(%i1) batch("temp/diffeq.sin_lg_h.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sin_lg_h.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,[2,40],convfloat)
(%i191) completearray(array_y_higher_work,[2,40],convfloat)
(%i192) completearray(array_y_higher_work2,[2,40],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)-cos(c(x)))
(%o238) exact_soln_y(x) := block(c(2.0) - cos(c(x)))
(%i239) 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)
(%i240) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i241) 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)
(%i242) 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)
(%i243) 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))
(%i244) 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))
(%i245) 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)
(%i246) 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)
(%i247) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i248) 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[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp2[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_tmp1_g[1]*array_x[2]/c(1),
array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1),
array_tmp2[2]:array_tmp1[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp2[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_tmp1_g[2]*array_x[2]/c(2),
array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2),
array_tmp2[3]:array_tmp1[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp2[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_tmp1_g[3]*array_x[2]/c(3),
array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3),
array_tmp2[4]:array_tmp1[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp2[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_tmp1_g[4]*array_x[2]/c(4),
array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4),
array_tmp2[5]:array_tmp1[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp2[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp1_g[kkk]
:neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1),
array_tmp2[kkk]:array_tmp1[kkk],order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_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)
(%i249) exact_soln_y(x):=block(c(2.0)-cos(c(x)))
(%o249) exact_soln_y(x) := block(c(2.0) - cos(c(x)))
(%i250) 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:16,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 <= 2 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1_g),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_m1),zero_ats_ar(array_const_1),
array_const_1[1]:c(1),zero_ats_ar(array_const_0D0),
array_const_0D0[1]:c(0.0),zero_ats_ar(array_m1),
array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/sin_lg_hpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = sin ( x ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,""),omniout_str(always,"Digits:16,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,""),
omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,""),
omniout_str(always,"x_start:c(0.0),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_max_h:c(1.0),"),
omniout_str(always,"glob_min_h:c(1.0),"),
omniout_str(always,"glob_display_interval:c(1.0),"),
omniout_str(always,""),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,""),
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,""),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always,""),
omniout_str(always," (c(2.0) - cos(c(x))) "),
omniout_str(always,""),omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.0),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:false,glob_max_h:c(1.0),glob_min_h:c(1.0),
glob_display_interval:c(1.0),glob_type_given_pole:3,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = sin ( x ) ; "),
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,
"2015-04-24T22:26:49-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sin_lg_h"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 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,
"sin_lg_h diffeq.max"),
logitem_str(html_log_file,
"sin_lg_h maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i251) main():=(glob_iolevel:2,compile(all),main_prog())
(%i252) 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_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_max_h (declared type convfloat) assigned type any.
warning: variable glob_min_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
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: 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/sin_lg_hpostode.ode#################"
"diff ( y , x , 1 ) = sin ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
""
"Digits:16,"
"max_terms:40,"
""
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
""
"x_start:c(0.0),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:false,"
"glob_max_h:c(1.0),"
"glob_min_h:c(1.0),"
"glob_display_interval:c(1.0),"
""
""
""
""
""
""
""
""
"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) - cos(c(x))) "
""
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.0 " "
y[1] (closed_form) = 1. " "
y[1] (numeric) = 1. " "
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] = 1.000000000000000200E-2 " "
y[1] (closed_form) = 1.0000499995833347 " "
y[1] (numeric) = 1.0000499995833345 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.220335033423778400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.00000000000000120E-2 " "
y[1] (closed_form) = 1.0001999933334222 " "
y[1] (numeric) = 1.0001999933334222 " "
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] = 3.00000000000000200E-2 " "
y[1] (closed_form) = 1.0004499662510125 " "
y[1] (numeric) = 1.0004499662510125 " "
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] = 4.00000000000000300E-2 " "
y[1] (closed_form) = 1.000799893339022 " "
y[1] (numeric) = 1.000799893339022 " "
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] = 5.00000000000000300E-2 " "
y[1] (closed_form) = 1.0012497396050337 " "
y[1] (numeric) = 1.0012497396050337 " "
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] = 6.000000000000004000E-2 " "
y[1] (closed_form) = 1.0017994600647957 " "
y[1] (numeric) = 1.001799460064796 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.216457622273719500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000000500E-2 " "
y[1] (closed_form) = 1.0024489997467203 " "
y[1] (numeric) = 1.0024489997467205 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.215021462250282300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000000600E-2 " "
y[1] (closed_form) = 1.0031982936973807 " "
y[1] (numeric) = 1.003198293697381 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.213367051359958500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000000700E-2 " "
y[1] (closed_form) = 1.0040472669880058 " "
y[1] (numeric) = 1.004047266988006 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21149553637183300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000007 " "
y[1] (closed_form) = 1.0049958347219743 " "
y[1] (numeric) = 1.0049958347219747 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.4188164219896203000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000008 " "
y[1] (closed_form) = 1.0060439020433032 " "
y[1] (numeric) = 1.0060439020433034 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.2071065136824800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000009 " "
y[1] (closed_form) = 1.0071913641461339 " "
y[1] (numeric) = 1.007191364146134 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.204592025203412400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1300000000000001 " "
y[1] (closed_form) = 1.0084381062852121 " "
y[1] (numeric) = 1.0084381062852121 " "
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] = 0.1400000000000001 " "
y[1] (closed_form) = 1.0097840037873629 " "
y[1] (numeric) = 1.0097840037873633 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.397863386471088700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1500000000000001 " "
y[1] (closed_form) = 1.0112289220639576 " "
y[1] (numeric) = 1.011228922063958 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.39157939572831100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000011 " "
y[1] (closed_form) = 1.0127727166243732 " "
y[1] (numeric) = 1.0127727166243738 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.57732780357032500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000012 " "
y[1] (closed_form) = 1.0144152330904395 " "
y[1] (numeric) = 1.01441523309044 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.37778530293886200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000013 " "
y[1] (closed_form) = 1.0161563072118787 " "
y[1] (numeric) = 1.016156307211879 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.37028444047698700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000014 " "
y[1] (closed_form) = 1.0179957648827296 " "
y[1] (numeric) = 1.0179957648827305 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.72477519395614600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000015 " "
y[1] (closed_form) = 1.0199334221587584 " "
y[1] (numeric) = 1.0199334221587595 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.08852499634269660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000016 " "
y[1] (closed_form) = 1.0219690852758518 " "
y[1] (numeric) = 1.021969085275853 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0863567603177380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000017 " "
y[1] (closed_form) = 1.0241025506693946 " "
y[1] (numeric) = 1.0241025506693961 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.51773104505916740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000018 " "
y[1] (closed_form) = 1.0263336049946252 " "
y[1] (numeric) = 1.026333604994627 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.73077918403495430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000019 " "
y[1] (closed_form) = 1.0286620251479706 " "
y[1] (numeric) = 1.0286620251479726 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.94271917837913420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25000000000000017 " "
y[1] (closed_form) = 1.0310875782893554 " "
y[1] (numeric) = 1.0310875782893572 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.72279918486395480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000002 " "
y[1] (closed_form) = 1.0336100218654867 " "
y[1] (numeric) = 1.0336100218654887 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.93341918329943660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000002 " "
y[1] (closed_form) = 1.0362291036341096 " "
y[1] (numeric) = 1.0362291036341111 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4999696775782160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000002 " "
y[1] (closed_form) = 1.0389445616892292 " "
y[1] (numeric) = 1.038944561689231 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.70977057381392520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000002 " "
y[1] (closed_form) = 1.041756124487303 " "
y[1] (numeric) = 1.041756124487305 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.91830064383714440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3000000000000002 " "
y[1] (closed_form) = 1.044663510874394 " "
y[1] (numeric) = 1.0446635108743962 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.12551316872528350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3100000000000002 " "
y[1] (closed_form) = 1.0476664301142866 " "
y[1] (numeric) = 1.0476664301142886 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.90747874216727760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32000000000000023 " "
y[1] (closed_form) = 1.050764581917559 " "
y[1] (numeric) = 1.0507645819175608 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.69053741434503360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.33000000000000024 " "
y[1] (closed_form) = 1.053957656471613 " "
y[1] (numeric) = 1.0539576564716147 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.47473878569151280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.34000000000000025 " "
y[1] (closed_form) = 1.057245334471654 " "
y[1] (numeric) = 1.0572453344716557 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.68017467798802280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.35000000000000026 " "
y[1] (closed_form) = 1.060627287152621 " "
y[1] (numeric) = 1.0606272871526228 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.6748172151681010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.36000000000000026 " "
y[1] (closed_form) = 1.0641031763220652 " "
y[1] (numeric) = 1.0641031763220667 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.4606781269533450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000003 " "
y[1] (closed_form) = 1.0676726543939656 " "
y[1] (numeric) = 1.0676726543939667 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.03985338582577390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000003 " "
y[1] (closed_form) = 1.07133536442349 " "
y[1] (numeric) = 1.071335364423491 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.0362983072276280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3900000000000003 " "
y[1] (closed_form) = 1.0750909401426871 " "
