(%i1) batch("temp/diffeq.h2sin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.h2sin.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,40,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[40],convfloat)
(%i173) completearray(array_norms,[40],convfloat)
(%i174) completearray(array_fact_1,[40],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[40],convfloat)
(%i184) completearray(array_x,[40],convfloat)
(%i185) completearray(array_tmp0,[40],convfloat)
(%i186) completearray(array_tmp1_g,[40],convfloat)
(%i187) completearray(array_tmp1,[40],convfloat)
(%i188) completearray(array_tmp2,[40],convfloat)
(%i189) completearray(array_m1,[40],convfloat)
(%i190) completearray(array_y_higher,[3,40],convfloat)
(%i191) completearray(array_y_higher_work,[3,40],convfloat)
(%i192) completearray(array_y_higher_work2,[3,40],convfloat)
(%i193) completearray(array_y_set_initial,[2,40],convfloat)
(%i194) completearray(array_given_rad_poles,[2,3],convfloat)
(%i195) completearray(array_given_ord_poles,[2,3],convfloat)
(%i196) completearray(array_rad_test_poles,[2,4],convfloat)
(%i197) completearray(array_ord_test_poles,[2,4],convfloat)
(%i198) completearray(array_fact_2,[40,40],convfloat)
(%i199) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i200) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i201) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i202) 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))
(%i203) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i204) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i205) 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)
(%i206) 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)
(%i207) 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)
(%i208) 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)
(%i209) 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)
(%i210) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i211) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i212) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i213) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i214) log_revs(file,revs):=printf(file,revs)
(%i215) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i216) 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)
(%i217) logstart(file):=(printf(file,""),0)
(%i218) logend(file):=(printf(file,"
~%"),0)
(%i219) 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)
(%i220) 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)
(%i221) 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)
(%i222) 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)
(%i223) 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)
(%i224) c(in_val):=(ret:in_val,ret)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i229) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i230) 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)
(%i231) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i232) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i233) 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)
(%i234) log10(x):=log(x)/glob_log_10
(%i235) c(x):=x
(%i236) 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
(%i237) 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)
(%i238) exact_soln_y(x):=block(c(2.0)-sin(c(x)))
(%o238) exact_soln_y(x) := block(c(2.0) - sin(c(x)))
(%i239) exact_soln_yp(x):=block(neg(cos(c(x))))
(%o239) exact_soln_yp(x) := block(neg(cos(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(17)
*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]:sin(array_x[1]),
array_tmp1_g[1]:cos(array_x[1]),
array_tmp2[1]:array_tmp1[1]+array_const_0D0[1],
if not array_y_set_initial[1,3]
then (if 1 <= 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_tmp1_g[1]*array_x[2]/c(1),
array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1),
array_tmp2[2]:array_tmp1[2],
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_tmp1_g[2]*array_x[2]/c(2),
array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2),
array_tmp2[3]:array_tmp1[3],
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_tmp1_g[3]*array_x[2]/c(3),
array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3),
array_tmp2[4]:array_tmp1[4],
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_tmp1_g[4]*array_x[2]/c(4),
array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4),
array_tmp2[5]:array_tmp1[5],
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
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp1_g[kkk]
:neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1),
array_tmp2[kkk]:array_tmp1[kkk],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(c(2.0)-sin(c(x)))
(%o250) exact_soln_y(x) := block(c(2.0) - sin(c(x)))
(%i251) exact_soln_yp(x):=block(neg(cos(c(x))))
(%o251) exact_soln_yp(x) := block(neg(cos(c(x))))
(%i252) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 3 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 3 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 3 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1_g),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_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_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,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/h2sinpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 2 ) = sin ( x ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.1),"),
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(2.0) - sin(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_yp (x) := (block("),
omniout_str(always," (neg( cos(c(x)))) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float: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(0.1),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 ) = sin ( x ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T21:18:47-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"h2sin"),
logitem_str(html_log_file,
"diff ( y , x , 2 ) = sin ( x ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_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,
"h2sin diffeq.max"),
logitem_str(html_log_file,
"h2sin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i253) main():=(glob_iolevel:2,compile(all),main_prog())
(%i254) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp1_g in translation.
warning: encountered undefined variable array_const_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 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/h2sinpostode.ode#################"
"diff ( y , x , 2 ) = sin ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"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(2.0) - sin(c(x))) "
"));"
"exact_soln_yp (x) := (block("
" (neg( cos(c(x)))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = 1.9001665833531718 " "
y[1] (numeric) = 1.9001665833531718 " "
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] = 0.11000000000000001 " "
y[1] (closed_form) = 1.8902216991628251 " "
y[1] (numeric) = 1.8902216991628251 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = 1.8802877927110806 " "
y[1] (numeric) = 1.8802877927110808 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.180907549289982600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (closed_form) = 1.870365857380305 " "
y[1] (numeric) = 1.8703658573803057 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.561516118071693700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (closed_form) = 1.8604568853557635 " "
y[1] (numeric) = 1.8604568853557641 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.580485094916421000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (closed_form) = 1.8505618675264008 " "
y[1] (numeric) = 1.8505618675264015 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.5996300716252100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (closed_form) = 1.840681793385754 " "
y[1] (numeric) = 1.8406817933857549 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.82526867431229300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (closed_form) = 1.8308176509330039 " "
y[1] (numeric) = 1.830817650933005 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.06408302901916700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (closed_form) = 1.8209704265741757 " "
y[1] (numeric) = 1.8209704265741766 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.87750051696924650000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = 1.8111411050234993 " "
y[1] (numeric) = 1.8111411050235005 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.1299642614579800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = 1.8013306692049387 " "
y[1] (numeric) = 1.8013306692049396 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.930679496464381000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = 1.7915401001539004 " "
y[1] (numeric) = 1.7915401001539013 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.95762511608770100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = 1.7817703769191306 " "
y[1] (numeric) = 1.7817703769191315 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.984808543264029300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = 1.7720224764648114 " "
y[1] (numeric) = 1.7720224764648125 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.26528748574371200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = 1.7622973735728653 " "
y[1] (numeric) = 1.762297373572866 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.77991719652047300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = 1.752596040745477 " "
y[1] (numeric) = 1.7525960407454777 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.80084057756829130000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = 1.7429194481078447 " "
y[1] (numeric) = 1.7429194481078454 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.82194263480314500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = 1.7332685633111686 " "
y[1] (numeric) = 1.7332685633111695 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.12429774877693400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (closed_form) = 1.7236443514358861 " "
y[1] (numeric) = 1.723644351435887 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.15290998958239900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (closed_form) = 1.7140477748951644 " "
y[1] (numeric) = 1.714047774895165 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.886319999545149000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (closed_form) = 1.7044797933386602 " "
y[1] (numeric) = 1.704479793338661 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.21084745721977900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (closed_form) = 1.6949413635565564 " "
y[1] (numeric) = 1.6949413635565571 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.93012896550781800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (closed_form) = 1.6854334393838821 " "
y[1] (numeric) = 1.6854334393838826 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.634866494712490600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (closed_form) = 1.6759569716051315 " "
y[1] (numeric) = 1.675956971605132 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.649764984268901400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (closed_form) = 1.6665129078591854 " "
y[1] (numeric) = 1.666512907859186 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.99717164885817900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (closed_form) = 1.6571021925445484 " "
y[1] (numeric) = 1.657102192544549 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.019871663751878300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (closed_form) = 1.64772576672491 " "
y[1] (numeric) = 1.6477257667249103 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.695164564506103000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (closed_form) = 1.6383845680350377 " "
y[1] (numeric) = 1.6383845680350384 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.065796442248034700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (closed_form) = 1.6290795305870172 " "
y[1] (numeric) = 1.6290795305870176 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.726013073714338400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (closed_form) = 1.6198115848768384 " "
y[1] (numeric) = 1.6198115848768389 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.741610283543124400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (closed_form) = 1.6105816576913492 " "
y[1] (numeric) = 1.61058165769135 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.51464382733169800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (closed_form) = 1.6013906720155768 " "
y[1] (numeric) = 1.6013906720155775 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.159720837743298700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (closed_form) = 1.5922395469404296 " "
y[1] (numeric) = 1.59223954694043 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.789085415592163500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (closed_form) = 1.583129197570789 " "
