(%i1) batch("temp/diffeq.cos.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.cos.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(sin(c(x))+c(1.0))
(%o238) exact_soln_y(x) := block(sin(c(x)) + c(1.0))
(%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]:cos(array_x[1]),
array_tmp1_g[1]:sin(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]:neg(array_tmp1_g[1])*array_x[2]/c(1),
array_tmp1_g[2]: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]:neg(array_tmp1_g[2])*array_x[2]/c(2),
array_tmp1_g[3]: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]:neg(array_tmp1_g[3])*array_x[2]/c(3),
array_tmp1_g[4]: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]:neg(array_tmp1_g[4])*array_x[2]/c(4),
array_tmp1_g[5]: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]
:neg(array_tmp1_g[kkk-1])*array_x[2]/c(kkk-1),
array_tmp1_g[kkk]
: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(sin(c(x))+c(1.0))
(%o249) exact_soln_y(x) := block(sin(c(x)) + c(1.0))
(%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:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 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/cospostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = cos ( x ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.0),"),
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,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (c(1.0) + sin(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.0),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:false,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 ) = cos ( x ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:27:43-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"cos"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cos ( x ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_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,
"cos diffeq.max"),
logitem_str(html_log_file,
"cos 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_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/cospostode.ode#################"
"diff ( y , x , 1 ) = cos ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"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_type_given_pole:3,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (c(1.0) + sin(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) = 1.0099998333341667 " "
y[1] (numeric) = 1.0099998333341667 " "
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] = 2.00000000000000120E-2 " "
y[1] (closed_form) = 1.0199986666933332 " "
y[1] (numeric) = 1.0199986666933332 " "
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) = 1.0299955002024956 " "
y[1] (numeric) = 1.029995500202496 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.311564562784549500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000000300E-2 " "
y[1] (closed_form) = 1.0399893341866342 " "
y[1] (numeric) = 1.0399893341866344 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.135066174488128900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000000300E-2 " "
y[1] (closed_form) = 1.0499791692706784 " "
y[1] (numeric) = 1.0499791692706788 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.229504954450949400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.000000000000004000E-2 " "
y[1] (closed_form) = 1.0599640064794447 " "
y[1] (numeric) = 1.0599640064794447 " "
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] = 7.00000000000000500E-2 " "
y[1] (closed_form) = 1.0699428473375328 " "
y[1] (numeric) = 1.069942847337533 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.07529407274016110000000000000E-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) = 1.0799146939691728 " "
y[1] (numeric) = 1.079914693969173 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.056130971872578200000000000000E-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) = 1.0898785491980112 " "
y[1] (numeric) = 1.0898785491980114 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.03733347250868600000000000000E-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) = 1.0998334166468282 " "
y[1] (numeric) = 1.0998334166468287 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.037786114955496700000000000000E-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) = 1.1097783008371749 " "
y[1] (numeric) = 1.1097783008371753 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.00160292839622570000000000000E-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) = 1.1197122072889194 " "
y[1] (numeric) = 1.1197122072889196 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.98305067569685900000000000000E-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) = 1.129634142619695 " "
y[1] (numeric) = 1.1296341426196947 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.965632911998352300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1400000000000001 " "
y[1] (closed_form) = 1.1395431146442365 " "
y[1] (numeric) = 1.1395431146442363 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.948540621864520200000000000000E-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) = 1.1494381324735994 " "
y[1] (numeric) = 1.149438132473599 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.863532949741100000000000000000E-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) = 1.159318206614246 " "
y[1] (numeric) = 1.1593182066142456 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.83060670760111500000000000000E-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) = 1.1691823490669961 " "
y[1] (numeric) = 1.1691823490669955 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.69743304204572200000000000000E-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) = 1.1790295734258243 " "
y[1] (numeric) = 1.1790295734258238 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.76656548622188900000000000000E-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) = 1.1888588949765007 " "
y[1] (numeric) = 1.1888588949765 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.60313606257083200000000000000E-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) = 1.1986693307950613 " "
y[1] (numeric) = 1.1986693307950607 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.557277538195261000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000016 " "
y[1] (closed_form) = 1.2084598998460998 " "
y[1] (numeric) = 1.208459899846099 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.34967225485294800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000017 " "
y[1] (closed_form) = 1.2182296230808696 " "
y[1] (numeric) = 1.2182296230808687 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.2907307692448500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000018 " "