y[1] (numeric) = 1.0750909401426885 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2392138932668971000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4000000000000003 " "
y[1] (closed_form) = 1.078939005997115 " "
y[1] (numeric) = 1.078939005997116 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.02899516882247670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4100000000000003 " "
y[1] (closed_form) = 1.082879177183395 " "
y[1] (numeric) = 1.0828791771833959 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.20200848270355700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4200000000000003 " "
y[1] (closed_form) = 1.0869110596876919 " "
y[1] (numeric) = 1.0869110596876927 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.1715832384236700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4300000000000003 " "
y[1] (closed_form) = 1.091034250325115 " "
y[1] (numeric) = 1.0910342503251158 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.14070153558844700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.44000000000000034 " "
y[1] (closed_form) = 1.0952483367800367 " "
y[1] (numeric) = 1.0952483367800376 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.10937930580488800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.45000000000000034 " "
y[1] (closed_form) = 1.0995528976473232 " "
y[1] (numeric) = 1.0995528976473241 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.07763247771463400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.46000000000000035 " "
y[1] (closed_form) = 1.103947502474475 " "
y[1] (numeric) = 1.1039475024744763 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.20682154410779340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.47000000000000036 " "
y[1] (closed_form) = 1.1084317118046711 " "
y[1] (numeric) = 1.1084317118046725 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.2019392943757290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.48000000000000037 " "
y[1] (closed_form) = 1.1130050772207158 " "
y[1] (numeric) = 1.1130050772207172 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.19700049605972370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000004 " "
y[1] (closed_form) = 1.1176671413898787 " "
y[1] (numeric) = 1.11766714138988 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.19200751298230170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = 1.1224174381096275 " "
y[1] (numeric) = 1.1224174381096288 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.18696269704610930000000000000E-13 "%"
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) = 1.1272554923542488 " "
y[1] (numeric) = 1.1272554923542504 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.37884645053187680000000000000E-13 "%"
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) = 1.1321808203223502 " "
y[1] (numeric) = 1.1321808203223516 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.17672690230776880000000000000E-13 "%"
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) = 1.1371929294852392 " "
y[1] (numeric) = 1.137192929485241 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.56205406606276960000000000000E-13 "%"
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) = 1.142291318636176 " "
y[1] (numeric) = 1.1422913186361776 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.36069688101190360000000000000E-13 "%"
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) = 1.1474754779404943 " "
y[1] (numeric) = 1.1474754779404959 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.3545494124762660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = 1.1527448889865841 " "
y[1] (numeric) = 1.1527448889865852 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.63112511044130600000000000000E-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) = 1.1580990248377314 " "
y[1] (numeric) = 1.1580990248377327 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.15039180672556090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = 1.1635373500848134 " "
y[1] (numeric) = 1.1635373500848145 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.54179102668452600000000000000E-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) = 1.1690593208998368 " "
y[1] (numeric) = 1.169059320899838 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.13960652443601230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = 1.1746643850903218 " "
y[1] (numeric) = 1.1746643850903233 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.32319686729559430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = 1.1803519821545208 " "
y[1] (numeric) = 1.180351982154522 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.12870368304746900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = 1.1861215433374663 " "
y[1] (numeric) = 1.1861215433374677 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.12321341521333550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = 1.1919724916878485 " "
y[1] (numeric) = 1.1919724916878496 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.31416649601591300000000000000E-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) = 1.1979042421157078 " "
y[1] (numeric) = 1.1979042421157087 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.41443588288365300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = 1.2039162014509444 " "
y[1] (numeric) = 1.2039162014509452 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.37741064228310900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = 1.2100077685026354 " "
y[1] (numeric) = 1.210007768502636 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.505202793858287000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = 1.216178334119151 " "
y[1] (numeric) = 1.2161783341191519 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.30302781083015800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = 1.2224272812490724 " "
y[1] (numeric) = 1.2224272812490729 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.632847668421581600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = 1.2287539850028937 " "
y[1] (numeric) = 1.228753985002894 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.807071290389413200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = 1.2351578127155118 " "
y[1] (numeric) = 1.235157812715512 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.79770230685634500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = 1.241638124009492 " "
y[1] (numeric) = 1.2416381240094923 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.78831980616063800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = 1.2481942708591054 " "
y[1] (numeric) = 1.2481942708591054 " "
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] = 0.7300000000000005 " "
y[1] (closed_form) = 1.2548255976551301 " "
y[1] (numeric) = 1.2548255976551301 " "
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] = 0.7400000000000005 " "
y[1] (closed_form) = 1.2615314412704124 " "
y[1] (numeric) = 1.261531441270413 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.28035840394331000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = 1.2683111311261794 " "
y[1] (numeric) = 1.26831113112618 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.252132528267016000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = 1.2751639892590951 " "
y[1] (numeric) = 1.2751639892590958 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.22390704557251300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = 1.282089330389057 " "
y[1] (numeric) = 1.2820893303890575 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.463793039407802600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = 1.289086461987723 " "
y[1] (numeric) = 1.2890864619877236 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.16748747595984100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = 1.2961546843477643 " "
y[1] (numeric) = 1.2961546843477647 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.42620533808842400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = 1.3032932906528352 " "
y[1] (numeric) = 1.3032932906528356 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.40743877863142400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = 1.3105015670482534 " "
y[1] (numeric) = 1.3105015670482538 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.388696519076432300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = 1.317778792712387 " "
y[1] (numeric) = 1.317778792712387 " "
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] = 0.8300000000000006 " "
y[1] (closed_form) = 1.3251242399287335 " "
y[1] (numeric) = 1.325124239928733 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.35130243994288530000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = 1.3325371741586922 " "
y[1] (numeric) = 1.332537174158692 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.66632953459794400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = 1.3400168541150184 " "
y[1] (numeric) = 1.3400168541150175 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.62811379552909600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = 1.3475625318359485 " "
y[1] (numeric) = 1.3475625318359477 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.5909996658192300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = 1.3551734527599995 " "
y[1] (numeric) = 1.3551734527599983 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.1924791425336200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = 1.3628488558014205 " "
y[1] (numeric) = 1.362848855801419 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.14048761009613880000000000000E-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) = 1.3705879734263036 " "
y[1] (numeric) = 1.370587973426302 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.13404776972442510000000000000E-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) = 1.378390031729336 " "
y[1] (numeric) = 1.3783900317293347 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.66538932292420400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = 1.386254250511189 " "
y[1] (numeric) = 1.3862542505111877 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.61055758032054100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = 1.3941798433565378 " "
y[1] (numeric) = 1.394179843356536 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.2741231684454768000000000000E-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) = 1.4021660177127022 " "
y[1] (numeric) = 1.4021660177127009 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.50149706040846000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = 1.4102119749689024 " "
y[1] (numeric) = 1.4102119749689006 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.25963817562917940000000000000E-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) = 1.418316910536117 " "
y[1] (numeric) = 1.4183169105361155 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.09588500491592980000000000000E-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) = 1.426480013927544 " "
y[1] (numeric) = 1.4264800139275426 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.33954641174424800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = 1.4347004688396463 " "
y[1] (numeric) = 1.4347004688396445 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.23813777020434680000000000000E-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) = 1.4429774532337833 " "
y[1] (numeric) = 1.4429774532337816 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.2310357555617710000000000000E-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) = 1.4513101394184131 " "
y[1] (numeric) = 1.4513101394184111 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.37696374472110100000000000000E-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) = 1.4596976941318607 " "
y[1] (numeric) = 1.4596976941318591 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.06481790080488510000000000000E-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) = 1.4681392786256442 " "
y[1] (numeric) = 1.4681392786256435 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.537265806270612000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999985 " "
y[1] (closed_form) = 1.4766340487483491 " "
y[1] (numeric) = 1.4766340487483491 " "
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] = 1.0299999999999974 " "
y[1] (closed_form) = 1.4851811550300424 " "
y[1] (numeric) = 1.4851811550300433 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.98026992661483700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = 1.4937797427672184 " "
y[1] (numeric) = 1.4937797427672201 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.18916918508317680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = 1.5024289521082688 " "
y[1] (numeric) = 1.5024289521082714 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.7734850325943150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = 1.5111279181394672 " "
y[1] (numeric) = 1.5111279181394706 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.20409472546590240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = 1.5198757709714596 " "
y[1] (numeric) = 1.5198757709714639 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.77578442538039260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = 1.5286716358262529 " "
y[1] (numeric) = 1.5286716358262578 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.19557267490630000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = 1.537514633124691 " "