y[1] (numeric) = 1.5831291975707895 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.805135617051907600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (closed_form) = 1.5740605349340002 " "
y[1] (numeric) = 1.5740605349340007 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.82129689420542600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (closed_form) = 1.5650344658887696 " "
y[1] (numeric) = 1.56503446588877 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.83756824229342560000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = 1.55605189303448 " "
y[1] (numeric) = 1.5560518930344802 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.42697429256050580000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = 1.5471137146209315 " "
y[1] (numeric) = 1.5471137146209317 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.435218386512952200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (closed_form) = 1.538220824458517 " "
y[1] (numeric) = 1.5382208244585167 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.443515790414521500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (closed_form) = 1.5293741118288418 " "
y[1] (numeric) = 1.5293741118288415 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.45186585288479890000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = 1.5205744613957968 " "
y[1] (numeric) = 1.5205744613957968 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = 1.5118227531170922 " "
y[1] (numeric) = 1.5118227531170922 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (closed_form) = 1.503119862156263 " "
y[1] (numeric) = 1.503119862156263 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (closed_form) = 1.4944666587951527 " "
y[1] (numeric) = 1.4944666587951527 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = 1.4858640083468866 " "
y[1] (numeric) = 1.4858640083468866 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (closed_form) = 1.4773127710693406 " "
y[1] (numeric) = 1.4773127710693403 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.503030429800631700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = 1.4688138020791164 " "
y[1] (numeric) = 1.468813802079116 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.02345477160856700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (closed_form) = 1.4603679512660306 " "
y[1] (numeric) = 1.4603679512660301 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.040940534644507000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = 1.451976063208126 " "
y[1] (numeric) = 1.4519760632081258 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.52925802670896700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = 1.443638977087216 " "
y[1] (numeric) = 1.4436389770872153 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.61426870116191200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = 1.4353575266049643 " "
y[1] (numeric) = 1.4353575266049636 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.64089122346188600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = 1.4271325398995183 " "
y[1] (numeric) = 1.4271325398995176 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.66763805148746100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = 1.4189648394626946 " "
y[1] (numeric) = 1.4189648394626937 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.25934057701135900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = 1.41085524205773 " "
y[1] (numeric) = 1.410855242057729 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.86914909148225600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = 1.4028045586376074 " "
y[1] (numeric) = 1.402804558637606 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.10800340995808770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = 1.3948135942639601 " "
y[1] (numeric) = 1.3948135942639581 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.43273728657615620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = 1.3868831480265658 " "
y[1] (numeric) = 1.3868831480265638 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.44092993499045860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = 1.3790140129634398 " "
y[1] (numeric) = 1.3790140129634376 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.6101693154507352000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = 1.371206975981531 " "
y[1] (numeric) = 1.3712069759815284 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.943204276067120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = 1.3634628177780317 " "
y[1] (numeric) = 1.3634628177780286 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.27994810596772350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = 1.3557823127623085 " "
y[1] (numeric) = 1.3557823127623054 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.2928640089844812000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = 1.3481662289784628 " "
y[1] (numeric) = 1.3481662289784597 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.305816895670140300000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = 1.3406153280285265 " "
y[1] (numeric) = 1.3406153280285231 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.48443308400289860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = 1.3331303649963018 " "
y[1] (numeric) = 1.3331303649962982 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.66494093307248050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = 1.3257120883718545 " "
y[1] (numeric) = 1.3257120883718507 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.84734394204809700000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = 1.3183612399766655 " "
y[1] (numeric) = 1.3183612399766613 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.20006942380243740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = 1.3110785548894484 " "
y[1] (numeric) = 1.3110785548894441 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.21784493983377900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = 1.3038647613726428 " "
y[1] (numeric) = 1.3038647613726386 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.2356480660879320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = 1.2967205807995894 " "
y[1] (numeric) = 1.2967205807995852 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 3.2534746159223843000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = 1.2896467275823917 " "
y[1] (numeric) = 1.2896467275823873 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.44349503125220060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = 1.2826439091004769 " "
y[1] (numeric) = 1.282643909100472 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.8085249332969934000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = 1.275712825629857 " "
y[1] (numeric) = 1.275712825629852 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.00327237499884100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = 1.2688541702731038 " "
y[1] (numeric) = 1.2688541702730987 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.02491163517750940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = 1.262068628890037 " "
y[1] (numeric) = 1.2620686288900316 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.22248869531568870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = 1.2553568800291401 " "
y[1] (numeric) = 1.255356880029135 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 4.0681865010029440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = 1.2487195948597067 " "
y[1] (numeric) = 1.2487195948597014 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.2676278486680360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = 1.2421574371047226 " "
y[1] (numeric) = 1.2421574371047168 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.6476876083495170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = 1.2356710629744945 " "
y[1] (numeric) = 1.2356710629744883 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 5.0314757091865370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = 1.2292611211010303 " "
y[1] (numeric) = 1.2292611211010238 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 5.2383447522185780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = 1.2229282524731757 " "
y[1] (numeric) = 1.222928252473169 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.4470392145078450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = 1.2166730903725163 " "
y[1] (numeric) = 1.2166730903725091 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.8400464461866990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = 1.210496260310049 " "
y[1] (numeric) = 1.210496260310042 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.8698465997582360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = 1.2043983799636335 " "
y[1] (numeric) = 1.2043983799636258 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.4526499716902270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = 1.1983800591162224 " "
y[1] (numeric) = 1.1983800591162144 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.6703427819019510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = 1.1924418995948853 " "
y[1] (numeric) = 1.1924418995948776 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.5173499648212370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = 1.1865844952106257 " "
y[1] (numeric) = 1.186584495210618 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.5495219293225280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = 1.1808084316990013 " "
y[1] (numeric) = 1.1808084316989933 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.7696042496915110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = 1.1751142866615494 " "
y[1] (numeric) = 1.1751142866615412 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 6.991362861876590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = 1.169502629508029 " "
y[1] (numeric) = 1.1695026295080204 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 7.4046345630869470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (closed_form) = 1.1639740213994791 " "
y[1] (numeric) = 1.16397402139947 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 7.8213333240723790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (closed_form) = 1.1585290151921033 " "
y[1] (numeric) = 1.1585290151920937 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 8.2414146616717610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0099999999999996 " "
y[1] (closed_form) = 1.153168155381985 " "
y[1] (numeric) = 1.1531681553819748 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 8.8573828360427210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999985 " "
y[1] (closed_form) = 1.1478919780506378 " "
y[1] (numeric) = 1.1478919780506271 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 9.28496865576260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999974 " "
y[1] (closed_form) = 1.142701010811398 " "
y[1] (numeric) = 1.1427010108113866 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 9.9100943676732770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = 1.1375957727566635 " "
y[1] (numeric) = 1.1375957727566515 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.0540131172337337000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = 1.1325767744059854 " "
y[1] (numeric) = 1.132576774405973 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.097894478926023000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = 1.1276445176550167 " "
y[1] (numeric) = 1.1276445176550034 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.1814606542145864000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = 1.1227994957253218 " "
y[1] (numeric) = 1.1227994957253078 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.2458867467909115000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = 1.1180421931150564 " "
y[1] (numeric) = 1.1180421931150415 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.3306285417124794000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = 1.113373085550517 " "
y[1] (numeric) = 1.1133730855505017 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.3760955728736265000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = 1.1087926399385695 " "
y[1] (numeric) = 1.1087926399385537 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.4218318540201225000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = 1.1043013143199576 " "
y[1] (numeric) = 1.1043013143199407 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.5281508547958628000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = 1.0998995578235005 " "
y[1] (numeric) = 1.0998995578234831 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.5746418898853380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = 1.09558781062118 " "
y[1] (numeric) = 1.0955878106211625 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.6011061476789998000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = 1.091366503884123 " "