y[1] (closed_form) = 1.2279775235351886 " "
y[1] (numeric) = 1.2279775235351877 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.23285567266063900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000019 " "
y[1] (closed_form) = 1.2377026264271347 " "
y[1] (numeric) = 1.2377026264271342 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.588012179726975400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25000000000000017 " "
y[1] (closed_form) = 1.2474039592545232 " "
y[1] (numeric) = 1.2474039592545225 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.34016113892399800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000002 " "
y[1] (closed_form) = 1.2570805518921553 " "
y[1] (numeric) = 1.2570805518921548 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.532702889895324400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000002 " "
y[1] (closed_form) = 1.2667314366888314 " "
y[1] (numeric) = 1.2667314366888307 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.258682270618721000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000002 " "
y[1] (closed_form) = 1.2763556485641139 " "
y[1] (numeric) = 1.2763556485641132 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.21902978628634700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000002 " "
y[1] (closed_form) = 1.2859522251048356 " "
y[1] (numeric) = 1.2859522251048352 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.453388090011343400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3000000000000002 " "
y[1] (closed_form) = 1.2955202066613398 " "
y[1] (numeric) = 1.2955202066613392 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.14182497000007800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3100000000000002 " "
y[1] (closed_form) = 1.3050586364434438 " "
y[1] (numeric) = 1.305058636443443 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.10424433181368100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.32000000000000023 " "
y[1] (closed_form) = 1.314566560616118 " "
y[1] (numeric) = 1.3145665606161177 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.378217757508790700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.33000000000000024 " "
y[1] (closed_form) = 1.3240430283948685 " "
y[1] (numeric) = 1.324043028394868 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.35403910844521400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.34000000000000025 " "
y[1] (closed_form) = 1.3334870921408146 " "
y[1] (numeric) = 1.333487092140814 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.9954275425768500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.35000000000000026 " "
y[1] (closed_form) = 1.3428978074554516 " "
y[1] (numeric) = 1.342897807455451 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.96042074889746800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.36000000000000026 " "
y[1] (closed_form) = 1.3522742332750903 " "
y[1] (numeric) = 1.3522742332750897 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.92602608541742200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000003 " "
y[1] (closed_form) = 1.3616154319649623 " "
y[1] (numeric) = 1.3616154319649616 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.89223167670616700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000003 " "
y[1] (closed_form) = 1.370920469412983 " "
y[1] (numeric) = 1.3709204694129824 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.859025958379095700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3900000000000003 " "
y[1] (closed_form) = 1.3801884151231616 " "
y[1] (numeric) = 1.3801884151231611 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.21759844514007300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4000000000000003 " "
y[1] (closed_form) = 1.3894183423086508 " "
y[1] (numeric) = 1.38941834230865 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.39244777943792100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4100000000000003 " "
y[1] (closed_form) = 1.3986093279844232 " "
y[1] (numeric) = 1.3986093279844223 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.35043969698175300000000000000E-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) = 1.4077604530595704 " "
y[1] (numeric) = 1.4077604530595698 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.7318690713845896000000000000E-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) = 1.416870802429211 " "
y[1] (numeric) = 1.4168708024292103 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.70144358704416900000000000000E-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) = 1.425939465066 " "
y[1] (numeric) = 1.4259394650659991 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.22872458094857400000000000000E-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) = 1.4349655341112304 " "
y[1] (numeric) = 1.4349655341112295 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.18954531371537900000000000000E-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) = 1.44394810696552 " "
y[1] (numeric) = 1.4439481069655193 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.61328084826389500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.47000000000000036 " "
y[1] (closed_form) = 1.4528862853790687 " "
y[1] (numeric) = 1.4528862853790678 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.11319983289946900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.48000000000000037 " "
y[1] (closed_form) = 1.4617791755414833 " "
y[1] (numeric) = 1.4617791755414828 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.038004763514021700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000004 " "
y[1] (closed_form) = 1.4706258881711585 " "
y[1] (numeric) = 1.470625888171158 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.019729309962870000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = 1.4794255386042032 " "
y[1] (numeric) = 1.4794255386042023 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.00353580848750800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = 1.4881772468829078 " "
y[1] (numeric) = 1.4881772468829069 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.96823007179069200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (closed_form) = 1.496880137843737 " "
y[1] (numeric) = 1.4968801378437362 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.93353066318022300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (closed_form) = 1.5055333412048473 " "
y[1] (numeric) = 1.5055333412048464 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.89942710261955700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = 1.5141359916531134 " "
y[1] (numeric) = 1.5141359916531125 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.86590916929742900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (closed_form) = 1.5226872289306594 " "