y[1] (numeric) = 1.537514633124697 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.89928278002258270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = 1.5464038785744134 " "
y[1] (numeric) = 1.5464038785744205 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 4.5948069945034653000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = 1.5553384832582828 " "
y[1] (numeric) = 1.5553384832582908 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 5.1394637651833190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = 1.5643175537232765 " "
y[1] (numeric) = 1.5643175537232854 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 5.6777373467819670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = 1.5733401920698302 " "
y[1] (numeric) = 1.57334019206984 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 6.2096949318051580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = 1.5824054960416285 " "
y[1] (numeric) = 1.5824054960416392 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 6.7354044605271760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = 1.5915125591158281 " "
y[1] (numeric) = 1.5915125591158399 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 7.3944525248136440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = 1.6006604705937113 " "
y[1] (numeric) = 1.6006604705937237 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 7.768354441332329000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = 1.6098483156917531 " "
y[1] (numeric) = 1.6098483156917665 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 8.2757339096119220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = 1.6190751756331005 " "
y[1] (numeric) = 1.6190751756331145 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 8.6400003661392590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = 1.6283401277394483 " "
y[1] (numeric) = 1.6283401277394636 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 9.4090156465631840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = 1.6376422455233066 " "
y[1] (numeric) = 1.6376422455233226 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 9.7623345992112950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = 1.6469805987806487 " "
y[1] (numeric) = 1.6469805987806658 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.0381078314999942000000000000E-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) = 1.6563542536839309 " "
y[1] (numeric) = 1.656354253683949 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.0992610767507344000000000000E-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) = 1.6657622728754742 " "
y[1] (numeric) = 1.6657622728754933 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.1463722245665377000000000000E-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) = 1.6752037155611994 " "
y[1] (numeric) = 1.6752037155612194 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.1929304034857695000000000000E-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) = 1.684677637604706 " "
y[1] (numeric) = 1.684677637604727 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.252123076665872000000000000E-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) = 1.694183091621684 " "
y[1] (numeric) = 1.6941830916217062 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.3106293293984456000000000000E-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) = 1.7037191270746534 " "
y[1] (numeric) = 1.7037191270746768 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 1.3684581658222286000000000000E-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) = 1.7132847903680155 " "
y[1] (numeric) = 1.7132847903680397 " "
absolute error = 2.420286193682841300000000000000E-14 " "
relative error = 1.4126584250846944000000000000E-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) = 1.7228791249434123 " "
y[1] (numeric) = 1.7228791249434374 " "
absolute error = 2.509104035652854000000000000000E-14 " "
relative error = 1.4563436281319297000000000000E-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) = 1.7325011713753815 " "
y[1] (numeric) = 1.7325011713754073 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 1.4867045746846896000000000000E-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) = 1.742149967467298 " "
y[1] (numeric) = 1.7421499674673249 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 1.5421977268115478000000000000E-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) = 1.7518245483475936 " "
y[1] (numeric) = 1.7518245483476216 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.597056066313479000000000000E-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) = 1.7615239465662422 " "
y[1] (numeric) = 1.7615239465662715 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.6638938066801880000000000000E-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) = 1.7712471921915047 " "
y[1] (numeric) = 1.7712471921915351 " "
absolute error = 3.04201108747292900000000000000E-14 " "
relative error = 1.7174401748573280000000000000E-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) = 1.7809933129069215 " "
y[1] (numeric) = 1.780993312906953 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 1.7703791289306364000000000000E-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) = 1.7907613341085424 " "
y[1] (numeric) = 1.790761334108575 " "
absolute error = 3.2640556923979600000000000000E-14 " "
relative error = 1.822719549628224200000000000E-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) = 1.8005502790023877 " "
y[1] (numeric) = 1.800550279002421 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.8498062024243275000000000000E-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) = 1.8103591687021252 " "
y[1] (numeric) = 1.8103591687021594 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 1.888844476257695000000000000E-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) = 1.820187022326959 " "
y[1] (numeric) = 1.820187022326994 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.9274419138152168000000000000E-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) = 1.8300328570997162 " "
y[1] (numeric) = 1.8300328570997526 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 1.9898722072901506000000000000E-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) = 1.839895688445125 " "
y[1] (numeric) = 1.8398956884451623 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 2.0274787240210350000000000000E-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) = 1.849774530088269 " "
y[1] (numeric) = 1.8497745300883077 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 2.088674085868822000000000000E-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) = 1.859668394153217 " "
y[1] (numeric) = 1.8596683941532566 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 2.1253219015238703000000000000E-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) = 1.869576291261807 " "
y[1] (numeric) = 1.8695762912618477 " "
absolute error = 4.06341627012807300000000000000E-14 " "
relative error = 2.1734423404490263000000000000E-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) = 1.8794972306325848 " "
y[1] (numeric) = 1.8794972306326265 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 2.2210400231266064000000000000E-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) = 1.8894302201798807 " "
y[1] (numeric) = 1.8894302201799233 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 2.2563714547524935000000000000E-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) = 1.8993742666130176 " "
y[1] (numeric) = 1.8993742666130609 " "
absolute error = 4.329869796038110500000000000000E-14 " "
relative error = 2.2796295980987336000000000000E-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) = 1.9093283755356383 " "
y[1] (numeric) = 1.9093283755356831 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 2.3491511868550832000000000000E-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) = 1.9192915515451463 " "
y[1] (numeric) = 1.9192915515451923 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 2.394802039454521000000000000E-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) = 1.9292627983322428 " "
y[1] (numeric) = 1.9292627983322896 " "
absolute error = 4.685141163918160600000000000000E-14 " "
relative error = 2.428461880863636000000000000E-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) = 1.9392411187805587 " "
y[1] (numeric) = 1.939241118780607 " "
absolute error = 4.818367926873179400000000000000E-14 " "
relative error = 2.4846667493844624000000000000E-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) = 1.9492255150663642 " "
y[1] (numeric) = 1.949225515066414 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 2.551679686047697000000000000E-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) = 1.9592149887583512 " "
y[1] (numeric) = 1.959214988758402 " "
absolute error = 5.08482145278321700000000000000E-14 " "
relative error = 2.595336133073233000000000000E-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) = 1.969208540917475 " "
y[1] (numeric) = 1.969208540917527 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 2.638544190360323000000000000E-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) = 1.9792051721968476 " "
y[1] (numeric) = 1.9792051721969006 " "
absolute error = 5.30686605770824800000000000000E-14 " "
relative error = 2.681311736780586000000000000E-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) = 1.9892038829416716 " "
y[1] (numeric) = 1.9892038829417256 " "
absolute error = 5.39568389967826100000000000000E-14 " "
relative error = 2.7124840977582565000000000000E-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) = 1.9992036732892047 " "
y[1] (numeric) = 1.9992036732892597 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 2.754449822053811600000000000E-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) = 2.009203543268745 " "
y[1] (numeric) = 2.009203543268802 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 2.8291518323887815000000000000E-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) = 2.0192024929016283 " "
y[1] (numeric) = 2.019202492901685 " "
absolute error = 5.68434188608080100000000000000E-14 " "
relative error = 2.8151420702300667000000000000E-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) = 2.0291995223012234 " "
y[1] (numeric) = 2.029199522301282 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 2.8888128080047165000000000000E-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) = 2.039193631772921 " "
y[1] (numeric) = 2.039193631772981 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 2.939987767499783000000000000E-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) = 2.0491838219141028 " "
y[1] (numeric) = 2.0491838219141636 " "
absolute error = 6.08402217494585800000000000000E-14 " "
relative error = 2.96899775895307000000000000E-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) = 2.05916909371408 " "
y[1] (numeric) = 2.059169093714142 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 3.019299851032125000000000000E-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) = 2.0691484486539924 " "
y[1] (numeric) = 2.069148448654056 " "
absolute error = 6.35047570085589500000000000000E-14 " "
relative error = 3.0691252263639957000000000000E-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) = 2.0791208888066635 " "
y[1] (numeric) = 2.079120888806728 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 3.097123201201551000000000000E-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) = 2.0890854169363875 " "
y[1] (numeric) = 2.0890854169364537 " "
absolute error = 6.61692922676593300000000000000E-14 " "
relative error = 3.1673808898008393000000000000E-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) = 2.0990410365986554 " "
y[1] (numeric) = 2.099041036598723 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 3.215828500741983000000000000E-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) = 2.1089867522397974 " "
y[1] (numeric) = 2.108986752239866 " "
absolute error = 6.8833827526759700000000000000E-14 " "
relative error = 3.2638340403824934000000000000E-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) = 2.1189215692965373 " "
y[1] (numeric) = 2.1189215692966066 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 3.269489429927763000000000000E-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) = 2.128844494295449 " "
y[1] (numeric) = 2.1288444942955187 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 3.2751103301950980000000000000E-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) = 2.1387545349523007 " "
y[1] (numeric) = 2.138754534952372 " "
absolute error = 7.14983627858600800000000000000E-14 " "
relative error = 3.3429905871575233000000000000E-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) = 2.148650700271286 " "
y[1] (numeric) = 2.148650700271358 " "
absolute error = 7.23865412055602100000000000000E-14 " "
relative error = 3.3689301474837574000000000000E-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) = 2.158532000644119 " "
y[1] (numeric) = 2.1585320006441933 " "
absolute error = 7.41628980449604600000000000000E-14 " "
relative error = 3.4358025742879790000000000000E-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) = 2.168397447948997 " "
