.70617371221009 " "
y[1] (numeric) = 4.706173712210277 " "
absolute error = 1.87405646556726420000000000000E-13 " "
relative error = 3.982123440758372000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999696 " "
y[1] (closed_form) = 4.7434213772607485 " "
y[1] (numeric) = 4.743421377260942 " "
absolute error = 1.9362289549462730000000000000E-13 " "
relative error = 4.081924840639848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999685 " "
y[1] (closed_form) = 4.781043387568662 " "
y[1] (numeric) = 4.781043387568861 " "
absolute error = 1.98951966012828050000000000000E-13 " "
relative error = 4.161266691913509400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999674 " "
y[1] (closed_form) = 4.819043505366212 " "
y[1] (numeric) = 4.819043505366415 " "
absolute error = 2.03392858111328680000000000000E-13 " "
relative error = 4.220606389729455500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999663 " "
y[1] (closed_form) = 4.857425530696844 " "
y[1] (numeric) = 4.8574255306970535 " "
absolute error = 2.09610107049229550000000000000E-13 " "
relative error = 4.315251067146242000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3599999999999652 " "
y[1] (closed_form) = 4.896193301795079 " "
y[1] (numeric) = 4.896193301795295 " "
absolute error = 2.15827355987130430000000000000E-13 " "
relative error = 4.408064442798902400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3699999999999641 " "
y[1] (closed_form) = 4.935350695470332 " "
y[1] (numeric) = 4.935350695470555 " "
absolute error = 2.22932783344731430000000000000E-13 " "
relative error = 4.517060632577525000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.379999999999963 " "
y[1] (closed_form) = 4.974901627494601 " "
y[1] (numeric) = 4.97490162749483 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 4.60612187819348000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.389999999999962 " "
y[1] (closed_form) = 5.014850052994050 " "
y[1] (numeric) = 5.0148500529942845 " "
absolute error = 2.3536728122053320000000000000E-13 " "
relative error = 4.693406158375768000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999608 " "
y[1] (closed_form) = 5.055199966844516 " "
y[1] (numeric) = 5.055199966844758 " "
absolute error = 2.4247270857813420000000000000E-13 " "
relative error = 4.796500834159623000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999597 " "
y[1] (closed_form) = 5.095955404071011 " "
y[1] (numeric) = 5.09595540407126 " "
absolute error = 2.48689957516035070000000000000E-13 " "
relative error = 4.880143914080642000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999586 " "
y[1] (closed_form) = 5.137120440251222 " "
y[1] (numeric) = 5.137120440251476 " "
absolute error = 2.5401902803423580000000000000E-13 " "
relative error = 4.9447746259539416000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999575 " "
y[1] (closed_form) = 5.1786991919230685 " "
y[1] (numeric) = 5.17869919192333 " "
absolute error = 2.6112445539183680000000000000E-13 " "
relative error = 5.0422788757280630000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999564 " "
y[1] (closed_form) = 5.220695816996370 " "
y[1] (numeric) = 5.220695816996637 " "
absolute error = 2.6734170432973770000000000000E-13 " "
relative error = 5.120805994085820000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4499999999999553 " "
y[1] (closed_form) = 5.263114515168627 " "
y[1] (numeric) = 5.263114515168903 " "
absolute error = 2.76223488526738950000000000000E-13 " "
relative error = 5.248289539029514000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4599999999999542 " "
y[1] (closed_form) = 5.305959528345010 " "
y[1] (numeric) = 5.305959528345290 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 5.3063457710307730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4699999999999531 " "
y[1] (closed_form) = 5.349235141062537 " "
y[1] (numeric) = 5.349235141062826 " "
absolute error = 2.8865798640254070000000000000E-13 " "
relative error = 5.396247852084579000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.479999999999952 " "
y[1] (closed_form) = 5.392945680918546 " "
y[1] (numeric) = 5.392945680918841 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 5.4842646534827730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.489999999999951 " "
y[1] (closed_form) = 5.437095519003447 " "
y[1] (numeric) = 5.4370955190037495 " "
absolute error = 3.0286884111774270000000000000E-13 " "
relative error = 5.570416043992085000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999498 " "
y[1] (closed_form) = 5.48168907033784 " "
y[1] (numeric) = 5.481689070338152 " "
absolute error = 3.11750625314743960000000000000E-13 " "
relative error = 5.687127112000363000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999487 " "
y[1] (closed_form) = 5.5267307943140205 " "
y[1] (numeric) = 5.52673079431434 " "
absolute error = 3.1974423109204510000000000000E-13 " "
relative error = 5.785413529115666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999476 " "
y[1] (closed_form) = 5.57222519514192 " "
y[1] (numeric) = 5.572225195142248 " "
absolute error = 3.2773783686934620000000000000E-13 " "
relative error = 5.8816330171846010000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999465 " "
y[1] (closed_form) = 5.618176822299533 " "
y[1] (numeric) = 5.618176822299870 " "
absolute error = 3.35731442646647340000000000000E-13 " "
relative error = 5.975807691101321000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999454 " "
y[1] (closed_form) = 5.664590270987872 " "
y[1] (numeric) = 5.664590270988215 " "
absolute error = 3.43725048423948460000000000000E-13 " "
relative error = 6.067959587198967000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5499999999999443 " "
y[1] (closed_form) = 5.711470182590479 " "
y[1] (numeric) = 5.711470182590832 " "
absolute error = 3.5260683262094970000000000000E-13 " "
relative error = 6.173661445274714000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5599999999999432 " "
y[1] (closed_form) = 5.758821245137584 " "
y[1] (numeric) = 5.758821245137945 " "
absolute error = 3.60600438398250840000000000000E-13 " "
relative error = 6.261705704144246000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999942 " "
y[1] (closed_form) = 5.8066481937749 " "
y[1] (numeric) = 5.80664819377527 " "
absolute error = 3.6948222259525210000000000000E-13 " "
relative error = 6.363089518517081000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.579999999999941 " "
y[1] (closed_form) = 5.854955811237147 " "
y[1] (numeric) = 5.8549558112375255 " "
absolute error = 3.78364006792253350000000000000E-13 " "
relative error = 6.462286292000303000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.58999999999994 " "
y[1] (closed_form) = 5.903748928326327 " "
y[1] (numeric) = 5.903748928326714 " "
absolute error = 3.8724579098925460000000000000E-13 " "
relative error = 6.559320114905973000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999388 " "
y[1] (closed_form) = 5.953032424394812 " "
y[1] (numeric) = 5.953032424395209 " "