y[1] (numeric) = 1.091366503884105 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.6479901971443664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = 1.0872360597394854 " "
y[1] (numeric) = 1.087236059739467 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.6950966667895080000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = 1.0831968912282397 " "
y[1] (numeric) = 1.0831968912282208 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.7424155821963835000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = 1.0792494022638714 " "
y[1] (numeric) = 1.0792494022638521 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.7899366530067898000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = 1.075393987591987 " "
y[1] (numeric) = 1.0753939875919671 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.837649277041117000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = 1.0716310327508407 " "
y[1] (numeric) = 1.0716310327508205 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.8855425450221966000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = 1.0679609140327813 " "
y[1] (numeric) = 1.0679609140327606 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.933605245912029000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = 1.0643839984466221 " "
y[1] (numeric) = 1.064383998446601 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.9818258728676136000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = 1.0609006436809405 " "
y[1] (numeric) = 1.0609006436809194 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.9883329879684697000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = 1.0575111980683107 " "
y[1] (numeric) = 1.0575111980682892 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 2.0366996318403763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = 1.0542160005504693 " "
y[1] (numeric) = 1.0542160005504473 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 2.0851908789185294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = 1.0510153806444222 " "
y[1] (numeric) = 1.0510153806443998 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 2.133794187072459200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = 1.047909658409493 " "
y[1] (numeric) = 1.04790965840947 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 2.1824967566374937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = 1.0448991444153164 " "
y[1] (numeric) = 1.044899144415293 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 2.231285540019678000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = 1.0419841397107836 " "
y[1] (numeric) = 1.0419841397107599 " "
absolute error = 2.37587727269783500000000000000E-14 " "
relative error = 2.280147251912386000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = 1.039164935793936 " "
y[1] (numeric) = 1.0391649357939117 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 2.3504359799334917000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = 1.0364418145828158 " "
y[1] (numeric) = 1.0364418145827914 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 2.3566114564361587000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = 1.0338150483872746 " "
y[1] (numeric) = 1.03381504838725 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.3840774213073315000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = 1.0312848998817432 " "
y[1] (numeric) = 1.0312848998817186 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.389926503287765000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = 1.0288516220789639 " "
y[1] (numeric) = 1.0288516220789392 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.395578781017544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = 1.0265154583046892 " "
y[1] (numeric) = 1.026515458304664 " "
absolute error = 2.509104035652854000000000000000E-14 " "
relative error = 2.4442924997902024000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = 1.0242766421733491 " "
y[1] (numeric) = 1.0242766421733243 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 2.4279569334740977000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = 1.0221353975646918 " "
y[1] (numeric) = 1.0221353975646672 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.411319596738508200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = 1.0200919386013938 " "
y[1] (numeric) = 1.020091938601369 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 2.437917094580746000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = 1.018146469627648 " "
y[1] (numeric) = 1.0181464696276232 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 2.442575453873398200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = 1.016299185188731 " "
y[1] (numeric) = 1.0162991851887064 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.4251668707282717000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = 1.0145502700115472 " "
y[1] (numeric) = 1.0145502700115225 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.4293474532708914000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = 1.0128998989861566 " "
y[1] (numeric) = 1.0128998989861322 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 2.4113840435961245000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = 1.0113482371482871 " "
y[1] (numeric) = 1.0113482371482623 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 2.4589943244205345000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = 1.0098954396628288 " "
y[1] (numeric) = 1.0098954396628042 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.440544850356715000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = 1.00854165180832 " "
y[1] (numeric) = 1.0085416518082955 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 2.4218044438679823000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = 1.0072870089624173 " "
y[1] (numeric) = 1.0072870089623933 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.3807333082360962000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = 1.0061316365883606 " "
y[1] (numeric) = 1.0061316365883366 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.3834671786306896000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = 1.0050756502224243 " "
y[1] (numeric) = 1.0050756502224008 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 2.341786721909402000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = 1.0041191554623645 " "
y[1] (numeric) = 1.0041191554623414 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 2.299790695813371000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = 1.003262247956861 " "
y[1] (numeric) = 1.003262247956838 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 2.2796227361145190000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = 1.0025050133959494 " "
y[1] (numeric) = 1.002505013395927 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 2.237046677847444300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = 1.0018475275024552 " "
y[1] (numeric) = 1.0018475275024334 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 2.1720242537205586000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = 1.0012898560244199 " "
y[1] (numeric) = 1.0012898560243984 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 2.1510581125075084000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = 1.0008320547285263 " "
y[1] (numeric) = 1.0008320547285054 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 2.085484049430699000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = 1.0004741693945227 " "
y[1] (numeric) = 1.000474169394502 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 2.0640361230440543000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = 1.0002162358106443 " "
y[1] (numeric) = 1.000216235810624 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 2.0423687320518782000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = 1.0000582797700344 " "
y[1] (numeric) = 1.0000582797700144 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.9982849847359085000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = 1.0000003170681655 " "
y[1] (numeric) = 1.0000003170681462 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.9317874503394694000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = 1.0000423535012595 " "
y[1] (numeric) = 1.0000423535012406 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.887299208133377300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = 1.000184384865708 " "
y[1] (numeric) = 1.0001843848656893 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.8648308347872228000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = 1.0004263969584928 " "
y[1] (numeric) = 1.0004263969584746 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.819989722303178800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = 1.0007683655786068 " "
y[1] (numeric) = 1.0007683655785893 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.7528055834314488000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = 1.0012102565294727 " "
y[1] (numeric) = 1.0012102565294558 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.6854991111255777000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = 1.0017520256223635 " "
y[1] (numeric) = 1.0017520256223473 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.6180906796227218000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = 1.0023936186808216 " "
y[1] (numeric) = 1.002393618680806 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.5506006877026393000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = 1.0031349715460756 " "
y[1] (numeric) = 1.0031349715460605 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.5051846025895038000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = 1.003976010083457 " "
y[1] (numeric) = 1.0039760100834423 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.4596906477709415000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = 1.0049166501898126 " "
y[1] (numeric) = 1.0049166501897986 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.3920368527712930000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = 1.005956797801916 " "
y[1] (numeric) = 1.0059567978019026 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.3243785741706635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = 1.0070963489058724 " "
y[1] (numeric) = 1.0070963489058595 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.2787840110475374000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = 1.0083351895475214 " "
y[1] (numeric) = 1.008335189547509 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.2331710729426777000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = 1.0096731958438312 " "
y[1] (numeric) = 1.0096731958438196 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 1.143569969335654900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = 1.0111102339952869 " "
y[1] (numeric) = 1.011110233995276 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0760632496354745000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = 1.012646160299271 " "
y[1] (numeric) = 1.0126461602992605 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 1.0305768036875047000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = 1.0142808211644327 " "
y[1] (numeric) = 1.0142808211644234 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 9.1945674336470850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 1.0160140531260486 " "
y[1] (numeric) = 1.0160140531260398 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 8.7417926648494510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 1.0178456828623659 " "
y[1] (numeric) = 1.0178456828623579 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 7.8534555010555850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 1.0197755272119378 " "
y[1] (numeric) = 1.0197755272119307 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 6.9676386302652430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 1.0218033931919375 " "
y[1] (numeric) = 1.021803393191931 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.3018909368764830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 1.023929078017457 " "
y[1] (numeric) = 1.023929078017451 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.855097253985430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 1.0261523691217849 " "
y[1] (numeric) = 1.02615236912178 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 4.7604833895490750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 1.0284730441776637 " "
y[1] (numeric) = 1.0284730441776597 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.8861523024614486000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 1.0308908711195215 " "
y[1] (numeric) = 1.0308908711195182 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.23086484436363950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 1.0334056081666791 " "
y[1] (numeric) = 1.0334056081666765 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.57840216662595270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 1.0360170038475274 " "