y[1] (numeric) = 2.1683974479490726 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 3.48161107392551960000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 2.1782460556494114 " "
y[1] (numeric) = 2.178246055649488 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 3.506644435145699000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 2.1880768388927985 " "
y[1] (numeric) = 2.1880768388928753 " "
absolute error = 7.68274333040608300000000000000E-14 " "
relative error = 3.511185344977955000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 2.1978888146090263 " "
y[1] (numeric) = 2.1978888146091045 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 3.5561262432428614000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 2.2076810016087003 " "
y[1] (numeric) = 2.2076810016087793 " "
absolute error = 7.90478793533111500000000000000E-14 " "
relative error = 3.5805843007078597000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 2.2174524206812802 " "
y[1] (numeric) = 2.2174524206813606 " "
absolute error = 8.03801469828613300000000000000E-14 " "
relative error = 3.62488711068559000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 2.227202094693002 " "
y[1] (numeric) = 2.2272020946930833 " "
absolute error = 8.12683254025614600000000000000E-14 " "
relative error = 3.6488976728339284000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 2.2369290486845888 " "
y[1] (numeric) = 2.2369290486846705 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 3.652883611148148000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 2.246632309968747 " "
y[1] (numeric) = 2.2466323099688297 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 3.676640483874315000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 2.256310908227435 " "
y[1] (numeric) = 2.2563109082275186 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 3.700233471698313000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 2.265963875608892 " "
y[1] (numeric) = 2.265963875608977 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 3.7628635305715213000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 2.2755902468244233 " "
y[1] (numeric) = 2.27559024682451 " "
absolute error = 8.65973959207622100000000000000E-14 " "
relative error = 3.8054916099947483000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 2.2851890592449307 " "
y[1] (numeric) = 2.2851890592450177 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 3.808940217811667700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 2.29475935299717 " "
y[1] (numeric) = 2.294759352997258 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 3.831759676040454300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 2.3043001710597415 " "
y[1] (numeric) = 2.304300171059831 " "
absolute error = 8.97060203897126500000000000000E-14 " "
relative error = 3.8929832804055686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 2.31381055935879 " "
y[1] (numeric) = 2.3138105593588802 " "
absolute error = 9.01501095995627100000000000000E-14 " "
relative error = 3.896175044881175000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 2.3232895668634104 " "
y[1] (numeric) = 2.3232895668635014 " "
absolute error = 9.10382880192628400000000000000E-14 " "
relative error = 3.918508020598154000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 2.3327362456807514 " "
y[1] (numeric) = 2.332736245680844 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 3.959751378658626000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 2.3421496511508035 " "
y[1] (numeric) = 2.342149651150897 " "
absolute error = 9.32587340685131500000000000000E-14 " "
relative error = 3.981758126458355700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 2.3515288419408646 " "
y[1] (numeric) = 2.351528841940959 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 4.0036469384958895000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 2.3608728801396714 " "
y[1] (numeric) = 2.360872880139767 " "
absolute error = 9.54791801177634600000000000000E-14 " "
relative error = 4.044232153326054000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 2.3701808313511905 " "
y[1] (numeric) = 2.370180831351287 " "
absolute error = 9.63673585374635900000000000000E-14 " "
relative error = 4.065823048721838300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 2.3794517647880573 " "
y[1] (numeric) = 2.379451764788155 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 4.105972124033205000000000000E-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) = 2.3886847533646542 " "
y[1] (numeric) = 2.388684753364753 " "
absolute error = 9.8587804586713900000000000000E-14 " "
relative error = 4.127284039798264000000000000E-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) = 2.397878873789818 " "
y[1] (numeric) = 2.3978788737899173 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 4.148499079488258700000000000E-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) = 2.4070332066591664 " "
y[1] (numeric) = 2.4070332066592672 " "
absolute error = 1.00808250635964210000000000000E-13 " "
relative error = 4.188070623914686000000000000E-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) = 2.4161468365470427 " "
y[1] (numeric) = 2.4161468365471443 " "
absolute error = 1.01696429055664340000000000000E-13 " "
relative error = 4.209033470871351000000000000E-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) = 2.4252188520980527 " "
y[1] (numeric) = 2.425218852098155 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 4.211600044967192000000000000E-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) = 2.4342483461182 " "
y[1] (numeric) = 2.434248346118304 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 4.268951246105468500000000000E-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) = 2.443234415665608 " "
y[1] (numeric) = 2.443234415665713 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 4.289602866291601000000000000E-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) = 2.4521761621408107 " "
y[1] (numeric) = 2.4521761621409164 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 4.310181037403205000000000000E-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) = 2.461072691376611 " "
y[1] (numeric) = 2.461072691376718 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 4.330689245281831300000000000E-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) = 2.4699231137275 " "
y[1] (numeric) = 2.4699231137276074 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 4.351130939518467000000000000E-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) = 2.4787265441586173 " "
y[1] (numeric) = 2.4787265441587256 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 4.371509534150586000000000000E-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) = 2.487482102334256 " "
y[1] (numeric) = 2.4874821023343654 " "
absolute error = 1.0924594562311540000000000000E-13 " "
relative error = 4.391828408357144600000000000E-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) = 2.4961889127058954 " "
y[1] (numeric) = 2.496188912706005 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 4.394300218009553600000000000E-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) = 2.5048461045997534 " "
y[1] (numeric) = 2.504846104599864 " "
absolute error = 1.10578213252665590000000000000E-13 " "
relative error = 4.414571140702265300000000000E-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) = 2.5134528123038553 " "
y[1] (numeric) = 2.513452812303967 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 4.4524599918642416000000000000E-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) = 2.522008175154603 " "
y[1] (numeric) = 2.522008175154716 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 4.490181658702356300000000000E-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) = 2.53051133762284 " "
y[1] (numeric) = 2.5305113376229538 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 4.492642891235308400000000000E-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) = 2.538961449399406 " "
y[1] (numeric) = 2.5389614493995216 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 4.5476544981937095000000000000E-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) = 2.547357665480166 " "
y[1] (numeric) = 2.547357665480282 " "
absolute error = 1.15907283770866340000000000000E-13 " "
relative error = 4.5500985331409405000000000000E-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) = 2.555699146250507 " "
y[1] (numeric) = 2.5556991462506238 " "
absolute error = 1.16795462190566470000000000000E-13 " "
relative error = 4.570000438506947000000000000E-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) = 2.5639850575693046 " "
y[1] (numeric) = 2.5639850575694223 " "
absolute error = 1.1768364061026660000000000000E-13 " "
relative error = 4.589872326394616000000000000E-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) = 2.572214570852331 " "
y[1] (numeric) = 2.57221457085245 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 4.626982118384455000000000000E-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) = 2.580386863155116 " "
y[1] (numeric) = 2.580386863155235 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 4.6123280946444000000000000E-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) = 2.5885011172552397 " "
y[1] (numeric) = 2.58850111725536 " "
absolute error = 1.20348175869366970000000000000E-13 " "
relative error = 4.649338378380928000000000000E-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) = 2.596556521734054 " "
y[1] (numeric) = 2.5965565217341746 " "
absolute error = 1.20792265079217030000000000000E-13 " "
relative error = 4.652017549710358000000000000E-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) = 2.6045522710578233 " "
y[1] (numeric) = 2.6045522710579454 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 4.6888877626236725000000000000E-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) = 2.6124875656582787 " "
y[1] (numeric) = 2.6124875656584017 " "
absolute error = 1.23012711128467340000000000000E-13 " "
relative error = 4.708642932716556300000000000E-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) = 2.620361612012573 " "
y[1] (numeric) = 2.620361612012697 " "
absolute error = 1.23900889548167470000000000000E-13 " "
relative error = 4.7283889742608914000000000000E-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) = 2.628173622722633 " "
y[1] (numeric) = 2.6281736227227563 " "
absolute error = 1.2345680033831741000000000000E-13 " "
relative error = 4.697437006099446000000000000E-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) = 2.6359228165938964 " "
y[1] (numeric) = 2.6359228165940207 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 4.717322448716249600000000000E-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) = 2.643608418713434 " "
y[1] (numeric) = 2.643608418713559 " "
absolute error = 1.2478906796786760000000000000E-13 " "
relative error = 4.720406664032290600000000000E-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) = 2.6512296605274392 " "
y[1] (numeric) = 2.6512296605275645 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 4.723587663575083000000000000E-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) = 2.6587857799180816 " "
y[1] (numeric) = 2.6587857799182073 " "
absolute error = 1.25677246387567720000000000000E-13 " "
relative error = 4.726866200985921400000000000E-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) = 2.6662760212797183 " "
y[1] (numeric) = 2.6662760212798453 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 4.7635545983779215000000000000E-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) = 2.673699635594455 " "
y[1] (numeric) = 2.6736996355945823 " "
absolute error = 1.27453603226967970000000000000E-13 " "
relative error = 4.766937973518131000000000000E-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) = 2.6810558805070466 " "
y[1] (numeric) = 2.681055880507175 " "
absolute error = 1.2834178164666810000000000000E-13 " "
relative error = 4.7869864473841495000000000000E-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) = 2.688344020399133 " "
y[1] (numeric) = 2.6883440203992612 " "
absolute error = 1.2834178164666810000000000000E-13 " "
relative error = 4.774008857230015400000000000E-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) = 2.6955633264627967 " "
y[1] (numeric) = 2.6955633264629264 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 4.8106474814813815000000000000E-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) = 2.7027130767734486 " "
y[1] (numeric) = 2.7027130767735796 " "
absolute error = 1.31006316905768470000000000000E-13 " "
relative error = 4.84721511993298050000000000E-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) = 2.7097925563620158 " "
y[1] (numeric) = 2.709792556362147 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 4.850939818511235000000000000E-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) = 2.716801057286438 " "
y[1] (numeric) = 2.7168010572865704 " "
absolute error = 1.32338584535318660000000000000E-13 " "
relative error = 4.871117970908751500000000000E-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) = 2.7237378787024644 " "
y[1] (numeric) = 2.723737878702597 " "
absolute error = 1.32782673745168720000000000000E-13 " "
relative error = 4.875016600658496600000000000E-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) = 2.730602326933733 " "