absolute error = 3.970157536059560000000000000E-13 " "
relative error = 6.6691347418003820000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999377 " "
y[1] (closed_form) = 6.002811227833276 " "
y[1] (numeric) = 6.002811227833683 " "
absolute error = 4.06785716222657360000000000000E-13 " "
relative error = 6.776586848783637000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999366 " "
y[1] (closed_form) = 6.053090316563547 " "
y[1] (numeric) = 6.0530903165639645 " "
absolute error = 4.17443857259058860000000000000E-13 " "
relative error = 6.896375825035592000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999355 " "
y[1] (closed_form) = 6.103874718536397 " "
y[1] (numeric) = 6.103874718536825 " "
absolute error = 4.28101998295460360000000000000E-13 " "
relative error = 7.0136105021190830000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999344 " "
y[1] (closed_form) = 6.155169512234343 " "
y[1] (numeric) = 6.1551695122347825 " "
absolute error = 4.396483177515620000000000000E-13 " "
relative error = 7.14274914570092000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6499999999999333 " "
y[1] (closed_form) = 6.206979827179501 " "
y[1] (numeric) = 6.206979827179950 " "
absolute error = 4.49418280368263370000000000000E-13 " "
relative error = 7.240530707065024000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6599999999999322 " "
y[1] (closed_form) = 6.259310844446542 " "
y[1] (numeric) = 6.259310844447001 " "
absolute error = 4.5918824298496475000000000000E-13 " "
relative error = 7.336083067233687000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.669999999999931 " "
y[1] (closed_form) = 6.312167797180801 " "
y[1] (numeric) = 6.312167797181273 " "
absolute error = 4.7162274086076650000000000000E-13 " "
relative error = 7.471644544547865000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.67999999999993 " "
y[1] (closed_form) = 6.365555971121599 " "
y[1] (numeric) = 6.365555971122081 " "
absolute error = 4.822808818971680000000000000E-13 " "
relative error = 7.576414127612973000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.689999999999929 " "
y[1] (closed_form) = 6.4194807051308205 " "
y[1] (numeric) = 6.419480705131314 " "
absolute error = 4.9382720135326963000000000000E-13 " "
relative error = 7.692634716676916000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999278 " "
y[1] (closed_form) = 6.473947391726805 " "
y[1] (numeric) = 6.473947391727310 " "
absolute error = 5.0448534238967110000000000000E-13 " "
relative error = 7.792546214298307000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999267 " "
y[1] (closed_form) = 6.528961477623600 " "
y[1] (numeric) = 6.528961477624114 " "
absolute error = 5.1514348342607260000000000000E-13 " "
relative error = 7.890129007371227000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999256 " "
y[1] (closed_form) = 6.584528464275638 " "
y[1] (numeric) = 6.584528464276165 " "
absolute error = 5.2668980288217430000000000000E-13 " "
relative error = 7.998899324981734000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999245 " "
y[1] (closed_form) = 6.640653908427895 " "
y[1] (numeric) = 6.640653908428433 " "
absolute error = 5.3823612233827590000000000000E-13 " "
relative error = 8.105167499471414000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999234 " "
y[1] (closed_form) = 6.697343422671555 " "
y[1] (numeric) = 6.697343422672104 " "
absolute error = 5.4889426337467740000000000000E-13 " "
relative error = 8.195701321162425000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7499999999999223 " "
y[1] (closed_form) = 6.754602676005283 " "
y[1] (numeric) = 6.754602676005844 " "
absolute error = 5.6132876125047910000000000000E-13 " "
relative error = 8.310315027773812000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7599999999999212 " "
y[1] (closed_form) = 6.812437394402130 " "
y[1] (numeric) = 6.8124373944027035 " "
absolute error = 5.7287508070658080000000000000E-13 " "
relative error = 8.4092527760669000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.76999999999992 " "
y[1] (closed_form) = 6.870853361382132 " "
y[1] (numeric) = 6.870853361382718 " "
absolute error = 5.8619775700208270000000000000E-13 " "
relative error = 8.531658677171418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.779999999999919 " "
y[1] (closed_form) = 6.929856418590665 " "
y[1] (numeric) = 6.929856418591263 " "
absolute error = 5.9774407645818430000000000000E-13 " "
relative error = 8.625634361696461000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999179 " "
y[1] (closed_form) = 6.989452466382621 " "
y[1] (numeric) = 6.989452466383230 " "
absolute error = 6.0929039591428590000000000000E-13 " "
relative error = 8.71728363337197000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999168 " "
y[1] (closed_form) = 7.049647464412443 " "
y[1] (numeric) = 7.049647464413064 " "
absolute error = 6.2083671537038750000000000000E-13 " "
relative error = 8.80663492046168000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999157 " "
y[1] (closed_form) = 7.110447432230095 " "
y[1] (numeric) = 7.11044743223073 " "
absolute error = 6.3504757008558950000000000000E-13 " "
relative error = 8.931190000886000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999146 " "
y[1] (closed_form) = 7.171858449883026 " "
y[1] (numeric) = 7.1718584498836755 " "
absolute error = 6.4925842480079150000000000000E-13 " "
relative error = 9.052861672296126000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999135 " "
y[1] (closed_form) = 7.233886658524178 " "
y[1] (numeric) = 7.233886658524843 " "
absolute error = 6.6435745793569370000000000000E-13 " "
relative error = 9.183962775430499000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999124 " "
y[1] (closed_form) = 7.296538261026105 " "
y[1] (numeric) = 7.296538261026782 " "
absolute error = 6.7768013423119560000000000000E-13 " "
relative error = 9.287693834910338000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8499999999999113 " "
y[1] (closed_form) = 7.359819522601267 " "
y[1] (numeric) = 7.359819522601959 " "
absolute error = 6.9189098894639760000000000000E-13 " "
relative error = 9.400923308264146000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8599999999999102 " "
y[1] (closed_form) = 7.423736771428557 " "
y[1] (numeric) = 7.423736771429263 " "
absolute error = 7.0521366524189940000000000000E-13 " "
relative error = 9.499443298636713000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.869999999999909 " "
y[1] (closed_form) = 7.488296399286122 " "
y[1] (numeric) = 7.48829639928684 " "
absolute error = 7.1853634153740130000000000000E-13 " "
relative error = 9.59545807516248000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.879999999999908 " "
y[1] (closed_form) = 7.553504862190546 " "
y[1] (numeric) = 7.553504862191279 " "
absolute error = 7.3274719625260330000000000000E-13 " "
relative error = 9.700757590299661000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999069 " "
y[1] (closed_form) = 7.619368681042461 " "
y[1] (numeric) = 7.619368681043208 " "
absolute error = 7.4695805096780530000000000000E-13 " "