y[1] (numeric) = 1.036017003847526 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.28595150909922740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 1.0387247970246745 " "
y[1] (numeric) = 1.038724797024674 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.27533078176349200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 1.041528716921059 " "
y[1] (numeric) = 1.0415287169210594 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.26382107987255500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 1.044428483147028 " "
y[1] (numeric) = 1.0444284831470294 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.27559488375485030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 1.0474238057283753 " "
y[1] (numeric) = 1.0474238057283776 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.11991176552095000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 1.050514385135339 " "
y[1] (numeric) = 1.050514385135342 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.9591450749624440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 1.0536999123125537 " "
y[1] (numeric) = 1.0536999123125579 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.0038415532525730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 1.0569800687099562 " "
y[1] (numeric) = 1.0569800687099618 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 5.2518635757256200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 1.0603545263146406 " "
y[1] (numeric) = 1.0603545263146472 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.2821801411109470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 1.0638229476836583 " "
y[1] (numeric) = 1.063822947683666 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.3053144691959320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 1.0673849859777624 " "
y[1] (numeric) = 1.0673849859777715 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 8.5290958009746180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 1.0710402849960923 " "
y[1] (numeric) = 1.0710402849961027 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 9.7438878608702830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 1.0747884792117919 " "
y[1] (numeric) = 1.0747884792118032 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 1.0536282319923433000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = 1.0786291938085633 " "
y[1] (numeric) = 1.0786291938085757 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.1528056117131805000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = 1.0825620447181474 " "
y[1] (numeric) = 1.082562044718161 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.2511727125952743000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = 1.0865866386587308 " "
y[1] (numeric) = 1.0865866386587453 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 1.3282787406573330000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = 1.0907025731742728 " "
y[1] (numeric) = 1.0907025731742888 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.4657718747352597000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 1.0949094366747523 " "
y[1] (numeric) = 1.0949094366747694 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.5615386995980637000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 1.0992068084773243 " "
y[1] (numeric) = 1.0992068084773432 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.7170373466638703000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 1.1035942588483902 " "
y[1] (numeric) = 1.1035942588484104 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.8309318742979908000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 1.108071349046569 " "
y[1] (numeric) = 1.1080713490465908 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.9638059680341524000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 1.1126376313665718 " "
y[1] (numeric) = 1.1126376313665953 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 2.115399251160045000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 1.1172926491839714 " "
y[1] (numeric) = 1.1172926491839967 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 2.265573391173861000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 1.122035937000866 " "
y[1] (numeric) = 1.1220359370008925 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 2.3747325475354353000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 1.1268670204924258 " "
y[1] (numeric) = 1.126867020492454 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 2.5024838168709646000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 1.1317854165543282 " "
y[1] (numeric) = 1.1317854165543575 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 2.589703615314007000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 1.1367906333510656 " "
y[1] (numeric) = 1.136790633351096 " "
absolute error = 3.04201108747292900000000000000E-14 " "
relative error = 2.675964243746095000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 1.141882170365129 " "
y[1] (numeric) = 1.141882170365161 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 2.8001508333368885000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 1.1470595184470598 " "
y[1] (numeric) = 1.1470595184470935 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 2.9423739052615216000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 1.1523221598663647 " "
y[1] (numeric) = 1.1523221598664 " "
absolute error = 3.53050921830799800000000000000E-14 " "
relative error = 3.0638213351007954000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = 1.157669568363287 " "
y[1] (numeric) = 1.1576695683633238 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 3.1839313587267404000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 1.1631012092014335 " "
y[1] (numeric) = 1.163101209201472 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 3.3217884180072466000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 1.1686165392212464 " "
y[1] (numeric) = 1.1686165392212868 " "
absolute error = 4.0412118096355700000000000000E-14 " "
relative error = 3.458116220337417000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 1.1742150068943198 " "
y[1] (numeric) = 1.174215006894362 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 3.5929088529825737000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 1.179896052378552 " "
y[1] (numeric) = 1.179896052378596 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 3.7261614433345647000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 1.1856591075741285 " "
y[1] (numeric) = 1.185659107574174 " "
absolute error = 4.55191440096314200000000000000E-14 " "
relative error = 3.8391426101186943000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 1.1915035961803326 " "
y[1] (numeric) = 1.19150359618038 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 3.969396399696099000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 1.1974289337531738 " "
y[1] (numeric) = 1.1974289337532231 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 4.1166453309969790000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 1.2034345277638328 " "
y[1] (numeric) = 1.2034345277638836 " "
absolute error = 5.08482145278321700000000000000E-14 " "
relative error = 4.225258072187442000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 1.209519777657913 " "
y[1] (numeric) = 1.2095197776579656 " "
absolute error = 5.26245713672324200000000000000E-14 " "
relative error = 4.3508648919436000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 1.2156840749154958 " "
y[1] (numeric) = 1.2156840749155502 " "
absolute error = 5.44009282066326700000000000000E-14 " "
relative error = 4.474923158832542000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 1.2219268031119928 " "
y[1] (numeric) = 1.2219268031120492 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 4.615606230039362400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 1.2282473379797865 " "
y[1] (numeric) = 1.2282473379798446 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 4.73647975382916030000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 1.2346450474706572 " "
y[1] (numeric) = 1.2346450474707171 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 4.855812077534234500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 1.2411192918189868 " "
y[1] (numeric) = 1.241119291819049 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 5.00938868558627000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = 1.2476694236057364 " "
y[1] (numeric) = 1.2476694236058001 " "
absolute error = 6.37268016134839900000000000000E-14 " "
relative error = 5.10766717591868000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = 1.2542947878231852 " "
y[1] (numeric) = 1.2542947878232507 " "
absolute error = 6.55031584528842400000000000000E-14 " "
relative error = 5.222309706521563000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = 1.2609947219404325 " "
y[1] (numeric) = 1.2609947219405002 " "
absolute error = 6.77236045021345500000000000000E-14 " "
relative error = 5.370649323410389000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = 1.26776855596965 " "
y[1] (numeric) = 1.2677685559697198 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 5.499584732414593000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = 1.27461561253308 " "
y[1] (numeric) = 1.2746156125331518 " "
absolute error = 7.17204073907851100000000000000E-14 " "
relative error = 5.626826369108495000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = 1.281535206930772 " "
y[1] (numeric) = 1.2815352069308457 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 5.752382645160732000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = 1.2885266472090517 " "
y[1] (numeric) = 1.2885266472091277 " "
absolute error = 7.59392548843607100000000000000E-14 " "
relative error = 5.893495105347266000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = 1.2955892342297182 " "
y[1] (numeric) = 1.295589234229796 " "
absolute error = 7.79376563286859900000000000000E-14 " "
relative error = 6.015614692493426000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = 1.3027222617399548 " "
y[1] (numeric) = 1.3027222617400345 " "
absolute error = 7.97140131680862400000000000000E-14 " "
relative error = 6.119033619769253000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = 1.3099250164429543 " "
y[1] (numeric) = 1.309925016443036 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 6.237945957723451000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = 1.317196778069249 " "
y[1] (numeric) = 1.3171967780693328 " "
absolute error = 8.3710816056736800000000000000E-14 " "
relative error = 6.3552247811781290000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = 1.3245368194487361 " "
y[1] (numeric) = 1.3245368194488218 " "
absolute error = 8.57092175010620800000000000000E-14 " "
relative error = 6.4708822165271120000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = 1.331944406583394 " "
y[1] (numeric) = 1.3319444065834818 " "
absolute error = 8.77076189453873700000000000000E-14 " "
relative error = 6.584930910920561000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = 1.3394187987206827 " "
y[1] (numeric) = 1.3394187987207722 " "
absolute error = 8.94839757847876200000000000000E-14 " "
relative error = 6.680806322134370000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = 1.3469592484276165 " "
y[1] (numeric) = 1.346959248427708 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 6.7917702288250790000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = 1.3545650016655089 " "
y[1] (numeric) = 1.3545650016656026 " "
absolute error = 9.37028232783632100000000000000E-14 " "
relative error = 6.9175582687542260000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = 1.3622352978653738 " "
y[1] (numeric) = 1.36223529786547 " "
absolute error = 9.61453139325385600000000000000E-14 " "
relative error = 7.057907990139333000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = 1.3699693700039837 " "
y[1] (numeric) = 1.3699693700040818 " "
absolute error = 9.81437153768638400000000000000E-14 " "
relative error = 7.163935013859357000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = 1.377766444680569 " "
y[1] (numeric) = 1.3777664446806697 " "
absolute error = 1.00586206031039180000000000000E-13 " "
relative error = 7.300671780721136000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = 1.3856257421941605 " "
y[1] (numeric) = 1.3856257421942633 " "
absolute error = 1.0280665208028950000000000000E-13 " "
relative error = 7.419510835407368000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = 1.3935464766215553 " "
y[1] (numeric) = 1.3935464766216603 " "
absolute error = 1.05027098129539810000000000000E-13 " "
relative error = 7.536677096279004000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = 1.401527855895912 " "
y[1] (numeric) = 1.4015278558960191 " "
absolute error = 1.07247544178790120000000000000E-13 " "