y[1] (numeric) = 2.730602326933867 " "
absolute error = 1.33670852164868850000000000000E-13 " "
relative error = 4.895288151130064000000000000E-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) = 2.737393715541142 " "
y[1] (numeric) = 2.7373937155412764 " "
absolute error = 1.34559030584568970000000000000E-13 " "
relative error = 4.915589227104244000000000000E-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) = 2.7441113653914893 " "
y[1] (numeric) = 2.7441113653916247 " "
absolute error = 1.3544720900426910000000000000E-13 " "
relative error = 4.935922452438276700000000000E-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) = 2.750754604725388 " "
y[1] (numeric) = 2.7507546047255245 " "
absolute error = 1.36335387423969220000000000000E-13 " "
relative error = 4.956290437168233000000000000E-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) = 2.7573227692244413 " "
y[1] (numeric) = 2.7573227692245785 " "
absolute error = 1.37223565843669350000000000000E-13 " "
relative error = 4.976695778066873000000000000E-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) = 2.763815202077672 " "
y[1] (numeric) = 2.76381520207781 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 4.9971410591976370000000000000E-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) = 2.7702312540472063 " "
y[1] (numeric) = 2.770231254047345 " "
absolute error = 1.38555833473219540000000000000E-13 " "
relative error = 5.001598089357866000000000000E-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) = 2.7765702835331925 " "
y[1] (numeric) = 2.776570283533332 " "
absolute error = 1.39444011892919660000000000000E-13 " "
relative error = 5.022167553975144000000000000E-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) = 2.782831656637965 " "
y[1] (numeric) = 2.7828316566381055 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 5.042784028199533000000000000E-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) = 2.7890147472294315 " "
y[1] (numeric) = 2.7890147472295728 " "
absolute error = 1.4122036873231990000000000000E-13 " "
relative error = 5.063450054274767000000000000E-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) = 2.7951189370036853 " "
y[1] (numeric) = 2.795118937003827 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 5.0682801388777960000000000000E-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) = 2.8011436155468354 " "
y[1] (numeric) = 2.801143615546978 " "
absolute error = 1.4255263636187010000000000000E-13 " "
relative error = 5.089087027551109000000000000E-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) = 2.8070881803960486 " "
y[1] (numeric) = 2.8070881803961916 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 5.094130158445714000000000000E-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) = 2.812952037099793 " "
y[1] (numeric) = 2.8129520370999375 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 5.130872880082104000000000000E-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) = 2.8187345992772856 " "
y[1] (numeric) = 2.8187345992774313 " "
absolute error = 1.45661260830820540000000000000E-13 " "
relative error = 5.167611766931431000000000000E-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) = 2.824435288677127 " "
y[1] (numeric) = 2.824435288677273 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 5.172904850268373000000000000E-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) = 2.8300535352351277 " "
y[1] (numeric) = 2.830053535235275 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 5.20971125933034000000000000E-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) = 2.8355887771313135 " "
y[1] (numeric) = 2.8355887771314627 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 5.262186665182695000000000000E-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) = 2.8410404608461084 " "
y[1] (numeric) = 2.8410404608462585 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 5.283351469222591000000000000E-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) = 2.8464080412156836 " "
y[1] (numeric) = 2.8464080412158346 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 5.304591933506984000000000000E-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) = 2.8516909814864744 " "
y[1] (numeric) = 2.8516909814866267 " "
absolute error = 1.52322598978571480000000000000E-13 " "
relative error = 5.341483350316298000000000000E-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) = 2.8568887533688567 " "
y[1] (numeric) = 2.8568887533690104 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 5.3783986662739700000000000000E-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) = 2.8620008370899743 " "
y[1] (numeric) = 2.862000837090128 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 5.3687918122468080000000000000E-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) = 2.867026721445714 " "
y[1] (numeric) = 2.867026721445869 " "
absolute error = 1.54987134237671850000000000000E-13 " "
relative error = 5.405848961167643000000000000E-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) = 2.8719659038518293 " "
y[1] (numeric) = 2.871965903851985 " "
absolute error = 1.55875312657371980000000000000E-13 " "
relative error = 5.4274778279336400000000000000E-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) = 2.8768178903941948 " "
y[1] (numeric) = 2.8768178903943515 " "
absolute error = 1.5676349107707210000000000000E-13 " "
relative error = 5.449197587393746000000000000E-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) = 2.8815821958782006 " "
y[1] (numeric) = 2.881582195878358 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 5.4555993756413070000000000000E-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) = 2.8862583438772678 " "
y[1] (numeric) = 2.886258343877425 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 5.44676053065079000000000000E-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) = 2.8908458667804933 " "
y[1] (numeric) = 2.890845866780651 " "
absolute error = 1.57651669496772230000000000000E-13 " "
relative error = 5.453478904164039000000000000E-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) = 2.89534430583941 " "
y[1] (numeric) = 2.8953443058395685 " "
absolute error = 1.58539847916472350000000000000E-13 " "
relative error = 5.4756820318994470000000000000E-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) = 2.8997532112138606 " "
y[1] (numeric) = 2.899753211214019 " "
absolute error = 1.58539847916472350000000000000E-13 " "
relative error = 5.4673565772208000000000000E-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) = 2.9040721420169815 " "
y[1] (numeric) = 2.904072142017141 " "
absolute error = 1.59428026336172480000000000000E-13 " "
relative error = 5.489809431023434000000000000E-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) = 2.908300666359292 " "
y[1] (numeric) = 2.9083006663594517 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 5.497097236034946000000000000E-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) = 2.9124383613918807 " "
y[1] (numeric) = 2.912438361392041 " "
absolute error = 1.6031620475587260000000000000E-13 " "
relative error = 5.504535542488048000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = 2.9164848133486934 " "
y[1] (numeric) = 2.916484813348854 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 5.512125186797681000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = 2.920439617587906 " "
y[1] (numeric) = 2.920439617588067 " "
absolute error = 1.60760293965722670000000000000E-13 " "
relative error = 5.504660770849981000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = 2.9243023786323903 " "
y[1] (numeric) = 2.9243023786325524 " "
absolute error = 1.62092561595272850000000000000E-13 " "
relative error = 5.542948047358862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = 2.928072710209261 " "
y[1] (numeric) = 2.928072710209423 " "
absolute error = 1.62092561595272850000000000000E-13 " "
relative error = 5.535810672669005000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = 2.9317502352885016 " "
y[1] (numeric) = 2.931750235288664 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 5.54401424953338000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = 2.93533458612067 " "
y[1] (numeric) = 2.9353345861208333 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 5.567502593999168000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = 2.938825404273669 " "
y[1] (numeric) = 2.938825404273833 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.591111585110758000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = 2.942222340668592 " "
y[1] (numeric) = 2.9422223406687564 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.584656379408247000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = 2.945525055614631 " "
y[1] (numeric) = 2.9455250556147954 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.578394498166529000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = 2.948733218843044 " "
y[1] (numeric) = 2.9487332188432083 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.572325315648342000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = 2.951846509540181 " "
y[1] (numeric) = 2.9518465095403457 " "
absolute error = 1.64757096854373230000000000000E-13 " "
relative error = 5.581492679984842000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = 2.9548646163795667 " "
y[1] (numeric) = 2.954864616379731 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.560762639807398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = 2.957787237553032 " "
y[1] (numeric) = 2.957787237553197 " "
absolute error = 1.64757096854373230000000000000E-13 " "
relative error = 5.570282228639145000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = 2.9606140808008954 " "
y[1] (numeric) = 2.960614080801061 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.594963435060862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = 2.963344863441188 " "
y[1] (numeric) = 2.9633448634413537 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.5898075623138100000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = 2.9659793123979217 " "
y[1] (numeric) = 2.965979312398087 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 5.569869802317069000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = 2.9685171642283947 " "
y[1] (numeric) = 2.9685171642285613 " "
absolute error = 1.66533453693773480000000000000E-13 " "
relative error = 5.6099878990277110000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = 2.9709581651495407 " "
y[1] (numeric) = 2.9709581651497077 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.62032629278773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = 2.9733020710633005 " "
y[1] (numeric) = 2.973302071063468 " "
absolute error = 1.6742163211347360000000000000E-13 " "
relative error = 5.6308315842796610000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = 2.9755486475810367 " "
y[1] (numeric) = 2.975548647581204 " "
absolute error = 1.6742163211347360000000000000E-13 " "
relative error = 5.6265802358693930000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = 2.9776976700469686 " "
y[1] (numeric) = 2.977697670047136 " "
absolute error = 1.6742163211347360000000000000E-13 " "
relative error = 5.622519498792259000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = 2.9797489235606416 " "
y[1] (numeric) = 2.9797489235608094 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.6335525451833380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = 2.981702202998413 " "
y[1] (numeric) = 2.9817022029985814 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.6447558835325880000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = 2.9835573130339674 " "
y[1] (numeric) = 2.9835573130341353 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.626361544656292000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = 2.9853140681578467 " "
y[1] (numeric) = 2.9853140681580146 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.623050623511412000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = 2.9869722926960027 " "
y[1] (numeric) = 2.9869722926961706 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.619928974025074000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = 2.988531820827363 " "
y[1] (numeric) = 2.988531820827531 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.616996284043271000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = 2.9899924966004146 " "
y[1] (numeric) = 2.989992496600582 " "
absolute error = 1.6742163211347360000000000000E-13 " "
relative error = 5.599399741097344000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = 2.991354173948797 " "
y[1] (numeric) = 2.991354173948965 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.611696628411244000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = 2.99261671670591 " "
y[1] (numeric) = 2.992616716706078 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.609329132803215000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = 2.993779998618531 " "
y[1] (numeric) = 2.9937799986186993 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.621983265665469000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = 2.9948439033594365 " "
y[1] (numeric) = 2.9948439033596053 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.634814540875596000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = 2.995808324539041 " "