relative error = 9.8034113092111000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999058 " "
y[1] (closed_form) = 7.68589444227864 " "
y[1] (numeric) = 7.685894442279402 " "
absolute error = 7.6205708410270740000000000000E-13 " "
relative error = 9.915008459012613000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999047 " "
y[1] (closed_form) = 7.7530887985306425 " "
y[1] (numeric) = 7.753088798531421 " "
absolute error = 7.7893247407700980000000000000E-13 " "
relative error = 1.004673742708367300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999999036 " "
y[1] (closed_form) = 7.820958469290092 " "
y[1] (numeric) = 7.820958469290885 " "
absolute error = 7.9314332879221180000000000000E-13 " "
relative error = 1.014125483349108300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999999025 " "
y[1] (closed_form) = 7.889510241580620 " "
y[1] (numeric) = 7.889510241581430 " "
absolute error = 8.1001871876651420000000000000E-13 " "
relative error = 1.026703425134576400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999999014 " "
y[1] (closed_form) = 7.9587509706365855 " "
y[1] (numeric) = 7.958750970637410 " "
absolute error = 8.2511775190141630000000000000E-13 " "
relative error = 1.03674276899182700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9499999999999003 " "
y[1] (closed_form) = 8.028687580588592 " "
y[1] (numeric) = 8.028687580589434 " "
absolute error = 8.4199314187571870000000000000E-13 " "
relative error = 1.048730733914036800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9599999999998992 " "
y[1] (closed_form) = 8.099327065155917 " "
y[1] (numeric) = 8.099327065156773 " "
absolute error = 8.5620399659092070000000000000E-13 " "
relative error = 1.057129795726354200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.969999999999898 " "
y[1] (closed_form) = 8.170676488345883 " "
y[1] (numeric) = 8.170676488346757 " "
absolute error = 8.7396756498492320000000000000E-13 " "
relative error = 1.069639173979649300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.979999999999897 " "
y[1] (closed_form) = 8.242742985160266 " "
y[1] (numeric) = 8.242742985161156 " "
absolute error = 8.8995477653952550000000000000E-13 " "
relative error = 1.079682792659853700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998959 " "
y[1] (closed_form) = 8.315533762308805 " "
y[1] (numeric) = 8.315533762309713 " "
absolute error = 9.077183449335280000000000000E-13 " "
relative error = 1.091593601661356700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998948 " "
y[1] (closed_form) = 8.389056098929872 " "
y[1] (numeric) = 8.389056098930798 " "
absolute error = 9.2548191332753050000000000000E-13 " "
relative error = 1.1032014834727200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998936 " "
y[1] (closed_form) = 8.463317347318402 " "
y[1] (numeric) = 8.463317347319341 " "
absolute error = 9.3969276804273250000000000000E-13 " "
relative error = 1.110312575411666200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998925 " "
y[1] (closed_form) = 8.538324933661112 " "
y[1] (numeric) = 8.538324933662068 " "
absolute error = 9.5567997959733470000000000000E-13 " "
relative error = 1.119282748106369800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998914 " "
y[1] (closed_form) = 8.614086358779147 " "
y[1] (numeric) = 8.614086358780124 " "
absolute error = 9.7699626167013780000000000000E-13 " "
relative error = 1.13418442882734800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998903 " "
y[1] (closed_form) = 8.690609198878155 " "
y[1] (numeric) = 8.69060919887915 " "
absolute error = 9.9475983006414030000000000000E-13 " "
relative error = 1.14463762815678200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998892 " "
y[1] (closed_form) = 8.767901106305912 " "
y[1] (numeric) = 8.767901106306923 " "
absolute error = 1.0107470416187425000000000000E-12 " "
relative error = 1.152781069681327600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999888 " "
y[1] (closed_form) = 8.845969810317571 " "
y[1] (numeric) = 8.8459698103186 " "
absolute error = 1.028510610012745000000000000E-12 " "
relative error = 1.162688356468426000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999887 " "
y[1] (closed_form) = 8.924823117848593 " "
y[1] (numeric) = 8.924823117849641 " "
absolute error = 1.0480505352461478000000000000E-12 " "
relative error = 1.174309587324112200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999886 " "
y[1] (closed_form) = 9.00446891429544 " "
y[1] (numeric) = 9.00446891429651 " "
absolute error = 1.0693668173189508000000000000E-12 " "
relative error = 1.187595656664692800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999885 " "
y[1] (closed_form) = 9.08491516430413 " "
y[1] (numeric) = 9.084915164305217 " "
absolute error = 1.0871303857129533000000000000E-12 " "
relative error = 1.19663240223137890000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998837 " "
y[1] (closed_form) = 9.166169912566701 " "
y[1] (numeric) = 9.166169912567808 " "
absolute error = 1.106670310946356000000000000E-12 " "
relative error = 1.207342130358204800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998826 " "
y[1] (closed_form) = 9.248241284625694 " "
y[1] (numeric) = 9.248241284626822 " "
absolute error = 1.127986593019159000000000000E-12 " "
relative error = 1.219676864285891600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998815 " "
y[1] (closed_form) = 9.331137487686705 " "
y[1] (numeric) = 9.331137487687853 " "
absolute error = 1.1475265182525618000000000000E-12 " "
relative error = 1.22978202793263810000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998804 " "
y[1] (closed_form) = 9.414866811439124 " "
y[1] (numeric) = 9.414866811440294 " "
absolute error = 1.170619157164765000000000000E-12 " "
relative error = 1.243373040330698300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998793 " "
y[1] (closed_form) = 9.499437628885097 " "
y[1] (numeric) = 9.49943762888629 " "
absolute error = 1.191935439237568000000000000E-12 " "
relative error = 1.254743160387968800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998782 " "
y[1] (closed_form) = 9.584858397176848 " "
y[1] (numeric) = 9.58485839717806 " "
absolute error = 1.2114753644709708000000000000E-12 " "
relative error = 1.263947065538080500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999877 " "
y[1] (closed_form) = 9.67113765846239 " "
y[1] (numeric) = 9.671137658463623 " "
absolute error = 1.2327916465437738000000000000E-12 " "
relative error = 1.274712128065991000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999876 " "
y[1] (closed_form) = 9.758284040739749 " "
y[1] (numeric) = 9.758284040741001 " "
absolute error = 1.2523315717771766000000000000E-12 " "
relative error = 1.283352243641230000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999875 " "
y[1] (closed_form) = 9.846306258719776 " "
y[1] (numeric) = 9.846306258721054 " "
absolute error = 1.27720056752878000000000000E-12 " "
relative error = 1.297136747496256000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999874 " "