relative error = 7.65218784112095000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = 1.4095690818859536 " "
y[1] (numeric) = 1.4095690818860633 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 7.781813338740666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = 1.4176693504757827 " "
y[1] (numeric) = 1.4176693504758948 " "
absolute error = 1.12132525487140810000000000000E-13 " "
relative error = 7.909638834295748000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = 1.4258278516452902 " "
y[1] (numeric) = 1.4258278516454042 " "
absolute error = 1.13908882326541060000000000000E-13 " "
relative error = 7.988964600116304000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = 1.434043769551158 " "
y[1] (numeric) = 1.4340437695512744 " "
absolute error = 1.1635137298071640000000000000E-13 " "
relative error = 8.113516159770582000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = 1.4423162826084421 " "
y[1] (numeric) = 1.4423162826085607 " "
absolute error = 1.18571819029966720000000000000E-13 " "
relative error = 8.220930489360385000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = 1.4506445635727305 " "
y[1] (numeric) = 1.450644563572851 " "
absolute error = 1.205702204742920000000000000E-13 " "
relative error = 8.31149293920385000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = 1.459027779622867 " "
y[1] (numeric) = 1.45902777962299 " "
absolute error = 1.23012711128467340000000000000E-13 " "
relative error = 8.431142494097266000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = 1.4674650924442323 " "
y[1] (numeric) = 1.4674650924443575 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 8.533978615404568000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = 1.4759556583125755 " "
y[1] (numeric) = 1.4759556583127036 " "
absolute error = 1.28119737041743060000000000000E-13 " "
relative error = 8.680459763148932000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = 1.4844986281783856 " "
y[1] (numeric) = 1.4844986281785157 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 8.765123524953007000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = 1.4930931477517946 " "
y[1] (numeric) = 1.4930931477519271 " "
absolute error = 1.3256062914024370000000000000E-13 " "
relative error = 8.878255810084261000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = 1.5017383575880074 " "
y[1] (numeric) = 1.5017383575881424 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 8.989789673565514000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = 1.5104333931732448 " "
y[1] (numeric) = 1.5104333931733824 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 9.11444726233810900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = 1.519177385011194 " "
y[1] (numeric) = 1.5191773850113341 " "
absolute error = 1.40110145707694760000000000000E-13 " "
relative error = 9.222764049154296000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = 1.527969458709958 " "
y[1] (numeric) = 1.5279694587101005 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 9.329547495159045000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = 1.5368087350694934 " "
y[1] (numeric) = 1.5368087350696384 " "
absolute error = 1.44995127016045440000000000000E-13 " "
relative error = 9.434819291906802000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = 1.5456943301695305 " "
y[1] (numeric) = 1.545694330169678 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 9.538601183459731000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = 1.5546253554579639 " "
y[1] (numeric) = 1.5546253554581138 " "
absolute error = 1.49880108324396130000000000000E-13 " "
relative error = 9.640914950872149000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = 1.563600917839707 " "
y[1] (numeric) = 1.5636009178398595 " "
absolute error = 1.5254464358349650000000000000E-13 " "
relative error = 9.755983246303944000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = 1.5726201197660017 " "
y[1] (numeric) = 1.5726201197661562 " "
absolute error = 1.5454304502782180000000000000E-13 " "
relative error = 9.827105928850577000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = 1.5816820593241707 " "
y[1] (numeric) = 1.5816820593243281 " "
absolute error = 1.5742962489184720000000000000E-13 " "
relative error = 9.953304076744384000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = 1.5907858303278104 " "
y[1] (numeric) = 1.5907858303279705 " "
absolute error = 1.60094160150947570000000000000E-13 " "
relative error = 1.006384122229434700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = 1.5999305224074067 " "
y[1] (numeric) = 1.5999305224075693 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 1.015898181381994800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = 1.609115221101372 " "
y[1] (numeric) = 1.6091152211015374 " "
absolute error = 1.65423230669148320000000000000E-13 " "
relative error = 1.028038443113620200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = 1.6183390079474909 " "
y[1] (numeric) = 1.618339007947659 " "
absolute error = 1.6808776592824870000000000000E-13 " "
relative error = 1.038643727320342400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = 1.6276009605747654 " "
y[1] (numeric) = 1.6276009605749355 " "
absolute error = 1.70086167372573980000000000000E-13 " "
relative error = 1.04501147082458300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = 1.6369001527956508 " "
y[1] (numeric) = 1.6369001527958236 " "
absolute error = 1.72750702631674360000000000000E-13 " "
relative error = 1.055352718592118100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = 1.6462356546986745 " "
y[1] (numeric) = 1.64623565469885 " "
absolute error = 1.75415237890774730000000000000E-13 " "
relative error = 1.065553630733885300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = 1.6556065327414258 " "
y[1] (numeric) = 1.655606532741604 " "
absolute error = 1.78301817754800140000000000000E-13 " "
relative error = 1.07695768426064500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = 1.6650118498439093 " "
y[1] (numeric) = 1.66501184984409 " "
absolute error = 1.80744308408975480000000000000E-13 " "
relative error = 1.085543676015998400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = 1.6744506654822522 " "
y[1] (numeric) = 1.6744506654824356 " "
absolute error = 1.83408843668075860000000000000E-13 " "
relative error = 1.095337398998572500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = 1.6839220357827571 " "
y[1] (numeric) = 1.6839220357829432 " "
absolute error = 1.86073378927176240000000000000E-13 " "
relative error = 1.10499996420963500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = 1.693425013616286 " "
y[1] (numeric) = 1.6934250136164748 " "
absolute error = 1.8873791418627660000000000000E-13 " "
relative error = 1.114533638446909100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = 1.702958648692975 " "
y[1] (numeric) = 1.7029586486931665 " "
absolute error = 1.914024494453770000000000000E-13 " "
relative error = 1.123940675789625400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = 1.7125219876572613 " "
y[1] (numeric) = 1.712521987657455 " "
absolute error = 1.9362289549462730000000000000E-13 " "
relative error = 1.130630128489646000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = 1.7221140741832173 " "
y[1] (numeric) = 1.7221140741834136 " "
absolute error = 1.96287430753727680000000000000E-13 " "
relative error = 1.139805043674734500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = 1.7317339490701844 " "
y[1] (numeric) = 1.731733949070383 " "
absolute error = 1.985078768029780000000000000E-13 " "
relative error = 1.146295462473102800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = 1.7413806503386902 " "
y[1] (numeric) = 1.7413806503388911 " "
absolute error = 2.00950367457153330000000000000E-13 " "
relative error = 1.153971519196963000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = 1.7510532133266465 " "
y[1] (numeric) = 1.75105321332685 " "
absolute error = 2.03392858111328680000000000000E-13 " "
relative error = 1.161545843172426700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = 1.7607506707858154 " "
y[1] (numeric) = 1.7607506707860214 " "
absolute error = 2.06057393370429050000000000000E-13 " "
relative error = 1.17028149862050900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = 1.7704720529785318 " "
y[1] (numeric) = 1.7704720529787403 " "
absolute error = 2.0849988402460440000000000000E-13 " "
relative error = 1.177651370852407400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = 1.7802163877746777 " "
y[1] (numeric) = 1.7802163877748887 " "
absolute error = 2.10942374678779740000000000000E-13 " "
relative error = 1.184925473820987900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = 1.7899827007488938 " "
y[1] (numeric) = 1.7899827007491074 " "
absolute error = 2.13606909937880120000000000000E-13 " "
relative error = 1.19334622534905600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = 1.7997700152780212 " "
y[1] (numeric) = 1.7997700152782374 " "
absolute error = 2.1627144519698050000000000000E-13 " "
relative error = 1.201661564316992800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = 1.8095773526387628 " "
y[1] (numeric) = 1.8095773526389818 " "
absolute error = 2.18935980456080870000000000000E-13 " "
relative error = 1.20987356598392400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = 1.8194037321055556 " "
y[1] (numeric) = 1.8194037321057774 " "
absolute error = 2.21822560320106280000000000000E-13 " "
relative error = 1.219204711993175600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = 1.8292481710486417 " "
y[1] (numeric) = 1.8292481710488662 " "
absolute error = 2.24487095579206650000000000000E-13 " "
relative error = 1.227209621592877200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = 1.8391096850323299 " "
y[1] (numeric) = 1.8391096850325572 " "
absolute error = 2.27373675443232060000000000000E-13 " "
relative error = 1.236324713494372200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = 1.8489872879134401 " "
y[1] (numeric) = 1.84898728791367 " "
absolute error = 2.2981616609740740000000000000E-13 " "
relative error = 1.242929941161208100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = 1.8588799919399155 " "
y[1] (numeric) = 1.858879991940148 " "
absolute error = 2.3248070135650778000000000000E-13 " "
relative error = 1.250649328437240200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = 1.8687868078495975 " "
y[1] (numeric) = 1.8687868078498322 " "
absolute error = 2.3470114740575810000000000000E-13 " "
relative error = 1.25590113553844800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = 1.8787067449691504 " "
y[1] (numeric) = 1.8787067449693877 " "
absolute error = 2.37365682664858470000000000000E-13 " "
relative error = 1.263452549475762900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = 1.888638811313129 " "
y[1] (numeric) = 1.8886388113133692 " "
absolute error = 2.4025226252888388000000000000E-13 " "
relative error = 1.272092160183035700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = 1.8985820136831755 " "
y[1] (numeric) = 1.8985820136834186 " "
absolute error = 2.4313884239290928000000000000E-13 " "
relative error = 1.28063386590937600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = 1.908535357767339 " "
y[1] (numeric) = 1.9085353577675845 " "
absolute error = 2.45581333047084630000000000000E-13 " "
relative error = 1.286752860237145000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = 1.9184978482395056 " "
y[1] (numeric) = 1.918497848239754 " "
absolute error = 2.482458683061850000000000000E-13 " "
relative error = 1.293959586840224300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = 1.9284684888589299 " "
y[1] (numeric) = 1.9284684888591812 " "
absolute error = 2.51354492775135440000000000000E-13 " "
relative error = 1.303389162059170000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = 1.938446282569859 " "
y[1] (numeric) = 1.9384462825701132 " "
absolute error = 2.54241072639160850000000000000E-13 " "
relative error = 1.311571411213446000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = 1.9484302316012365 " "
y[1] (numeric) = 1.9484302316014934 " "
absolute error = 2.5690560789826120000000000000E-13 " "
relative error = 1.31852608182502900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = 1.9584193375664791 " "
y[1] (numeric) = 1.9584193375667387 " "
absolute error = 2.5957014315736160000000000000E-13 " "
relative error = 1.325406352859556700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = 1.9684126015633148 " "
y[1] (numeric) = 1.9684126015635772 " "
absolute error = 2.624567230213870000000000000E-13 " "
relative error = 1.333342017892710500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = 1.9784090242736714 " "
y[1] (numeric) = 1.9784090242739365 " "
absolute error = 2.6512125828048740000000000000E-13 " "
relative error = 1.340073033572118400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = 1.9884076060636082 " "
y[1] (numeric) = 1.9884076060638758 " "
absolute error = 2.67563748934662700000000000000E-13 " "