y[1] (numeric) = 2.9958083245392095 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.6330005615092090000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = 2.996673165716028 " "
y[1] (numeric) = 2.996673165716197 " "
absolute error = 1.69197988952873860000000000000E-13 " "
relative error = 5.646194282666976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = 2.9974383404070024 " "
y[1] (numeric) = 2.997438340407171 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.6299373190812600000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = 2.9981037720951313 " "
y[1] (numeric) = 2.9981037720953 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.628687749693713000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = 2.998669394237802 " "
y[1] (numeric) = 2.9986693942379703 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.612816499764707000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = 2.99913515027327 " "
y[1] (numeric) = 2.9991351502734385 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.6119448474283650000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = 2.9995009936263206 " "
y[1] (numeric) = 2.999500993626489 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.611260369335349000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = 2.9997668877129233 " "
y[1] (numeric) = 2.9997668877130916 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.610762997037286000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = 2.999932805943891 " "
y[1] (numeric) = 2.9999328059440598 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.625255986022911000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = 2.999998731727539 " "
y[1] (numeric) = 2.999998731727707 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.595526409661472000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = 2.999964658471344 " "
y[1] (numeric) = 2.999964658471512 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.595589963011798000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = 2.9998305895826025 " "
y[1] (numeric) = 2.999830589582771 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.6106438516113810000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = 2.9995965384680927 " "
y[1] (numeric) = 2.9995965384682606 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.596276671563751000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = 2.9992625285327303 " "
y[1] (numeric) = 2.9992625285328987 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.611706508916796000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 2.9988285931772305 " "
y[1] (numeric) = 2.9988285931773992 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.627327287960484000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 2.998294775794767 " "
y[1] (numeric) = 2.9982947757949363 " "
absolute error = 1.69197988952873860000000000000E-13 " "
relative error = 5.643140571727943000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 2.9976611297666342 " "
y[1] (numeric) = 2.997661129766803 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 5.629518896158926000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 2.996927718456906 " "
y[1] (numeric) = 2.996927718457074 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.616078409119427000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 2.9960946152061023 " "
y[1] (numeric) = 2.9960946152062706 " "
absolute error = 1.68309810533173730000000000000E-13 " "
relative error = 5.617640033093402000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 2.9951619033238543 " "
y[1] (numeric) = 2.995161903324022 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 5.6045625158705500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 2.994129676080573 " "
y[1] (numeric) = 2.9941296760807403 " "
absolute error = 1.6742163211347360000000000000E-13 " "
relative error = 5.591662694203504000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 2.992998036698122 " "
y[1] (numeric) = 2.992998036698289 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.578939272804646000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 2.991767098339497 " "
y[1] (numeric) = 2.991767098339664 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.5812346822150740000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 2.9904369840975074 " "
y[1] (numeric) = 2.990436984097674 " "
absolute error = 1.66533453693773480000000000000E-13 " "
relative error = 5.568866843854665000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 2.98900782698247 " "
y[1] (numeric) = 2.989007826982637 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.5863869407192030000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 2.9874797699089046 " "
y[1] (numeric) = 2.9874797699090716 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.5892443050322340000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 2.9858529656812456 " "
y[1] (numeric) = 2.9858529656814126 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.5922895341072610000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 2.9841275769785596 " "
y[1] (numeric) = 2.9841275769787265 " "
absolute error = 1.66977542903623540000000000000E-13 " "
relative error = 5.595522932457497000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 2.98230377633828 " "
y[1] (numeric) = 2.982303776338446 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 5.5691632020078980000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 2.9803817461389492 " "
y[1] (numeric) = 2.9803817461391153 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 5.572754721742955000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 2.9783616785819875 " "
y[1] (numeric) = 2.978361678582153 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.561623911067036000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 2.976243775672466 " "
y[1] (numeric) = 2.976243775672632 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 5.580502707524232000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 2.974028249198911 " "
y[1] (numeric) = 2.974028249199077 " "
absolute error = 1.66089364483923420000000000000E-13 " "
relative error = 5.5846599482927410000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 2.9717153207121236 " "
y[1] (numeric) = 2.9717153207122893 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.574062701079292000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 2.969305221503025 " "
y[1] (numeric) = 2.9693052215031908 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.5785870066340240000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 2.966798192579528 " "
y[1] (numeric) = 2.9667981925796933 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 5.5683324358704220000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 2.964194484642436 " "
y[1] (numeric) = 2.9641944846426003 " "
absolute error = 1.64313007644523170000000000000E-13 " "
relative error = 5.543260015354353000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 2.9614943580603716 " "
y[1] (numeric) = 2.9614943580605355 " "
absolute error = 1.6386891843467310000000000000E-13 " "
relative error = 5.533318609527892000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 2.9586980828437444 " "
y[1] (numeric) = 2.958698082843908 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 5.523538551380266000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 2.955805938617745 " "
y[1] (numeric) = 2.9558059386179085 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 5.528943124772500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 2.9528182145943864 " "
y[1] (numeric) = 2.95281821459455 " "
absolute error = 1.63424829224823040000000000000E-13 " "
relative error = 5.534537426553766000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 2.9497352095435807 " "
y[1] (numeric) = 2.9497352095437432 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 5.5102115701521760000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 2.946557231763264 " "
y[1] (numeric) = 2.946557231763427 " "
absolute error = 1.62980740014972980000000000000E-13 " "
relative error = 5.531226010412255000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 2.943284599048566 " "
y[1] (numeric) = 2.9432845990487286 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 5.522287951958973000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 2.9399176386600314 " "
y[1] (numeric) = 2.939917638660193 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 5.498401392601584000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 2.9364566872908924 " "
y[1] (numeric) = 2.9364566872910536 " "
absolute error = 1.61204383175572730000000000000E-13 " "
relative error = 5.489758588072218000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 2.932902091033403 " "
y[1] (numeric) = 2.932902091033564 " "
absolute error = 1.61204383175572730000000000000E-13 " "
relative error = 5.496412023722641000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 2.9292542053442254 " "
y[1] (numeric) = 2.9292542053443866 " "
absolute error = 1.61204383175572730000000000000E-13 " "
relative error = 5.503256865910315000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 2.9255133950088896 " "
y[1] (numeric) = 2.925513395009051 " "
absolute error = 1.61204383175572730000000000000E-13 " "
relative error = 5.5102937983670690000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 2.9216800341053117 " "
y[1] (numeric) = 2.921680034105472 " "
absolute error = 1.6031620475587260000000000000E-13 " "
relative error = 5.4871239452805200000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 2.917754505966387 " "
y[1] (numeric) = 2.917754505966547 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 5.47928604751041000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 2.913737203141659 " "
y[1] (numeric) = 2.9137372031418183 " "
absolute error = 1.59428026336172480000000000000E-13 " "
relative error = 5.4715993660743830000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 2.9096285273580618 " "
y[1] (numeric) = 2.9096285273582203 " "
absolute error = 1.58539847916472350000000000000E-13 " "
relative error = 5.448800299618531000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 2.90542888947975 " "
y[1] (numeric) = 2.905428889479908 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 5.44139143377662000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 2.901138709467012 " "
y[1] (numeric) = 2.90113870946717 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 5.449438118581622000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 2.8967584163342734 " "
y[1] (numeric) = 2.8967584163344307 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 5.427017296315022000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 2.8922884481071978 " "
y[1] (numeric) = 2.892288448107355 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 5.435404632266316000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 2.8877292517788824 " "
y[1] (numeric) = 2.887729251779039 " "
absolute error = 1.5676349107707210000000000000E-13 " "
relative error = 5.42860765012868000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 2.8830812832651613 " "
y[1] (numeric) = 2.8830812832653177 " "
absolute error = 1.56319401867222040000000000000E-13 " "
relative error = 5.421956112530634000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 2.8783450073590124 " "
y[1] (numeric) = 2.878345007359168 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 5.4000206038585970000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 2.8735208976840796 " "
y[1] (numeric) = 2.8735208976842346 " "
absolute error = 1.54987134237671850000000000000E-13 " "
relative error = 5.393631706753346000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 2.8686094366473096 " "
y[1] (numeric) = 2.8686094366474637 " "
absolute error = 1.54098955817971730000000000000E-13 " "
relative error = 5.371904374618353000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 2.863611115390714 " "
y[1] (numeric) = 2.863611115390868 " "
absolute error = 1.54098955817971730000000000000E-13 " "
relative error = 5.381280823703826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 2.8585264337422527 " "
y[1] (numeric) = 2.8585264337424054 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 5.344246125736412000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 2.8533559001658535 " "
y[1] (numeric) = 2.853355900166006 " "
absolute error = 1.52322598978571480000000000000E-13 " "
relative error = 5.338366621903619000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 2.8481000317105654 " "
y[1] (numeric) = 2.8481000317107172 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 5.33262554256225900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 2.842759353958854 " "
y[1] (numeric) = 2.842759353959005 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 5.311400387751806000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 2.8373344009740435 " "
y[1] (numeric) = 2.837334400974194 " "
absolute error = 1.50546242139171230000000000000E-13 " "
relative error = 5.305904093909036000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 2.831825715246912 " "
y[1] (numeric) = 2.831825715247062 " "
absolute error = 1.4965806371947110000000000000E-13 " "
relative error = 5.28486138513726100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 2.8262338476414417 " "
y[1] (numeric) = 2.826233847641591 " "