y[1] (closed_form) = 9.935213114697621 " "
y[1] (numeric) = 9.935213114698923 " "
absolute error = 1.3020695632803836000000000000E-12 " "
relative error = 1.310560275102877800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998727 " "
y[1] (closed_form) = 10.025013499432973 " "
y[1] (numeric) = 10.025013499434298 " "
absolute error = 1.3251622021925868000000000000E-12 " "
relative error = 1.321855778316447800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998716 " "
y[1] (closed_form) = 10.115716393039136 " "
y[1] (numeric) = 10.115716393040485 " "
absolute error = 1.3482548411047900000000000000E-12 " "
relative error = 1.332831792350916700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998705 " "
y[1] (closed_form) = 10.207330865881058 " "
y[1] (numeric) = 10.207330865882431 " "
absolute error = 1.3731238368563936000000000000E-12 " "
relative error = 1.345233004493061300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998694 " "
y[1] (closed_form) = 10.29986607948237 " "
y[1] (numeric) = 10.299866079483767 " "
absolute error = 1.3962164757685970000000000000E-12 " "
relative error = 1.355567601553480700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998683 " "
y[1] (closed_form) = 10.393331287441546 " "
y[1] (numeric) = 10.393331287442965 " "
absolute error = 1.4193091146808000000000000000E-12 " "
relative error = 1.36559595323953300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999867 " "
y[1] (closed_form) = 10.487735836357265 " "
y[1] (numeric) = 10.487735836358711 " "
absolute error = 1.4459544672718040000000000000E-12 " "
relative error = 1.378709847228600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999866 " "
y[1] (closed_form) = 10.583089166763095 " "
y[1] (numeric) = 10.583089166764568 " "
absolute error = 1.4725998198628076000000000000E-12 " "
relative error = 1.391465002947917000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999865 " "
y[1] (closed_form) = 10.679400814071535 " "
y[1] (numeric) = 10.679400814073036 " "
absolute error = 1.5010215292932116000000000000E-12 " "
relative error = 1.405529725333855300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999864 " "
y[1] (closed_form) = 10.776680409527575 " "
y[1] (numeric) = 10.776680409529103 " "
absolute error = 1.5276668818842154000000000000E-12 " "
relative error = 1.417567213493329300000000000E-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) = 10.87493768117183 " "
y[1] (numeric) = 10.874937681173382 " "
absolute error = 1.552535877635819000000000000E-12 " "
relative error = 1.427627378797563200000000000E-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) = 10.974182454813342 " "
y[1] (numeric) = 10.974182454814919 " "
absolute error = 1.5774048733874224000000000000E-12 " "
relative error = 1.437378027823442400000000000E-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) = 11.074424655012182 " "
y[1] (numeric) = 11.074424655013788 " "
absolute error = 1.6058265828178264000000000000E-12 " "
relative error = 1.450031611430977800000000000E-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) = 11.175674306071905 " "
y[1] (numeric) = 11.17567430607354 " "
absolute error = 1.6360246490876307000000000000E-12 " "
relative error = 1.463915826715489200000000000E-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) = 11.277941533041993 " "
y[1] (numeric) = 11.277941533043654 " "
absolute error = 1.6608936448392342000000000000E-12 " "
relative error = 1.472692192961956600000000000E-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) = 11.381236562730363 " "
y[1] (numeric) = 11.381236562732052 " "
absolute error = 1.6893153542696382000000000000E-12 " "
relative error = 1.484298604073976400000000000E-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) = 11.485569724726066 " "
y[1] (numeric) = 11.485569724727783 " "
absolute error = 1.7177370637000422000000000000E-12 " "
relative error = 1.495561043003472700000000000E-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) = 11.590951452432247 " "
y[1] (numeric) = 11.59095145243399 " "
absolute error = 1.7426060594516457000000000000E-12 " "
relative error = 1.503419341029141300000000000E-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) = 11.69739228410949 " "
y[1] (numeric) = 11.697392284111265 " "
absolute error = 1.7745804825608502000000000000E-12 " "
relative error = 1.517073583119510600000000000E-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) = 11.80490286392967 " "
y[1] (numeric) = 11.804902863931476 " "
absolute error = 1.8065549056700547000000000000E-12 " "
relative error = 1.530342880829669600000000000E-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) = 11.913493943040356 " "
y[1] (numeric) = 11.913493943042191 " "
absolute error = 1.8349766151004587000000000000E-12 " "
relative error = 1.54025059640242500000000000E-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) = 12.023176380639956 " "
y[1] (numeric) = 12.023176380641821 " "
absolute error = 1.865174681370263000000000000E-12 " "
relative error = 1.55131607681778500000000000E-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) = 12.13396114506363 " "
y[1] (numeric) = 12.133961145065522 " "
absolute error = 1.8918200339612667000000000000E-12 " "
relative error = 1.559111662996301700000000000E-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) = 12.245859314880143 " "
y[1] (numeric) = 12.245859314882065 " "
absolute error = 1.922018100231071000000000000E-12 " "
relative error = 1.569524890666999200000000000E-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) = 12.358882079999724 " "
y[1] (numeric) = 12.358882080001681 " "
absolute error = 1.957545237019076000000000000E-12 " "
relative error = 1.583917723583555500000000000E-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) = 12.47304074279307 " "
y[1] (numeric) = 12.473040742795062 " "
absolute error = 1.9912960169676808000000000000E-12 " "
relative error = 1.596480006784434200000000000E-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) = 12.588346719221596 " "
y[1] (numeric) = 12.58834671922362 " "
absolute error = 2.0250467969162855000000000000E-12 " "
relative error = 1.608667795767151400000000000E-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) = 12.70481153997903 " "
y[1] (numeric) = 12.704811539981085 " "
absolute error = 2.0552448631860898000000000000E-12 " "
relative error = 1.617690161494109200000000000E-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) = 12.822446851644505 " "
y[1] (numeric) = 12.822446851646593 " "
absolute error = 2.0872192862952943000000000000E-12 " "
relative error = 1.627785484661692400000000000E-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) = 12.941264417847215 " "
y[1] (numeric) = 12.94126441784934 " "
absolute error = 2.1245227799226996000000000000E-12 " "
relative error = 1.641665536941493700000000000E-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) = 13.061276120442797 " "
y[1] (numeric) = 13.061276120444957 " "
absolute error = 2.1600499167107046000000000000E-12 " "
relative error = 1.653781680129947400000000000E-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) = 13.182493960701521 " "