relative error = 1.34561821287915300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = 1.9984073470832782 " "
y[1] (numeric) = 1.9984073470835488 " "
absolute error = 2.70672373403613160000000000000E-13 " "
relative error = 1.354440443779721700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = 2.008407247366913 " "
y[1] (numeric) = 2.008407247367187 " "
absolute error = 2.74003042477488630000000000000E-13 " "
relative error = 1.364280291443458500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = 2.0184063069328166 " "
y[1] (numeric) = 2.018406306933093 " "
absolute error = 2.76223488526738950000000000000E-13 " "
relative error = 1.368522718037330800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = 2.0284035258833657 " "
y[1] (numeric) = 2.028403525883644 " "
absolute error = 2.78443934575989260000000000000E-13 " "
relative error = 1.37272456403726400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = 2.038397904504996 " "
y[1] (numeric) = 2.0383979045052776 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 1.381244350883061900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 2.0483884433681743 " "
y[1] (numeric) = 2.048388443368458 " "
absolute error = 2.83773005094190000000000000E-13 " "
relative error = 1.385347618089373700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 2.058374143427339 " "
y[1] (numeric) = 2.0583741434276255 " "
absolute error = 2.8643754035329040000000000000E-13 " "
relative error = 1.391571795962961200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 2.068354006120806 " "
y[1] (numeric) = 2.0683540061210954 " "
absolute error = 2.89546164822240800000000000000E-13 " "
relative error = 1.3998868857332800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 2.078327033470622 " "
y[1] (numeric) = 2.0783270334709147 " "
absolute error = 2.92654789291191260000000000000E-13 " "
relative error = 1.408126750882336700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 2.0882922281823637 " "
y[1] (numeric) = 2.0882922281826586 " "
absolute error = 2.9487523534044160000000000000E-13 " "
relative error = 1.412040093627600600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 2.098248593744864 " "
y[1] (numeric) = 2.0982485937451614 " "
absolute error = 2.97539770599541950000000000000E-13 " "
relative error = 1.418038698972774200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 2.108195134529863 " "
y[1] (numeric) = 2.1081951345301633 " "
absolute error = 3.00204305858642330000000000000E-13 " "
relative error = 1.423987281545402400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 2.1181308558915712 " "
y[1] (numeric) = 2.118130855891874 " "
absolute error = 3.0286884111774270000000000000E-13 " "
relative error = 1.4298873002832400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 2.1280547642661327 " "
y[1] (numeric) = 2.1280547642664382 " "
absolute error = 3.0553337637684310000000000000E-13 " "
relative error = 1.43574019572850300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 2.1379658672709794 " "
y[1] (numeric) = 2.137965867271287 " "
absolute error = 3.0775382242609340000000000000E-13 " "
relative error = 1.439470232604451400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 2.14786317380407 " "
y[1] (numeric) = 2.1478631738043803 " "
absolute error = 3.10418357685193770000000000000E-13 " "
relative error = 1.445242702007937300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 2.1577456941429993 " "
y[1] (numeric) = 2.1577456941433115 " "
absolute error = 3.121947145245940000000000000E-13 " "
relative error = 1.446855926405125600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 2.1676124400439685 " "
y[1] (numeric) = 2.167612440044284 " "
absolute error = 3.1574742820339450000000000000E-13 " "
relative error = 1.456659974681589200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 2.1774624248406096 " "
y[1] (numeric) = 2.177462424840928 " "
absolute error = 3.1841196346249490000000000000E-13 " "
relative error = 1.462307499913816600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 2.187294663542652 " "
y[1] (numeric) = 2.187294663542972 " "
absolute error = 3.20188320301895150000000000000E-13 " "
relative error = 1.46385544498747200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 2.1971081729344184 " "
y[1] (numeric) = 2.197108172934741 " "
absolute error = 3.22408766351145460000000000000E-13 " "
relative error = 1.467423271747890500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 2.2069019716731475 " "
y[1] (numeric) = 2.206901971673473 " "
absolute error = 3.2551739082009590000000000000E-13 " "
relative error = 1.474997054687060300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 2.2166750803871267 " "
y[1] (numeric) = 2.2166750803874558 " "
absolute error = 3.2907010449889640000000000000E-13 " "
relative error = 1.48452115247051300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 2.2264265217736297 " "
y[1] (numeric) = 2.226426521773961 " "
absolute error = 3.3129055054814670000000000000E-13 " "
relative error = 1.487992293068050600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 2.236155320696643 " "
y[1] (numeric) = 2.2361553206969775 " "
absolute error = 3.34399175017097150000000000000E-13 " "
relative error = 1.495420161211877300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 2.2458605042843827 " "
y[1] (numeric) = 2.24586050428472 " "
absolute error = 3.3750779948604760000000000000E-13 " "
relative error = 1.502799478606043300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 2.2555411020265765 " "
y[1] (numeric) = 2.255541102026917 " "
absolute error = 3.40616423954998000000000000000E-13 " "
relative error = 1.510131753524501500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 2.265196145871518 " "
y[1] (numeric) = 2.2651961458718617 " "
absolute error = 3.43725048423948460000000000000E-13 " "
relative error = 1.51741847632229100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 2.2748246703228685 " "
y[1] (numeric) = 2.2748246703232144 " "
absolute error = 3.4594549447319880000000000000E-13 " "
relative error = 1.520756737810911300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 2.2844257125362066 " "
y[1] (numeric) = 2.2844257125365552 " "
absolute error = 3.48610029732299150000000000000E-13 " "
relative error = 1.526029180197182300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 2.2939983124153116 " "
y[1] (numeric) = 2.293998312415663 " "
absolute error = 3.51274564991399530000000000000E-13 " "
relative error = 1.531276475184275600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 2.303541512708173 " "
y[1] (numeric) = 2.303541512708527 " "
absolute error = 3.5393910025049990000000000000E-13 " "
relative error = 1.536499769150629000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 2.313054359102714 " "
y[1] (numeric) = 2.3130543591030706 " "
absolute error = 3.5660363550960030000000000000E-13 " "
relative error = 1.541700194404142200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 2.3225359003222223 " "
y[1] (numeric) = 2.322535900322582 " "
absolute error = 3.5971225997855070000000000000E-13 " "
relative error = 1.548790957025229200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 2.3319851882204774 " "
y[1] (numeric) = 2.3319851882208398 " "
absolute error = 3.6237679523765110000000000000E-13 " "
relative error = 1.55394123885571700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 2.341401277876564 " "
y[1] (numeric) = 2.341401277876929 " "
absolute error = 3.65041330496751470000000000000E-13 " "
relative error = 1.559072056319241700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 2.3507832276893628 " "
y[1] (numeric) = 2.3507832276897305 " "
absolute error = 3.67705865755851850000000000000E-13 " "
relative error = 1.564184487215685000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 2.360130099471711 " "
y[1] (numeric) = 2.3601300994720815 " "
absolute error = 3.7037040101495220000000000000E-13 " "
relative error = 1.569279596484344200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 2.36944095854422 " "
y[1] (numeric) = 2.3694409585445926 " "
absolute error = 3.72590847064202530000000000000E-13 " "
relative error = 1.572484200210338400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 2.378714873828741 " "
y[1] (numeric) = 2.3787148738291166 " "
absolute error = 3.75699471533153000000000000000E-13 " "
relative error = 1.579422047033460500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 2.387950917941473 " "
y[1] (numeric) = 2.387950917941852 " "
absolute error = 3.7880809600210340000000000000E-13 " "
relative error = 1.586331164330018800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 2.397148167285703 " "
y[1] (numeric) = 2.3971481672860846 " "
absolute error = 3.8147263126120380000000000000E-13 " "
relative error = 1.591360252433399500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 2.40630570214416 " "
y[1] (numeric) = 2.4063057021445444 " "
absolute error = 3.84581255730154200000000000000E-13 " "
relative error = 1.59822276690559180000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 2.4154226067709894 " "
y[1] (numeric) = 2.4154226067713767 " "
absolute error = 3.8724579098925460000000000000E-13 " "
relative error = 1.603221688427171600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 2.424497969483326 " "
y[1] (numeric) = 2.4244979694837157 " "
absolute error = 3.8946623703850490000000000000E-13 " "
relative error = 1.60637889551007700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 2.4335308827524615 " "
y[1] (numeric) = 2.4335308827528532 " "
absolute error = 3.91686683087755200000000000000E-13 " "
relative error = 1.609540630299030300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 2.4425204432945966 " "
y[1] (numeric) = 2.442520443294991 " "
absolute error = 3.9435121834685560000000000000E-13 " "
relative error = 1.614525763456597700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 2.451465752161168 " "
y[1] (numeric) = 2.451465752161565 " "
absolute error = 3.970157536059560000000000000E-13 " "
relative error = 1.619503569470445000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 2.460365914828743 " "
y[1] (numeric) = 2.460365914829143 " "
absolute error = 4.0012437807490640000000000000E-13 " "
relative error = 1.626279959673224700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 2.469220041288472 " "
y[1] (numeric) = 2.469220041288875 " "
absolute error = 4.0278891333400680000000000000E-13 " "
relative error = 1.631239446460292500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 2.4780272461350883 " "
y[1] (numeric) = 2.4780272461354937 " "
absolute error = 4.05453448593107170000000000000E-13 " "
relative error = 1.63619447375117380000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 2.4867866486554453 " "
y[1] (numeric) = 2.486786648655854 " "
absolute error = 4.0856207306205760000000000000E-13 " "
relative error = 1.64293174600627200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 2.4954973729165912 " "
y[1] (numeric) = 2.4954973729170025 " "
absolute error = 4.112266083211580000000000000E-13 " "
relative error = 1.647874338735690300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 2.5041585478533586 " "
y[1] (numeric) = 2.504158547853771 " "
absolute error = 4.12558875950708170000000000000E-13 " "
relative error = 1.647495029036265500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 2.5127693073554713 " "
y[1] (numeric) = 2.512769307355886 " "
absolute error = 4.1477932199995850000000000000E-13 " "
relative error = 1.650686041037675600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 2.5213287903541546 " "
y[1] (numeric) = 2.521328790354572 " "
absolute error = 4.17443857259058860000000000000E-13 " "
relative error = 1.65565022243855500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 2.529836140908242 " "
y[1] (numeric) = 2.529836140908662 " "
absolute error = 4.20108392518159230000000000000E-13 " "
relative error = 1.660615032431844700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 2.5382905082897667 " "
y[1] (numeric) = 2.5382905082901894 " "
absolute error = 4.2277292777725960000000000000E-13 " "
relative error = 1.66558132883738700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 2.5466910470690367 " "
y[1] (numeric) = 2.5466910470694613 " "
absolute error = 4.24549284616659860000000000000E-13 " "
relative error = 1.667062383186487300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 2.5550369171991747 " "
y[1] (numeric) = 2.5550369171996015 " "
absolute error = 4.26769730665910200000000000000E-13 " "
relative error = 1.67030749259675700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 2.5633272841001213 " "
y[1] (numeric) = 2.563327284100551 " "
absolute error = 4.2987835513486060000000000000E-13 " "
relative error = 1.677032651278368400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 2.571561318742096 " "
y[1] (numeric) = 2.571561318742529 " "
absolute error = 4.32986979603811050000000000000E-13 " "
relative error = 1.68375133211138400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 2.579738197728496 " "