absolute error = 1.49213974509621040000000000000E-13 " "
relative error = 5.2796046807713250000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 2.820559357339733 " "
y[1] (numeric) = 2.8205593573398815 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 5.258736913440366000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 2.814802811786088 " "
y[1] (numeric) = 2.8148028117862363 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 5.269491541960027000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 2.8089647866302645 " "
y[1] (numeric) = 2.808964786630412 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 5.248823992809546000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 2.8030458656699127 " "
y[1] (numeric) = 2.803045865670059 " "
absolute error = 1.46549439250520660000000000000E-13 " "
relative error = 5.228221237667695000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 2.7970466407921966 " "
y[1] (numeric) = 2.7970466407923427 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 5.223557873861187000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 2.790967711914605 " "
y[1] (numeric) = 2.79096771191475 " "
absolute error = 1.45217171620970480000000000000E-13 " "
relative error = 5.203111845437705000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 2.7848096869249592 " "
y[1] (numeric) = 2.784809686925103 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 5.166776913588691000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 2.7785731816206267 " "
y[1] (numeric) = 2.7785731816207697 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 5.14640847027524000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 2.7722588196469413 " "
y[1] (numeric) = 2.772258819647083 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 5.110073306943669000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 2.7658672324348377 " "
y[1] (numeric) = 2.7658672324349793 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 5.121882073040088000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 2.7593990591377118 " "
y[1] (numeric) = 2.759399059137852 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 5.085606949379492000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 2.752854946567502 " "
y[1] (numeric) = 2.7528549465676417 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 5.08156455091084000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 2.7462355491300126 " "
y[1] (numeric) = 2.7462355491301516 " "
absolute error = 1.3899992268306960000000000000E-13 " "
relative error = 5.061471246598048000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 2.7395415287594713 " "
y[1] (numeric) = 2.7395415287596085 " "
absolute error = 1.37223565843669350000000000000E-13 " "
relative error = 5.008997469215494000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 2.7327735548523364 " "
y[1] (numeric) = 2.7327735548524723 " "
absolute error = 1.35891298214119160000000000000E-13 " "
relative error = 4.972651245575375000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 2.7259323042003594 " "
y[1] (numeric) = 2.725932304200494 " "
absolute error = 1.34559030584568970000000000000E-13 " "
relative error = 4.93625723490009000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 2.7190184609229036 " "
y[1] (numeric) = 2.7190184609230377 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 4.932476307247906600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 2.7120327163985354 " "
y[1] (numeric) = 2.7120327163986686 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 4.912431997942056000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 2.704975769195886 " "
y[1] (numeric) = 2.704975769196019 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 4.925247925404648300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 2.697848325003795 " "
y[1] (numeric) = 2.697848325003927 " "
absolute error = 1.3189449532546860000000000000E-13 " "
relative error = 4.888877336174303000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 2.690651096560742 " "
y[1] (numeric) = 2.6906510965608734 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 4.885449707085462000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 2.6833848035835737 " "
y[1] (numeric) = 2.6833848035837042 " "
absolute error = 1.3056222769591840000000000000E-13 " "
relative error = 4.8655797529134387000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 2.676050172695532 " "
y[1] (numeric) = 2.6760501726956623 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 4.862320587771452600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 2.6686479373535947 " "
y[1] (numeric) = 2.6686479373537235 " "
absolute error = 1.28785870856518160000000000000E-13 " "
relative error = 4.825884638204867000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 2.661178837775126 " "
y[1] (numeric) = 2.6611788377752545 " "
absolute error = 1.2834178164666810000000000000E-13 " "
relative error = 4.822741704723912000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 2.6536436208638614 " "
y[1] (numeric) = 2.6536436208639884 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 4.786231015292532500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 2.6460430401352077 " "
y[1] (numeric) = 2.646043040135337 " "
absolute error = 1.29229960066368220000000000000E-13 " "
relative error = 4.8838948613536090000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 2.6383778556409077 " "
y[1] (numeric) = 2.6383778556410395 " "
absolute error = 1.3189449532546860000000000000E-13 " "
relative error = 4.9990752857281370000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 2.6306488338930234 " "
y[1] (numeric) = 2.6306488338931584 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 5.131932398389780000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 2.6228567477872886 " "
y[1] (numeric) = 2.6228567477874267 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 5.265699103844851000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 2.615002376525821 " "
y[1] (numeric) = 2.6150023765259616 " "
absolute error = 1.40776279522469850000000000000E-13 " "
relative error = 5.38340923840761900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 2.6070865055392005 " "
y[1] (numeric) = 2.6070865055393435 " "
absolute error = 1.42996725571720160000000000000E-13 " "
relative error = 5.4849244652181350000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 2.5991099264079303 " "
y[1] (numeric) = 2.5991099264080764 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 5.621360934225426000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 2.591073436783276 " "
y[1] (numeric) = 2.5910734367834243 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 5.724492173176767000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 2.5829778403075023 " "
y[1] (numeric) = 2.5829778403076533 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 5.845591432989063000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 2.5748239465335114 " "
y[1] (numeric) = 2.574823946533665 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 5.967587291355877000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 2.566612570843885 " "
y[1] (numeric) = 2.566612570844042 " "
absolute error = 1.5676349107707210000000000000E-13 " "
relative error = 6.107797213255654000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 2.5583445343693505 " "
y[1] (numeric) = 2.55834453436951 " "
absolute error = 1.59428026336172480000000000000E-13 " "
relative error = 6.2316871005598380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 2.550020663906664 " "
y[1] (numeric) = 2.5500206639068264 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 6.373934654949608000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 2.5416417918359357 " "
y[1] (numeric) = 2.541641791836101 " "
absolute error = 1.6520118606422330000000000000E-13 " "
relative error = 6.499782408161123000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 2.533208756037391 " "
y[1] (numeric) = 2.533208756037559 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 6.62660433820346000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 2.5247223998075814 " "
y[1] (numeric) = 2.524722399807752 " "
absolute error = 1.70530256582424040000000000000E-13 " "
relative error = 6.75441611305151000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 2.5161835717750582 " "
y[1] (numeric) = 2.516183571775232 " "
absolute error = 1.73638881051374480000000000000E-13 " "
relative error = 6.90088286876779000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = 2.507593125815509 " "
y[1] (numeric) = 2.507593125815686 " "
absolute error = 1.76747505520324920000000000000E-13 " "
relative error = 7.04849218562297000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 2.498951920966371 " "
y[1] (numeric) = 2.4989519209665505 " "
absolute error = 1.7941204077942530000000000000E-13 " "
relative error = 7.179491500982731000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 2.4902608213409287 " "
y[1] (numeric) = 2.4902608213411104 " "
absolute error = 1.8163248682867560000000000000E-13 " "
relative error = 7.2937133842419000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 2.481520696041901 " "
y[1] (numeric) = 2.481520696042086 " "
absolute error = 1.84741111297626050000000000000E-13 " "
relative error = 7.444673404992898000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 2.4727324190745352 " "
y[1] (numeric) = 2.4727324190747235 " "
absolute error = 1.88293824976426550000000000000E-13 " "
relative error = 7.614807955925087000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 2.4638968692592043 " "
y[1] (numeric) = 2.4638968692593957 " "
absolute error = 1.914024494453770000000000000E-13 " "
relative error = 7.768281693662126000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 2.455014930143527 " "
y[1] (numeric) = 2.455014930143722 " "
absolute error = 1.9495516312417750000000000000E-13 " "
relative error = 7.941098880110675000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 2.446087489914013 " "
y[1] (numeric) = 2.4460874899142113 " "
absolute error = 1.985078768029780000000000000E-13 " "
relative error = 8.115322024313862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 2.4371154413072458 " "
y[1] (numeric) = 2.4371154413074474 " "
absolute error = 2.01616501271928430000000000000E-13 " "
relative error = 8.272751378727601000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 2.4280996815206097 " "
y[1] (numeric) = 2.4280996815208145 " "
absolute error = 2.04725125740878870000000000000E-13 " "
relative error = 8.431495926586865000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 2.41904111212257 " "
y[1] (numeric) = 2.4190411121227773 " "
absolute error = 2.07389660999979240000000000000E-13 " "
relative error = 8.573217708483124000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 2.4099406389625178 " "
y[1] (numeric) = 2.409940638962728 " "
absolute error = 2.10054196259079620000000000000E-13 " "
relative error = 8.716156442322505000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 2.4007991720801853 " "
y[1] (numeric) = 2.4007991720803985 " "
absolute error = 2.13162820728030060000000000000E-13 " "
relative error = 8.87882765068325100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 2.391617625614643 " "
y[1] (numeric) = 2.391617625614859 " "
absolute error = 2.1627144519698050000000000000E-13 " "
relative error = 9.042893934242476000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 2.382396917712886 " "
y[1] (numeric) = 2.3823969177131055 " "
absolute error = 2.19380069665930930000000000000E-13 " "
relative error = 9.208376154068272000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 2.3731379704380213 " "
y[1] (numeric) = 2.373137970438244 " "
absolute error = 2.22488694134881370000000000000E-13 " "
relative error = 9.375295364466971000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 2.363841709677059 " "
y[1] (numeric) = 2.3638417096772852 " "
absolute error = 2.26041407813681870000000000000E-13 " "
relative error = 9.562459571142898000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 2.3545090650483305 " "
y[1] (numeric) = 2.354509065048559 " "
absolute error = 2.28705943072782250000000000000E-13 " "
relative error = 9.713529944217380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 2.34514096980852 " "
y[1] (numeric) = 2.3451409698087518 " "
absolute error = 2.3181456754173269000000000000E-13 " "
relative error = 9.884888393752307000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 2.3357383607593447 " "
y[1] (numeric) = 2.3357383607595805 " "
absolute error = 2.35811370430383250000000000000E-13 " "
relative error = 1.009579559046679100000000000E-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) = 2.326302178153875 " "
y[1] (numeric) = 2.326302178154114 " "
absolute error = 2.39364084109183750000000000000E-13 " "
relative error = 1.028946653435798300000000000E-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) = 2.3168333656025073 " "
y[1] (numeric) = 2.31683336560275 " "
absolute error = 2.42916797787984250000000000000E-13 " "
relative error = 1.048486271798887700000000000E-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) = 2.307332869978606 " "
y[1] (numeric) = 2.3073328699788522 " "
absolute error = 2.4602542225693470000000000000E-13 " "