y[1] (numeric) = 13.182493960703713 " "
absolute error = 2.192024339819909000000000000E-12 " "
relative error = 1.662829769810308700000000000E-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) = 13.304930060508426 " "
y[1] (numeric) = 13.304930060510657 " "
absolute error = 2.2311041902867146000000000000E-12 " "
relative error = 1.676900352080059300000000000E-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) = 13.428596663575524 " "
y[1] (numeric) = 13.42859666357779 " "
absolute error = 2.2666313270747196000000000000E-12 " "
relative error = 1.687913773762270400000000000E-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) = 13.553506136666178 " "
y[1] (numeric) = 13.553506136668481 " "
absolute error = 2.303934820702124900000000000E-12 " "
relative error = 1.699881047361841700000000000E-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) = 13.679670970831788 " "
y[1] (numeric) = 13.67967097083413 " "
absolute error = 2.34123831432953000000000000E-12 " "
relative error = 1.71147268038945500000000000E-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) = 13.807103782660908 " "
y[1] (numeric) = 13.80710378266329 " "
absolute error = 2.382094521635736000000000000E-12 " "
relative error = 1.72526734001028720000000000E-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) = 13.935817315540916 " "
y[1] (numeric) = 13.935817315543337 " "
absolute error = 2.4211743721025414000000000000E-12 " "
relative error = 1.737375223340866500000000000E-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) = 14.065824440932364 " "
y[1] (numeric) = 14.065824440934827 " "
absolute error = 2.4638069362481474000000000000E-12 " "
relative error = 1.751626395306290500000000000E-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) = 14.197138159656125 " "
y[1] (numeric) = 14.197138159658628 " "
absolute error = 2.502886786714953000000000000E-12 " "
relative error = 1.76295163051056500000000000E-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) = 14.329771603193505 " "
y[1] (numeric) = 14.329771603196049 " "
absolute error = 2.5437429940211587000000000000E-12 " "
relative error = 1.77514552531616400000000000E-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) = 14.463738034999384 " "
y[1] (numeric) = 14.463738035001969 " "
absolute error = 2.5845992013273644000000000000E-12 " "
relative error = 1.78695106000478280000000000E-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) = 14.599050851828581 " "
y[1] (numeric) = 14.599050851831208 " "
absolute error = 2.6272317654729704000000000000E-12 " "
relative error = 1.799590803633581000000000000E-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) = 14.735723585075542 " "
y[1] (numeric) = 14.735723585078208 " "
absolute error = 2.666311615939776000000000000E-12 " "
relative error = 1.809420216486849500000000000E-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) = 14.873769902127483 " "
y[1] (numeric) = 14.87376990213019 " "
absolute error = 2.7071678232459817000000000000E-12 " "
relative error = 1.820095269094326700000000000E-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) = 15.01320360773115 " "
y[1] (numeric) = 15.0132036077339 " "
absolute error = 2.7498003873915877000000000000E-12 " "
relative error = 1.8315880202780702000000000E-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) = 15.1540386453733 " "
y[1] (numeric) = 15.154038645376092 " "
absolute error = 2.7924329515371940000000000000E-12 " "
relative error = 1.84269884542610400000000000E-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) = 15.296289098675057 " "
y[1] (numeric) = 15.296289098677894 " "
absolute error = 2.8368418725222000000000000E-12 " "
relative error = 1.85459483291795480000000000E-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) = 15.439969192800296 " "
y[1] (numeric) = 15.439969192803176 " "
absolute error = 2.879474436667806000000000000E-12 " "
relative error = 1.864948304437364600000000000E-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) = 15.585093295878162 " "
y[1] (numeric) = 15.585093295881085 " "
absolute error = 2.9238833576528120000000000000E-12 " "
relative error = 1.87607690383611700000000000E-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) = 15.731675920439901 " "
y[1] (numeric) = 15.73167592044287 " "
absolute error = 2.9682922786378185000000000000E-12 " "
relative error = 1.886825214077265700000000000E-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) = 15.87973172487012 " "
y[1] (numeric) = 15.879731724873137 " "
absolute error = 3.0162539133016253000000000000E-12 " "
relative error = 1.899436316406847600000000000E-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) = 16.029275514872644 " "
y[1] (numeric) = 16.02927551487571 " "
absolute error = 3.0659919048048323000000000000E-12 " "
relative error = 1.91274515305453090000000000E-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) = 16.180322244951093 " "
y[1] (numeric) = 16.18032224495421 " "
absolute error = 3.1157298963080393000000000000E-12 " "
relative error = 1.925629075329616200000000000E-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) = 16.332887019904348 " "
y[1] (numeric) = 16.33288701990751 " "
absolute error = 3.161915174132446000000000000E-12 " "
relative error = 1.935919332742046500000000000E-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) = 16.486985096337044 " "
y[1] (numeric) = 16.48698509634025 " "
absolute error = 3.204547738278052000000000000E-12 " "
relative error = 1.943683286879427000000000000E-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) = 16.642631884185235 " "
y[1] (numeric) = 16.642631884188486 " "
absolute error = 3.2507330161024584000000000000E-12 " "
relative error = 1.953256575476795500000000000E-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) = 16.799842948257414 " "
y[1] (numeric) = 16.799842948260714 " "
absolute error = 3.3004710076056654000000000000E-12 " "
relative error = 1.96458444151587220000000000E-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) = 16.958634009790998 " "
y[1] (numeric) = 16.95863400979435 " "
absolute error = 3.3502089991088724000000000000E-12 " "
relative error = 1.97551819160354700000000000E-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) = 17.119020948024463 " "
y[1] (numeric) = 17.119020948027867 " "
absolute error = 3.40349970429088000000000000E-12 " "
relative error = 1.988139225148646300000000000E-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) = 17.2810198017853 " "
y[1] (numeric) = 17.281019801788748 " "
absolute error = 3.4496849821152864000000000000E-12 " "
relative error = 1.996227665776356700000000000E-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) = 17.444646771093872 " "
y[1] (numeric) = 17.444646771097368 " "
absolute error = 3.495870259939693000000000000E-12 " "
relative error = 2.00397881700443480000000000E-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) = 17.60991821878347 " "
y[1] (numeric) = 17.609918218787016 " "
absolute error = 3.5456082514429000000000000E-12 " "