y[1] (numeric) = 2.5797381977289313 " "
absolute error = 4.35207425653061360000000000000E-13 " "
relative error = 1.68702167544082200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 2.5878571033782367 " "
y[1] (numeric) = 2.587857103378674 " "
absolute error = 4.3742787170231170000000000000E-13 " "
relative error = 1.69030921812214900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 2.5959172238075188 " "
y[1] (numeric) = 2.5959172238079584 " "
absolute error = 4.396483177515620000000000000E-13 " "
relative error = 1.693614548720914500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 2.6039177530110162 " "
y[1] (numeric) = 2.603917753011458 " "
absolute error = 4.4186876380081230000000000000E-13 " "
relative error = 1.696938251178868600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 2.611857890942476 " "
y[1] (numeric) = 2.6118578909429204 " "
absolute error = 4.4453329905991270000000000000E-13 " "
relative error = 1.701981185888735400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 2.619736843594721 " "
y[1] (numeric) = 2.6197368435951685 " "
absolute error = 4.4764192352886310000000000000E-13 " "
relative error = 1.7087285870844300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 2.6275538230790523 " "
y[1] (numeric) = 2.627553823079502 " "
absolute error = 4.49862369578113430000000000000E-13 " "
relative error = 1.712095735686777500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 2.6353080477040356 " "
y[1] (numeric) = 2.6353080477044877 " "
absolute error = 4.52082815627363740000000000000E-13 " "
relative error = 1.71548375918038400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 2.64299874205367 " "
y[1] (numeric) = 2.6429987420541248 " "
absolute error = 4.5474735088646410000000000000E-13 " "
relative error = 1.72057346698967800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 2.65062513706493 " "
y[1] (numeric) = 2.650625137065387 " "
absolute error = 4.5696779693571443000000000000E-13 " "
relative error = 1.724000087925373600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 2.6581864701046687 " "
y[1] (numeric) = 2.6581864701051283 " "
absolute error = 4.5963233219481480000000000000E-13 " "
relative error = 1.729119974704845800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 2.665681985045884 " "
y[1] (numeric) = 2.6656819850463465 " "
absolute error = 4.6229686745391520000000000000E-13 " "
relative error = 1.734253635832549200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 2.6731109323433278 " "
y[1] (numeric) = 2.6731109323437923 " "
absolute error = 4.6451731350316550000000000000E-13 " "
relative error = 1.737740502583467200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 2.680472569108461 " "
y[1] (numeric) = 2.680472569108928 " "
absolute error = 4.6673775955241580000000000000E-13 " "
relative error = 1.74125176631691890000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 2.6877661591837425 " "
y[1] (numeric) = 2.687766159184211 " "
absolute error = 4.6851411639181606000000000000E-13 " "
relative error = 1.743135706917676200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 2.694990973216242 " "
y[1] (numeric) = 2.694990973216713 " "
absolute error = 4.7117865165091644000000000000E-13 " "
relative error = 1.748349646932601300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 2.702146288730577 " "
y[1] (numeric) = 2.702146288731051 " "
absolute error = 4.7384318691001680000000000000E-13 " "
relative error = 1.753580806806060700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 2.7092313902011593 " "
y[1] (numeric) = 2.7092313902016345 " "
absolute error = 4.751754545395670000000000000E-13 " "
relative error = 1.753912405777512400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 2.7162455691237453 " "
y[1] (numeric) = 2.716245569124222 " "
absolute error = 4.7695181137896725000000000000E-13 " "
relative error = 1.755923016683763600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 2.7231881240862883 " "
y[1] (numeric) = 2.723188124086768 " "
absolute error = 4.7961634663806760000000000000E-13 " "
relative error = 1.76123104531749300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 2.7300583608390774 " "
y[1] (numeric) = 2.730058360839559 " "
absolute error = 4.8183679268731794000000000000E-13 " "
relative error = 1.764932206574611200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 2.7368555923641624 " "
y[1] (numeric) = 2.736855592364647 " "
absolute error = 4.8450132794641830000000000000E-13 " "
relative error = 1.770284589724715200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 2.743579138944056 " "
y[1] (numeric) = 2.743579138944542 " "
absolute error = 4.8627768478581856000000000000E-13 " "
relative error = 1.772420842115661800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 2.7502283282297015 " "
y[1] (numeric) = 2.75022832823019 " "
absolute error = 4.8849813083506890000000000000E-13 " "
relative error = 1.776209363494960800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 2.7568024953077126 " "
y[1] (numeric) = 2.7568024953082033 " "
absolute error = 4.9071857688431920000000000000E-13 " "
relative error = 1.780028049595716300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 2.7633009827668626 " "
y[1] (numeric) = 2.763300982767352 " "
absolute error = 4.893863092547690000000000000E-13 " "
relative error = 1.77102064634577700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 2.769723140763818 " "
y[1] (numeric) = 2.7697231407643064 " "
absolute error = 4.8849813083506890000000000000E-13 " "
relative error = 1.763707439366498400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 2.776068327088131 " "
y[1] (numeric) = 2.7760683270886184 " "
absolute error = 4.8760995241536875000000000000E-13 " "
relative error = 1.756476768447669300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 2.782335907226456 " "
y[1] (numeric) = 2.7823359072269436 " "
absolute error = 4.8760995241536875000000000000E-13 " "
relative error = 1.752520071889658900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 2.788525254426003 " "
y[1] (numeric) = 2.78852525442649 " "
absolute error = 4.8716586320551870000000000000E-13 " "
relative error = 1.747037658820838600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 2.794635749757209 " "
y[1] (numeric) = 2.7946357497576955 " "
absolute error = 4.8627768478581856000000000000E-13 " "
relative error = 1.74003959130654200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 2.800666782175634 " "
y[1] (numeric) = 2.80066678217612 " "
absolute error = 4.8583359557596850000000000000E-13 " "
relative error = 1.73470688718834230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 2.8066177485830615 " "
y[1] (numeric) = 2.806617748583547 " "
absolute error = 4.8538950636611844000000000000E-13 " "
relative error = 1.729446436413260600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 2.81248805388781 " "
y[1] (numeric) = 2.8124880538882953 " "
absolute error = 4.8538950636611844000000000000E-13 " "
relative error = 1.72583668647106230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 2.81827711106424 " "
y[1] (numeric) = 2.8182771110647256 " "
absolute error = 4.8538950636611844000000000000E-13 " "
relative error = 1.72229162441313400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 2.82398434121146 " "
y[1] (numeric) = 2.8239843412119447 " "
absolute error = 4.8494541715626840000000000000E-13 " "
relative error = 1.71723833620207630000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 2.8296091736112094 " "
y[1] (numeric) = 2.829609173611695 " "
absolute error = 4.8538950636611844000000000000E-13 " "
relative error = 1.715394164299565400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 2.835151045784936 " "
y[1] (numeric) = 2.835151045785422 " "
absolute error = 4.8583359557596850000000000000E-13 " "
relative error = 1.713607450644525600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 2.8406094035500415 " "
y[1] (numeric) = 2.8406094035505265 " "
absolute error = 4.8494541715626840000000000000E-13 " "
relative error = 1.707187959563217500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 2.8459837010752973 " "
y[1] (numeric) = 2.8459837010757822 " "
absolute error = 4.8494541715626840000000000000E-13 " "
relative error = 1.7039641406696798000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 2.8512734009354297 " "
y[1] (numeric) = 2.851273400935914 " "
absolute error = 4.8450132794641830000000000000E-13 " "
relative error = 1.699245424123361500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 2.8564779741648603 " "
y[1] (numeric) = 2.8564779741653448 " "
absolute error = 4.8450132794641830000000000000E-13 " "
relative error = 1.696149357104951600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = 2.861596900310604 " "
y[1] (numeric) = 2.8615969003110884 " "
absolute error = 4.8450132794641830000000000000E-13 " "
relative error = 1.693115224907566200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 2.8666296674843115 " "
y[1] (numeric) = 2.866629667484795 " "
absolute error = 4.8361314952671820000000000000E-13 " "
relative error = 1.68704438878959220000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 2.8715757724134594 " "
y[1] (numeric) = 2.871575772413943 " "
absolute error = 4.8361314952671820000000000000E-13 " "
relative error = 1.68413856312855800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 2.8764347204916767 " "
y[1] (numeric) = 2.8764347204921603 " "
absolute error = 4.8361314952671820000000000000E-13 " "
relative error = 1.681293672620016400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 2.881206025828204 " "
y[1] (numeric) = 2.8812060258286887 " "
absolute error = 4.8450132794641830000000000000E-13 " "
relative error = 1.681592095820874700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 2.8858892112964853 " "
y[1] (numeric) = 2.88588921129697 " "
absolute error = 4.8450132794641830000000000000E-13 " "
relative error = 1.678863228878963700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 2.890483808581875 " "
y[1] (numeric) = 2.8904838085823608 " "
absolute error = 4.8583359557596850000000000000E-13 " "
relative error = 1.680803726121986300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 2.894989358228474 " "
y[1] (numeric) = 2.8949893582289605 " "
absolute error = 4.8672177399566860000000000000E-13 " "
relative error = 1.681255831259799700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 2.8994054096850714 " "
y[1] (numeric) = 2.899405409685559 " "
absolute error = 4.8760995241536875000000000000E-13 " "
relative error = 1.68175844187423320000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 2.903731521350203 " "
y[1] (numeric) = 2.9037315213506902 " "
absolute error = 4.8716586320551870000000000000E-13 " "
relative error = 1.677723507230420600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 2.9079672606163065 " "
y[1] (numeric) = 2.9079672606167946 " "
absolute error = 4.8805404162521880000000000000E-13 " "
relative error = 1.6783340315935400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 2.9121122039129848 " "
y[1] (numeric) = 2.912112203913474 " "
absolute error = 4.893863092547690000000000000E-13 " "
relative error = 1.680520100143064700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 2.916165936749363 " "
y[1] (numeric) = 2.916165936749853 " "
absolute error = 4.9027448767446913000000000000E-13 " "
relative error = 1.68122973214952200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 2.920128053755535 " "
y[1] (numeric) = 2.9201280537560264 " "
absolute error = 4.9116266609416925000000000000E-13 " "
relative error = 1.68199016293991600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 2.9239981587231028 " "
y[1] (numeric) = 2.9239981587235953 " "
absolute error = 4.9249493372371944000000000000E-13 " "
relative error = 1.684320259417638700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 2.9277758646447936 " "
y[1] (numeric) = 2.9277758646452874 " "
absolute error = 4.9382720135326963000000000000E-13 " "
relative error = 1.686697425566701400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 2.931460793753164 " "
y[1] (numeric) = 2.931460793753659 " "
absolute error = 4.9515946898281980000000000000E-13 " "
relative error = 1.689121921869078400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 2.935052577558374 " "
y[1] (numeric) = 2.93505257755887 " "
absolute error = 4.9604764740251994000000000000E-13 " "
relative error = 1.69008095866948500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 2.9385508568850356 " "
y[1] (numeric) = 2.9385508568855334 " "
absolute error = 4.9782400424192020000000000000E-13 " "
relative error = 1.694113964628234000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 2.9419552819081316 " "
y[1] (numeric) = 2.9419552819086316 " "
absolute error = 5.0004445029117050000000000000E-13 " "
relative error = 1.699701057205890400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = 2.9452655121879974 " "
y[1] (numeric) = 2.9452655121884987 " "
absolute error = 5.0137671792072070000000000000E-13 " "