relative error = 1.066276242401105500000000000E-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) = 2.297801641323817 " "
y[1] (numeric) = 2.2978016413240665 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 1.086160491172542700000000000E-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) = 2.288240632753063 " "
y[1] (numeric) = 2.2882406327533156 " "
absolute error = 2.52686760404685630000000000000E-13 " "
relative error = 1.104284037211022300000000000E-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) = 2.278650800359233 " "
y[1] (numeric) = 2.2786508003594883 " "
absolute error = 2.553512956637860000000000000E-13 " "
relative error = 1.120624957643924600000000000E-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) = 2.2690331031175752 " "
y[1] (numeric) = 2.2690331031178346 " "
absolute error = 2.59348098552436570000000000000E-13 " "
relative error = 1.14298948832478900000000000E-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) = 2.2593885027897995 " "
y[1] (numeric) = 2.2593885027900624 " "
absolute error = 2.62900812231237070000000000000E-13 " "
relative error = 1.163592768161022400000000000E-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) = 2.249717963827901 " "
y[1] (numeric) = 2.249717963828167 " "
absolute error = 2.6600943670018750000000000000E-13 " "
relative error = 1.182412377805668300000000000E-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) = 2.2400224532777173 " "
y[1] (numeric) = 2.240022453277987 " "
absolute error = 2.695621503789880000000000000E-13 " "
relative error = 1.203390394522834600000000000E-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) = 2.2303029406822237 " "
y[1] (numeric) = 2.2303029406824963 " "
absolute error = 2.72670774847938450000000000000E-13 " "
relative error = 1.222572816787533100000000000E-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) = 2.2205603979845807 " "
y[1] (numeric) = 2.2205603979848565 " "
absolute error = 2.7577939931688890000000000000E-13 " "
relative error = 1.241936042663784700000000000E-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) = 2.2107957994309384 " "
y[1] (numeric) = 2.2107957994312177 " "
absolute error = 2.7933211299568940000000000000E-13 " "
relative error = 1.263491241785377700000000000E-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) = 2.2010101214730162 " "
y[1] (numeric) = 2.201010121473299 " "
absolute error = 2.8288482667448990000000000000E-13 " "
relative error = 1.285250003689989700000000000E-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) = 2.191204342670454 " "
y[1] (numeric) = 2.19120434267074 " "
absolute error = 2.8599345114344030000000000000E-13 " "
relative error = 1.305188409744094000000000000E-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) = 2.1813794435929617 " "
y[1] (numeric) = 2.1813794435932508 " "
absolute error = 2.89102075612390760000000000000E-13 " "
relative error = 1.325317685841071200000000000E-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) = 2.1715364067222587 " "
y[1] (numeric) = 2.171536406722551 " "
absolute error = 2.9221070008134120000000000000E-13 " "
relative error = 1.345640345594791600000000000E-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) = 2.1616762163538303 " "
y[1] (numeric) = 2.161676216354126 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 1.368213294491510400000000000E-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) = 2.151799858498496 " "
y[1] (numeric) = 2.151799858498795 " "
absolute error = 2.9931612743894220000000000000E-13 " "
relative error = 1.39100356502394200000000000E-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) = 2.1419083207838114 " "
y[1] (numeric) = 2.141908320784114 " "
absolute error = 3.02424751907892640000000000000E-13 " "
relative error = 1.411940693134910200000000000E-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) = 2.1320025923553048 " "
y[1] (numeric) = 2.1320025923556107 " "
absolute error = 3.05977465586693140000000000000E-13 " "
relative error = 1.435164603851011900000000000E-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) = 2.122083663777565 " "
y[1] (numeric) = 2.1220836637778735 " "
absolute error = 3.0864200084579350000000000000E-13 " "
relative error = 1.454428994078270600000000000E-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) = 2.1121525269351826 " "
y[1] (numeric) = 2.1121525269354944 " "
absolute error = 3.11750625314743960000000000000E-13 " "
relative error = 1.475985381449257700000000000E-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) = 2.1022101749335675 " "
y[1] (numeric) = 2.1022101749338824 " "
absolute error = 3.1485924978369440000000000000E-13 " "
relative error = 1.497753428929361500000000000E-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) = 2.0922576019996337 " "
y[1] (numeric) = 2.0922576019999526 " "
absolute error = 3.18856052672344960000000000000E-13 " "
relative error = 1.523980853827963700000000000E-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) = 2.082295803382381 " "
y[1] (numeric) = 2.0822958033827033 " "
absolute error = 3.22408766351145460000000000000E-13 " "
relative error = 1.548333170664034600000000000E-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) = 2.0723257752533697 " "
y[1] (numeric) = 2.072325775253695 " "
absolute error = 3.2551739082009590000000000000E-13 " "
relative error = 1.5707829083016500000000000E-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) = 2.062348514607104 " "
y[1] (numeric) = 2.0623485146074336 " "
absolute error = 3.29514193708746460000000000000E-13 " "
relative error = 1.597761927117938300000000000E-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) = 2.052365019161335 " "
y[1] (numeric) = 2.0523650191616674 " "
absolute error = 3.32178728967846840000000000000E-13 " "
relative error = 1.61851681287954400000000000E-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) = 2.0423762872572873 " "
y[1] (numeric) = 2.042376287257623 " "
absolute error = 3.35731442646647340000000000000E-13 " "
relative error = 1.64382755881631400000000000E-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) = 2.0323833177598267 " "
y[1] (numeric) = 2.032383317760166 " "
absolute error = 3.39284156325447840000000000000E-13 " "
relative error = 1.669390578837363600000000000E-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) = 2.0223871099575765 " "
y[1] (numeric) = 2.0223871099579185 " "
absolute error = 3.4194869158454820000000000000E-13 " "
relative error = 1.690817202606286500000000000E-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) = 2.0123886634629864 " "
y[1] (numeric) = 2.012388663463332 " "
absolute error = 3.4550140526334870000000000000E-13 " "
relative error = 1.71687215067490100000000000E-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) = 2.002388978112374 " "
y[1] (numeric) = 2.002388978112722 " "
absolute error = 3.4816594052244910000000000000E-13 " "
relative error = 1.738752781443396500000000000E-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) = 1.992389053865941 " "
y[1] (numeric) = 1.9923890538662925 " "
absolute error = 3.51496609596324560000000000000E-13 " "
relative error = 1.76419665082126700000000000E-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) = 1.9823898907077788 " "
y[1] (numeric) = 1.9823898907081339 " "
absolute error = 3.55049323275125060000000000000E-13 " "
relative error = 1.79101661554761400000000000E-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) = 1.972392488545871 " "
y[1] (numeric) = 1.9723924885462294 " "
absolute error = 3.58379992349000530000000000000E-13 " "
relative error = 1.81698112536016100000000000E-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) = 1.9623978471121024 " "
y[1] (numeric) = 1.9623978471124643 " "
absolute error = 3.61932706027801030000000000000E-13 " "
relative error = 1.844339090365530700000000000E-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) = 1.9524069658622876 " "
y[1] (numeric) = 1.9524069658626526 " "
absolute error = 3.65041330496751470000000000000E-13 " "
relative error = 1.869698976081708700000000000E-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) = 1.9424208438762258 " "
y[1] (numeric) = 1.9424208438765944 " "
absolute error = 3.68594044175551970000000000000E-13 " "
relative error = 1.897601363461477700000000000E-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) = 1.9324404797577939 " "
y[1] (numeric) = 1.9324404797581665 " "
absolute error = 3.72590847064202530000000000000E-13 " "
relative error = 1.928084466078364700000000000E-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) = 1.9224668715350868 " "
y[1] (numeric) = 1.9224668715354627 " "
absolute error = 3.759215161380780000000000000E-13 " "
relative error = 1.95541219307412700000000000E-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) = 1.9125010165606156 " "
y[1] (numeric) = 1.9125010165609948 " "
absolute error = 3.79252185211953500000000000000E-13 " "
relative error = 1.983016907849749800000000000E-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) = 1.9025439114115725 " "
y[1] (numeric) = 1.902543911411955 " "
absolute error = 3.8236080968090390000000000000E-13 " "
relative error = 2.00973447912282500000000000E-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) = 1.8925965517901755 " "
y[1] (numeric) = 1.8925965517905607 " "
absolute error = 3.8524738954492930000000000000E-13 " "
relative error = 2.03554946341062600000000000E-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) = 1.8826599324240967 " "
y[1] (numeric) = 1.8826599324244848 " "
absolute error = 3.88133969408954700000000000000E-13 " "
relative error = 2.061625483839754000000000000E-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) = 1.8727350469669923 " "
y[1] (numeric) = 1.8727350469673842 " "
absolute error = 3.91908727692680260000000000000E-13 " "
relative error = 2.092707819653400200000000000E-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) = 1.8628228878991375 " "
y[1] (numeric) = 1.8628228878995332 " "
absolute error = 3.9568348597640580000000000000E-13 " "
relative error = 2.124106851739681300000000000E-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) = 1.852924446428179 " "
y[1] (numeric) = 1.852924446428578 " "
absolute error = 3.98792110445356230000000000000E-13 " "
relative error = 2.152230822007311400000000000E-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) = 1.8430407123900152 " "
y[1] (numeric) = 1.8430407123904171 " "
absolute error = 4.01900734914306670000000000000E-13 " "
relative error = 2.180639484589195800000000000E-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) = 1.8331726741498133 " "
y[1] (numeric) = 1.833172674150219 " "
absolute error = 4.0567549319803220000000000000E-13 " "
relative error = 2.212969344997333400000000000E-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) = 1.8233213185031742 " "
y[1] (numeric) = 1.8233213185035833 " "
absolute error = 4.09006162271907670000000000000E-13 " "
relative error = 2.243193002359422400000000000E-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) = 1.813487630577453 " "
y[1] (numeric) = 1.8134876305778656 " "
absolute error = 4.12558875950708170000000000000E-13 " "
relative error = 2.27494728386617520000000000E-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) = 1.8036725937332476 " "
y[1] (numeric) = 1.803672593733663 " "
absolute error = 4.1544545581473360000000000000E-13 " "
relative error = 2.30333075558265900000000000E-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) = 1.7938771894660634 " "
y[1] (numeric) = 1.793877189466482 " "
absolute error = 4.185540802836840000000000000E-13 " "
relative error = 2.333237095278880600000000000E-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) = 1.784102397308164 " "
y[1] (numeric) = 1.7841023973085859 " "
absolute error = 4.2188474935755950000000000000E-13 " "
relative error = 2.364689100771878400000000000E-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) = 1.7743491947306198 " "
y[1] (numeric) = 1.7743491947310446 " "
absolute error = 4.2477132922158490000000000000E-13 " "
relative error = 2.393955656998358300000000000E-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) = 1.7646185570455608 " "
y[1] (numeric) = 1.7646185570459887 " "
absolute error = 4.27879953690535330000000000000E-13 " "
relative error = 2.424773059209576500000000000E-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) = 1.7549114573086468 " "
y[1] (numeric) = 1.754911457309078 " "
absolute error = 4.3121062276441080000000000000E-13 " "
relative error = 2.457164553622098700000000000E-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) = 1.7452288662217623 " "
y[1] (numeric) = 1.7452288662221966 " "
absolute error = 4.34319247233361240000000000000E-13 " "
relative error = 2.48860911963722500000000000E-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) = 1.7355717520359468 " "
y[1] (numeric) = 1.7355717520363845 " "
absolute error = 4.3764991630723670000000000000E-13 " "
relative error = 2.521646920064485000000000000E-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) = 1.7259410804545716 " "
y[1] (numeric) = 1.7259410804550124 " "
absolute error = 4.40758540776187150000000000000E-13 " "
relative error = 2.553728778853226500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = sin ( x ) ; "
Iterations = 5000
"Total Elapsed Time "= 1 Minutes 35 Seconds
"Elapsed Time(since restart) "= 1 Minutes 35 Seconds
"Time to Timeout "= 1 Minutes 24 Seconds
Percent Done = 100.0200000000001 "%"
(%o252) temp/diffeq.sin_lg_h.max