relative error = 2.013415512436058400000000000E-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) = 17.776850672136593 " "
y[1] (numeric) = 17.776850672140192 " "
absolute error = 3.5988989566249074000000000000E-12 " "
relative error = 2.02448623943599600000000000E-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) = 17.945460824537683 " "
y[1] (numeric) = 17.945460824541343 " "
absolute error = 3.659295089164516000000000000E-12 " "
relative error = 2.03912015687052580000000000E-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) = 18.115765537142494 " "
y[1] (numeric) = 18.11576553714621 " "
absolute error = 3.716138508025324000000000000E-12 " "
relative error = 2.05132844118907280000000000E-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) = 18.2877818405642 " "
y[1] (numeric) = 18.287781840567973 " "
absolute error = 3.772981926886132000000000000E-12 " "
relative error = 2.063116215941107600000000000E-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) = 18.461526936576497 " "
y[1] (numeric) = 18.461526936580334 " "
absolute error = 3.836930773104541000000000000E-12 " "
relative error = 2.078338799540305500000000000E-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) = 18.637018199833776 " "
y[1] (numeric) = 18.63701819983767 " "
absolute error = 3.893774191965349000000000000E-12 " "
relative error = 2.089268868128313600000000000E-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) = 18.8142731796086 " "
y[1] (numeric) = 18.814273179612556 " "
absolute error = 3.957723038183758000000000000E-12 " "
relative error = 2.103574770283043500000000000E-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) = 18.993309601546656 " "
y[1] (numeric) = 18.99330960155068 " "
absolute error = 4.0252245980809676000000000000E-12 " "
relative error = 2.11928551817698320000000000E-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) = 19.174145369439348 " "
y[1] (numeric) = 19.174145369443433 " "
absolute error = 4.085620730620576000000000000E-12 " "
relative error = 2.130796784889526200000000000E-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) = 19.356798567014152 " "
y[1] (numeric) = 19.356798567018295 " "
absolute error = 4.142464149481384000000000000E-12 " "
relative error = 2.140056443290442600000000000E-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) = 19.54128745974304 " "
y[1] (numeric) = 19.541287459747245 " "
absolute error = 4.206412995699793000000000000E-12 " "
relative error = 2.152577205757509300000000000E-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) = 19.727630496669025 " "
y[1] (numeric) = 19.727630496673296 " "
absolute error = 4.270361841918202000000000000E-12 " "
relative error = 2.164660293408904600000000000E-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) = 19.91584631225109 " "
y[1] (numeric) = 19.91584631225542 " "
absolute error = 4.330757974457810600000000000E-12 " "
relative error = 2.174528717764695500000000000E-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) = 20.105953728227636 " "
y[1] (numeric) = 20.10595372823203 " "
absolute error = 4.39470682067621960000000000E-12 " "
relative error = 2.18577386583074500000000000E-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) = 20.297971755498686 " "
y[1] (numeric) = 20.297971755503145 " "
absolute error = 4.458655666894628700000000000E-12 " "
relative error = 2.196601572118547500000000000E-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) = 20.491919596026985 " "
y[1] (numeric) = 20.491919596031508 " "
absolute error = 4.522604513113037700000000000E-12 " "
relative error = 2.207018474730834700000000000E-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) = 20.687816644758204 " "
y[1] (numeric) = 20.68781664476279 " "
absolute error = 4.586553359331446700000000000E-12 " "
relative error = 2.21703113387442400000000000E-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) = 20.885682491560466 " "
y[1] (numeric) = 20.885682491565127 " "
absolute error = 4.661160346586257000000000000E-12 " "
relative error = 2.23174911735335900000000000E-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) = 21.08553692318334 " "
y[1] (numeric) = 21.085536923188076 " "
absolute error = 4.735767333841068000000000000E-12 " "
relative error = 2.245979009732561600000000000E-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) = 21.28739992523654 " "
y[1] (numeric) = 21.28739992524135 " "
absolute error = 4.810374321095878000000000000E-12 " "
relative error = 2.259728448749208400000000000E-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) = 21.491291684188482 " "
y[1] (numeric) = 21.491291684193364 " "
absolute error = 4.881428594671888000000000000E-12 " "
relative error = 2.271351888199088500000000000E-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) = 21.697232589384978 " "
y[1] (numeric) = 21.697232589389927 " "
absolute error = 4.948930154569098000000000000E-12 " "
relative error = 2.280903859135603500000000000E-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) = 21.90524323508816 " "
y[1] (numeric) = 21.905243235093188 " "
absolute error = 5.027089855502709000000000000E-12 " "
relative error = 2.294925375423468600000000000E-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) = 22.115344422535948 " "
y[1] (numeric) = 22.11534442254105 " "
absolute error = 5.101696842757519000000000000E-12 " "
relative error = 2.30685841707208300000000000E-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) = 22.327557162022167 " "
y[1] (numeric) = 22.32755716202734 " "
absolute error = 5.172751116333529000000000000E-12 " "
relative error = 2.31675640948848100000000000E-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) = 22.541902674997612 " "
y[1] (numeric) = 22.541902675002863 " "
absolute error = 5.25091081726714000000000000E-12 " "
relative error = 2.32940000361690700000000000E-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) = 22.7584023961922 " "
y[1] (numeric) = 22.758402396197535 " "
absolute error = 5.336175945558352000000000000E-12 " "
relative error = 2.344705859692141300000000000E-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) = 22.97707797575847 " "
y[1] (numeric) = 22.977077975763883 " "
absolute error = 5.4143356464919630000000000000E-12 " "
relative error = 2.356407395319916300000000000E-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) = 23.19795128143661 " "
y[1] (numeric) = 23.197951281442105 " "
absolute error = 5.496048061104375000000000000E-12 " "
relative error = 2.369195449385396400000000000E-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) = 23.421044400741245 " "
y[1] (numeric) = 23.42104440074682 " "
absolute error = 5.574207762037986000000000000E-12 " "
relative error = 2.379999656147515400000000000E-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) = 23.646379643170217 " "
y[1] (numeric) = 23.646379643175873 " "
absolute error = 5.6559201766503970000000000000E-12 " "
relative error = 2.39187573827353200000000000E-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) = 23.873979542435556 " "
y[1] (numeric) = 23.873979542441294 " "
absolute error = 5.737632591262809000000000000E-12 " "