relative error = 1.7023141575723500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 2.9484812167043626 " "
y[1] (numeric) = 2.9484812167048657 " "
absolute error = 5.0315307476012090000000000000E-13 " "
relative error = 1.706482211619837200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 2.9516020738894557 " "
y[1] (numeric) = 2.95160207388996 " "
absolute error = 5.0448534238967110000000000000E-13 " "
relative error = 1.709191583962023400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 2.954627771660159 " "
y[1] (numeric) = 2.954627771660665 " "
absolute error = 5.0581761001922130000000000000E-13 " "
relative error = 1.711950367727743400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 2.9575580074492165 " "
y[1] (numeric) = 2.957558007449724 " "
absolute error = 5.0759396685862160000000000000E-13 " "
relative error = 1.716260393135627400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 2.9603924882354917 " "
y[1] (numeric) = 2.960392488236001 " "
absolute error = 5.0937032369802180000000000000E-13 " "
relative error = 1.72061753879677700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 2.9631309305732674 " "
y[1] (numeric) = 2.963130930573779 " "
absolute error = 5.1159076974727210000000000000E-13 " "
relative error = 1.726520973031375200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 2.9657730606205925 " "
y[1] (numeric) = 2.965773060621106 " "
absolute error = 5.1336712658667240000000000000E-13 " "
relative error = 1.73097238424321500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 2.9683186141666633 " "
y[1] (numeric) = 2.968318614167179 " "
absolute error = 5.1558757263592270000000000000E-13 " "
relative error = 1.736968431135451600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 2.970767336658247 " "
y[1] (numeric) = 2.970767336658764 " "
absolute error = 5.1691984026547290000000000000E-13 " "
relative error = 1.740021286375610400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 2.9731189832251346 " "
y[1] (numeric) = 2.973118983225654 " "
absolute error = 5.1958437552457330000000000000E-13 " "
relative error = 1.747607070070725500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 2.97537331870463 " "
y[1] (numeric) = 2.975373318705152 " "
absolute error = 5.2180482157382360000000000000E-13 " "
relative error = 1.753745717532341200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 2.977530117665063 " "
y[1] (numeric) = 2.977530117665587 " "
absolute error = 5.2402526762307390000000000000E-13 " "
relative error = 1.75993271911555700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 2.9795891644283348 " "
y[1] (numeric) = 2.9795891644288615 " "
absolute error = 5.2668980288217430000000000000E-13 " "
relative error = 1.7676591429786098000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 2.981550253091486 " "
y[1] (numeric) = 2.981550253092014 " "
absolute error = 5.2802207051172450000000000000E-13 " "
relative error = 1.77096485281183200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 2.983413187547283 " "
y[1] (numeric) = 2.9834131875478134 " "
absolute error = 5.3024251656097480000000000000E-13 " "
relative error = 1.777301644888472600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 2.985177781503834 " "
y[1] (numeric) = 2.9851777815043663 " "
absolute error = 5.3246296261022510000000000000E-13 " "
relative error = 1.783689286143580500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = 2.986843858503213 " "
y[1] (numeric) = 2.986843858503747 " "
absolute error = 5.3423931944962530000000000000E-13 " "
relative error = 1.788641605515150200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = 2.988411251939109 " "
y[1] (numeric) = 2.9884112519396457 " "
absolute error = 5.3690385470872570000000000000E-13 " "
relative error = 1.796619706743312300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = 2.989879805073484 " "
y[1] (numeric) = 2.989879805074023 " "
absolute error = 5.391243007579760000000000000E-13 " "
relative error = 1.803163792213799700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = 2.991249371052249 " "
y[1] (numeric) = 2.9912493710527897 " "
absolute error = 5.4045656838752620000000000000E-13 " "
relative error = 1.806792083661706300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = 2.992519812919947 " "
y[1] (numeric) = 2.9925198129204906 " "
absolute error = 5.4356519285647660000000000000E-13 " "
relative error = 1.81641301257114700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = 2.99369100363345 " "
y[1] (numeric) = 2.993691003633996 " "
absolute error = 5.457856389057270000000000000E-13 " "
relative error = 1.823119481079729400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = 2.9947628260746626 " "
y[1] (numeric) = 2.9947628260752115 " "
absolute error = 5.4889426337467740000000000000E-13 " "
relative error = 1.832847191088356500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = 2.995735173062234 " "
y[1] (numeric) = 2.995735173062786 " "
absolute error = 5.5200288784362780000000000000E-13 " "
relative error = 1.84262912425390280000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = 2.9966079473622758 " "
y[1] (numeric) = 2.996607947362831 " "
absolute error = 5.5511151231257830000000000000E-13 " "
relative error = 1.852466262065438600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = 2.9973810616980847 " "
y[1] (numeric) = 2.997381061698643 " "
absolute error = 5.5822013678152870000000000000E-13 " "
relative error = 1.862359590893272500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = 2.9980544387588726 " "
y[1] (numeric) = 2.9980544387594334 " "
absolute error = 5.6088467204062910000000000000E-13 " "
relative error = 1.870828844164760300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = 2.9986280112074932 " "
y[1] (numeric) = 2.9986280112080577 " "
absolute error = 5.6443738571942960000000000000E-13 " "
relative error = 1.882318792493841000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = 2.9991017216871803 " "
y[1] (numeric) = 2.9991017216877482 " "
absolute error = 5.6799009939823010000000000000E-13 " "
relative error = 1.89386740466642300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = 2.9994755228272805 " "
y[1] (numeric) = 2.999475522827852 " "
absolute error = 5.7154281307703060000000000000E-13 " "
relative error = 1.905475836449897500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = 2.9997493772479915 " "
y[1] (numeric) = 2.9997493772485666 " "
absolute error = 5.7509552675583110000000000000E-13 " "
relative error = 1.917145249258893600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = 2.9999232575640997 " "
y[1] (numeric) = 2.999923257564678 " "
absolute error = 5.7820415122478150000000000000E-13 " "
relative error = 1.92739647511608700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = 2.9999971463877175 " "
y[1] (numeric) = 2.9999971463882997 " "
absolute error = 5.8220095411343210000000000000E-13 " "
relative error = 1.940671693019633300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = 2.999971036330025 " "
y[1] (numeric) = 2.9999710363306105 " "
absolute error = 5.8530957858238250000000000000E-13 " "
relative error = 1.95105076513809700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = 2.999844930002006 " "
y[1] (numeric) = 2.999844930002595 " "
absolute error = 5.888622922611830000000000000E-13 " "
relative error = 1.962975773753709900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = 2.999618840014188 " "
y[1] (numeric) = 2.9996188400147807 " "
absolute error = 5.9285909514983360000000000000E-13 " "
relative error = 1.976448098142460600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = 2.9992927889753807 " "
y[1] (numeric) = 2.9992927889759784 " "
absolute error = 5.9774407645818430000000000000E-13 " "
relative error = 1.992950066946901400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = 2.998866809490418 " "
y[1] (numeric) = 2.998866809491019 " "
absolute error = 6.0129679013698480000000000000E-13 " "
relative error = 2.005080013003845400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = 2.998340944156892 " "
y[1] (numeric) = 2.9983409441574964 " "
absolute error = 6.0440541460593520000000000000E-13 " "
relative error = 2.0157994899939200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = 2.997715245560898 " "
y[1] (numeric) = 2.9977152455615057 " "
absolute error = 6.0751403907488570000000000000E-13 " "
relative error = 2.026590217247984700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = 2.9969897762717745 " "
y[1] (numeric) = 2.996989776272386 " "
absolute error = 6.1151084196353620000000000000E-13 " "
relative error = 2.040416843611157200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = 2.996164608835846 " "
y[1] (numeric) = 2.9961646088364615 " "
absolute error = 6.1550764485218680000000000000E-13 " "
relative error = 2.054318521208823600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = 2.9952398257691684 " "
y[1] (numeric) = 2.995239825769788 " "
absolute error = 6.1950444774083730000000000000E-13 " "
relative error = 2.068296643263784200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = 2.9942155195492774 " "
y[1] (numeric) = 2.994215519549902 " "
absolute error = 6.243894290491880000000000000E-13 " "
relative error = 2.08531892568367300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = 2.9930917926059415 " "
y[1] (numeric) = 2.99309179260657 " "
absolute error = 6.2838623193783860000000000000E-13 " "
relative error = 2.099455263918694500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = 2.991868757310919 " "
y[1] (numeric) = 2.9918687573115514 " "
absolute error = 6.3238303482648920000000000000E-13 " "
relative error = 2.113672377109458400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = 2.9905465359667196 " "
y[1] (numeric) = 2.990546535967357 " "
absolute error = 6.3726801613483990000000000000E-13 " "
relative error = 2.130941647189039700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = 2.989125260794376 " "
y[1] (numeric) = 2.989125260795018 " "
absolute error = 6.4215299744319050000000000000E-13 " "
relative error = 2.148297382735091500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = 2.9876050739202213 " "
y[1] (numeric) = 2.987605073920868 " "
absolute error = 6.4659388954169120000000000000E-13 " "
relative error = 2.164254891605386600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = 2.9859861273616763 " "
y[1] (numeric) = 2.9859861273623274 " "
absolute error = 6.5103478164019180000000000000E-13 " "
relative error = 2.180300757845200200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = 2.9842685830120472 " "
y[1] (numeric) = 2.9842685830127036 " "
absolute error = 6.5636385215839250000000000000E-13 " "
relative error = 2.199412800492370800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = 2.982452612624338 " "
y[1] (numeric) = 2.982452612624999 " "
absolute error = 6.6124883346674320000000000000E-13 " "
relative error = 2.217131064103959300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = 2.980538397794074 " "
y[1] (numeric) = 2.9805383977947404 " "
absolute error = 6.665779039849440000000000000E-13 " "
relative error = 2.236434546450685000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = 2.978526129941143 " "
y[1] (numeric) = 2.978526129941814 " "
absolute error = 6.7101879608344460000000000000E-13 " "
relative error = 2.252855159933427300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = 2.976416010290654 " "
y[1] (numeric) = 2.97641601029133 " "
absolute error = 6.7590377739179530000000000000E-13 " "
relative error = 2.270864607148083700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = 2.9742082498528126 " "
y[1] (numeric) = 2.9742082498534943 " "
absolute error = 6.8167693711984610000000000000E-13 " "
relative error = 2.291961019049627600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = 2.9719030694018236 " "
y[1] (numeric) = 2.9719030694025106 " "
absolute error = 6.8700600763804690000000000000E-13 " "
relative error = 2.311670305506718600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = 2.969500699453811 " "
y[1] (numeric) = 2.969500699454503 " "
absolute error = 6.9189098894639760000000000000E-13 " "
relative error = 2.329990995030441200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = 2.9670013802437674 " "
y[1] (numeric) = 2.967001380244465 " "
absolute error = 6.9766414867444840000000000000E-13 " "
relative error = 2.35141160809682100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = 2.964405361701531 " "
y[1] (numeric) = 2.9644053617022346 " "
absolute error = 7.0343730840249920000000000000E-13 " "
relative error = 2.37294574315145300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = 2.9617129034267933 " "
y[1] (numeric) = 2.9617129034275016 " "
absolute error = 7.0832228971084990000000000000E-13 " "
relative error = 2.391596730700329400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 2 ) = sin ( x ) ; "
Iterations = 4900
"Total Elapsed Time "= 2 Minutes 27 Seconds
"Elapsed Time(since restart) "= 2 Minutes 27 Seconds
"Time to Timeout "= 32 Seconds
Percent Done = 100.0204081632654 "%"
(%o254) temp/diffeq.h2sin.max