relative error = 2.403299617922631500000000000E-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) = 24.10386685871685 " "
y[1] (numeric) = 24.10386685872267 " "
absolute error = 5.822897719554021000000000000E-12 " "
relative error = 2.415752523727638400000000000E-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) = 24.3360645809373 " "
y[1] (numeric) = 24.336064580943212 " "
absolute error = 5.9117155615240340000000000000E-12 " "
relative error = 2.429199487806563400000000000E-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) = 24.570595929062634 " "
y[1] (numeric) = 24.570595929068627 " "
absolute error = 5.993427976136445000000000000E-12 " "
relative error = 2.439268462775576500000000000E-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) = 24.807484356423096 " "
y[1] (numeric) = 24.80748435642918 " "
absolute error = 6.0822458181064580000000000000E-12 " "
relative error = 2.45177855630962300000000000E-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) = 25.04675355205884 " "
y[1] (numeric) = 25.04675355206501 " "
absolute error = 6.17106366007647000000000000E-12 " "
relative error = 2.46381777472682080000000000E-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) = 25.288427443088818 " "
y[1] (numeric) = 25.288427443095074 " "
absolute error = 6.256328788367682000000000000E-12 " "
relative error = 2.473988864055483600000000000E-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) = 25.532530197103526 " "
y[1] (numeric) = 25.532530197109875 " "
absolute error = 6.348699344016495000000000000E-12 " "
relative error = 2.48651398627806500000000000E-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) = 25.779086224581786 " "
y[1] (numeric) = 25.779086224588227 " "
absolute error = 6.441069899665308000000000000E-12 " "
relative error = 2.498564085457533300000000000E-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) = 26.02812018133181 " "
y[1] (numeric) = 26.028120181338345 " "
absolute error = 6.533440455314121000000000000E-12 " "
relative error = 2.510146875685671000000000000E-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) = 26.279656970956808 " "
y[1] (numeric) = 26.279656970963433 " "
absolute error = 6.625811010962934000000000000E-12 " "
relative error = 2.521269976349199000000000000E-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) = 26.53372174734535 " "
y[1] (numeric) = 26.533721747352065 " "
absolute error = 6.714628852932947000000000000E-12 " "
relative error = 2.53060197015321900000000000E-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) = 26.7903399171868 " "
y[1] (numeric) = 26.79033991719361 " "
absolute error = 6.81055212226056000000000000E-12 " "
relative error = 2.542167118190012000000000000E-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) = 27.049537142511983 " "
y[1] (numeric) = 27.0495371425189 " "
absolute error = 6.917133532624575000000000000E-12 " "
relative error = 2.557209573007210300000000000E-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) = 27.311339343259444 " "
y[1] (numeric) = 27.311339343266464 " "
absolute error = 7.02016222930979000000000000E-12 " "
relative error = 2.57042034485298700000000000E-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) = 27.575772699867414 " "
y[1] (numeric) = 27.57577269987454 " "
absolute error = 7.126743639673805000000000000E-12 " "
relative error = 2.58442210024021230000000000E-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) = 27.842863655891925 " "
y[1] (numeric) = 27.842863655899155 " "
absolute error = 7.229772336359019000000000000E-12 " "
relative error = 2.596633890001864300000000000E-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) = 28.11263892065115 " "
y[1] (numeric) = 28.11263892065848 " "
absolute error = 7.329248319365433000000000000E-12 " "
relative error = 2.607100791943608400000000000E-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) = 28.385125471896384 " "
y[1] (numeric) = 28.38512547190382 " "
absolute error = 7.435829729729448000000000000E-12 " "
relative error = 2.61962193441474600000000000E-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) = 28.66035055850982 " "
y[1] (numeric) = 28.66035055851736 " "
absolute error = 7.542411140093463000000000000E-12 " "
relative error = 2.63165348403387700000000000E-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) = 28.938341703229472 " "
y[1] (numeric) = 28.93834170323712 " "
absolute error = 7.648992550457479000000000000E-12 " "
relative error = 2.64320348031686400000000000E-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) = 29.21912670540148 " "
y[1] (numeric) = 29.21912670540923 " "
absolute error = 7.752021247142693000000000000E-12 " "
relative error = 2.653063975970797000000000000E-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) = 29.502733643760042 " "
y[1] (numeric) = 29.5027336437679 " "
absolute error = 7.858602657506708000000000000E-12 " "
relative error = 2.663686271380088500000000000E-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) = 29.789190879235335 " "
y[1] (numeric) = 29.78919087924331 " "
absolute error = 7.975842208907125000000000000E-12 " "
relative error = 2.6774282796874200000000000E-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) = 30.078527057789625 " "
y[1] (numeric) = 30.07852705779771 " "
absolute error = 8.08597633294994000000000000E-12 " "
relative error = 2.68828866433998600000000000E-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) = 30.37077111328188 " "
y[1] (numeric) = 30.37077111329008 " "
absolute error = 8.199663170671556000000000000E-12 " "
relative error = 2.69985346769336500000000000E-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) = 30.66595227036119 " "
y[1] (numeric) = 30.6659522703695 " "
absolute error = 8.313350008393172000000000000E-12 " "
relative error = 2.710938155482642000000000000E-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) = 30.96410004738924 " "
y[1] (numeric) = 30.964100047397668 " "
absolute error = 8.427036846114788000000000000E-12 " "
relative error = 2.721550709763101400000000000E-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) = 31.265244259392198 " "
y[1] (numeric) = 31.265244259400745 " "
absolute error = 8.547829111194005000000000000E-12 " "
relative error = 2.733971639651018000000000000E-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) = 31.56941502104221 " "
y[1] (numeric) = 31.56941502105088 " "
absolute error = 8.668621376273222000000000000E-12 " "
relative error = 2.745892304464704000000000000E-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) = 31.876642749668928 " "
y[1] (numeric) = 31.876642749677718 " "
absolute error = 8.78941364135243900000000000E-12 " "
relative error = 2.757320998442888700000000000E-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) = 32.18695816830123 " "
y[1] (numeric) = 32.18695816831015 " "
absolute error = 8.917311333789257000000000000E-12 " "
relative error = 2.770473459207250500000000000E-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) = 32.500392308739585 " "
y[1] (numeric) = 32.50039230874863 " "
absolute error = 9.045209026226075000000000000E-12 " "
relative error = 2.78310764384027300000000000E-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) = 32.81697651465923 " "
y[1] (numeric) = 32.81697651466838 " "
absolute error = 9.15179043659009000000000000E-12 " "
relative error = 2.788736626148974300000000000E-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) = 33.13674244474457 " "
y[1] (numeric) = 33.13674244475385 " "
absolute error = 9.279688129026908000000000000E-12 " "
relative error = 2.800422565525493000000000000E-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) = 33.45972207585509 " "
y[1] (numeric) = 33.4597220758645 " "
absolute error = 9.407585821463726000000000000E-12 " "
relative error = 2.811615051713877000000000000E-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) = 33.785947706223055 " "
y[1] (numeric) = 33.7859477062326 " "
absolute error = 9.542588941258145000000000000E-12 " "
relative error = 2.824425416221339500000000000E-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) = 34.11545195868336 " "
y[1] (numeric) = 34.115451958693036 " "
absolute error = 9.677592061052565000000000000E-12 " "
relative error = 2.836718116111412400000000000E-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) = 34.448267783935826 " "
y[1] (numeric) = 34.44826778394565 " "
absolute error = 9.826806035562186000000000000E-12 " "
relative error = 2.852627045631796500000000000E-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) = 34.78442846384034 " "
y[1] (numeric) = 34.784428463850304 " "
absolute error = 9.961809155356605000000000000E-12 " "
relative error = 2.86387029923813800000000000E-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) = 35.12396761474503 " "
y[1] (numeric) = 35.12396761475511 " "
absolute error = 1.008260142043582200000000000E-11 " "
relative error = 2.870575878848934400000000000E-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) = 35.46691919084791 " "
y[1] (numeric) = 35.466919190858135 " "
absolute error = 1.022470996758784200000000000E-11 " "
relative error = 2.882886419474033300000000000E-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) = 35.813317487592414 " "
y[1] (numeric) = 35.813317487602774 " "
absolute error = 1.03597130873822610000000000E-11 " "
relative error = 2.892698530643356000000000000E-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) = 36.163197145096866 " "
y[1] (numeric) = 36.163197145107375 " "
absolute error = 1.050892706189188200000000000E-11 " "
relative error = 2.905972892752575000000000000E-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) = 36.51659315161860 " "
y[1] (numeric) = 36.516593151629245 " "
absolute error = 1.065103560904390200000000000E-11 " "
relative error = 2.916765965768029500000000000E-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) = 36.873540847052745 " "
y[1] (numeric) = 36.873540847063545 " "
absolute error = 1.080024958355352300000000000E-11 " "
relative error = 2.92899714414510070000000000E-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) = 37.23407592646631 " "
y[1] (numeric) = 37.23407592647727 " "
absolute error = 1.095656898542074500000000000E-11 " "
relative error = 2.94261874715486600000000000E-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) = 37.598234443667685 " "
y[1] (numeric) = 37.5982344436788 " "
absolute error = 1.111288838728796700000000000E-11 " "
relative error = 2.95569421057206200000000000E-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) = 37.96605281481206 " "
y[1] (numeric) = 37.966052814823314 " "
absolute error = 1.125499693443998700000000000E-11 " "
relative error = 2.96448961637881100000000000E-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) = 38.33756782204306 " "
y[1] (numeric) = 38.337567822054474 " "
absolute error = 1.141131633630720900000000000E-11 " "
relative error = 2.97653632835466750000000000E-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) = 38.71281661717101 " "
y[1] (numeric) = 38.712816617182575 " "
absolute error = 1.156763573817443100000000000E-11 " "
relative error = 2.9880635791929500000000000E-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) = 39.09183672538813 " "
y[1] (numeric) = 39.091836725399844 " "
absolute error = 1.171684971268405200000000000E-11 " "
relative error = 2.99726252183862340000000000E-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) = 39.47466604902108 " "
y[1] (numeric) = 39.47466604903296 " "
absolute error = 1.188027454190887500000000000E-11 " "
relative error = 3.00959469224021200000000000E-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) = 39.86134287132127 " "
y[1] (numeric) = 39.8613428713333 " "
absolute error = 1.202948851641849600000000000E-11 " "
relative error = 3.01783323137195640000000000E-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) = 40.25190586029315 " "
y[1] (numeric) = 40.25190586030535 " "
absolute error = 1.22000187730009200000000000E-11 " "
relative error = 3.030917049082076000000000000E-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) = 40.64639407256109 " "
y[1] (numeric) = 40.64639407257346 " "
absolute error = 1.237054902958334400000000000E-11 " "
relative error = 3.04345546802988250000000000E-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) = 41.044846957275055 " "
y[1] (numeric) = 41.04484695728759 " "
absolute error = 1.253397385880816700000000000E-11 " "
relative error = 3.053726542543866400000000000E-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) = 41.44730436005556 " "
y[1] (numeric) = 41.44730436006827 " "
absolute error = 1.271160954274819200000000000E-11 " "
relative error = 3.06693275691021400000000000E-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) = 41.853806526978275 " "
y[1] (numeric) = 41.85380652699117 " "
absolute error = 1.289635065404581800000000000E-11 " "
relative error = 3.081285007071708500000000000E-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) = 42.26439410859864 " "
y[1] (numeric) = 42.264394108611704 " "
absolute error = 1.306688091062824200000000000E-11 " "
relative error = 3.091699570341125400000000000E-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) = 42.67910816401697 " "
y[1] (numeric) = 42.67910816403021 " "
absolute error = 1.324451659456826700000000000E-11 " "
relative error = 3.10327866825830360000000000E-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) = 43.0979901649844 " "
y[1] (numeric) = 43.09799016499784 " "
absolute error = 1.343636313322349500000000000E-11 " "
relative error = 3.117631026826876400000000000E-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) = 43.521082000050114 " "
y[1] (numeric) = 43.52108200006373 " "
absolute error = 1.36139988171635200000000000E-11 " "
relative error = 3.128138867767084600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "
Iterations = 8752
"Total Elapsed Time "= 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 3 Minutes 0 Seconds
"Expected Time Remaining "= 25 Seconds
"Optimized Time Remaining "= 25 Seconds
"Expected Total Time "= 3 Minutes 25 Seconds
"Time to Timeout "= 0.0 Seconds
Percent Done = 87.52999999999702 "%"
(%o255) temp/diffeq.diff.max