y[1] (numeric) = 1.5226872289306583 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.29120861810100700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = 1.5311861979208836 " "
y[1] (numeric) = 1.5311861979208825 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.25073819325611300000000000000E-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) = 1.5396320487339694 " "
y[1] (numeric) = 1.5396320487339683 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.21096333073922700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = 1.548023936791874 " "
y[1] (numeric) = 1.5480239367918724 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.00406214499265250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = 1.556361022912784 " "
y[1] (numeric) = 1.5563610229127827 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 8.56014517156695600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = 1.5646424733950357 " "
y[1] (numeric) = 1.5646424733950342 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 9.93397700052586900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = 1.5728674601004817 " "
y[1] (numeric) = 1.5728674601004802 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 9.88202931209424900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = 1.5810351605373054 " "
y[1] (numeric) = 1.581035160537304 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 8.42655282313534800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = 1.58914475794227 " "
y[1] (numeric) = 1.5891447579422682 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.11780681433980570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = 1.5971954413623926 " "
y[1] (numeric) = 1.5971954413623912 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 8.34129371427316500000000000000E-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) = 1.6051864057360399 " "
y[1] (numeric) = 1.605186405736039 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.533179302579885000000000000000E-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) = 1.6131168519734342 " "
y[1] (numeric) = 1.6131168519734334 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.505976945275581000000000000000E-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) = 1.6209859870365602 " "
y[1] (numeric) = 1.6209859870365595 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.10943598588967800000000000000E-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) = 1.628793024018469 " "
y[1] (numeric) = 1.6287930240184685 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.726492582553123300000000000000E-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) = 1.6365371822219683 " "
y[1] (numeric) = 1.6365371822219683 " "
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] = 0.7000000000000005 " "
y[1] (closed_form) = 1.6442176872376915 " "
y[1] (numeric) = 1.6442176872376912 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.350457464656455200000000000000E-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) = 1.6518337710215372 " "
y[1] (numeric) = 1.6518337710215367 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.688461863662142000000000000000E-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) = 1.6593846719714735 " "
y[1] (numeric) = 1.6593846719714733 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.338114113475723800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = 1.6668696350036982 " "
y[1] (numeric) = 1.666869635003698 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.332105404418976500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = 1.6742879116281455 " "
y[1] (numeric) = 1.6742879116281453 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.326203237704237600000000000000E-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) = 1.6816387600233345 " "
y[1] (numeric) = 1.6816387600233347 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.320406083658241800000000000000E-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) = 1.6889214451105516 " "
y[1] (numeric) = 1.6889214451105519 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.314712448988395200000000000000E-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) = 1.6961352386273572 " "
y[1] (numeric) = 1.6961352386273572 " "
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] = 0.7800000000000006 " "
y[1] (closed_form) = 1.7032794192004106 " "
y[1] (numeric) = 1.7032794192004104 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.303629941288600700000000000000E-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) = 1.7103532724176083 " "
y[1] (numeric) = 1.7103532724176083 " "
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] = 0.8000000000000006 " "
y[1] (closed_form) = 1.7173560908995231 " "
y[1] (numeric) = 1.7173560908995231 " "
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] = 0.8100000000000006 " "
y[1] (closed_form) = 1.724287174370143 " "
y[1] (numeric) = 1.7242871743701431 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.287747239702928000000000000000E-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) = 1.7311458297268962 " "
y[1] (numeric) = 1.7311458297268965 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.282645292569377600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = 1.737931371109963 " "
y[1] (numeric) = 1.7379313711099633 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.277637360232575200000000000000E-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) = 1.7446431199708599 " "
y[1] (numeric) = 1.7446431199708596 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.272722211111806400000000000000E-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) = 1.7512804051402933 " "
y[1] (numeric) = 1.7512804051402928 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.535797286069030000000000000000E-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) = 1.7578425628952774 " "
y[1] (numeric) = 1.757842562895277 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.526330965149801000000000000000E-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) = 1.7643289370255055 " "
y[1] (numeric) = 1.7643289370255049 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.775564753237758400000000000000E-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) = 1.7707388788989697 " "
y[1] (numeric) = 1.770738878898969 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.76189749213215600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = 1.7770717475268243 " "
y[1] (numeric) = 1.7770717475268236 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.748491391538702500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = 1.7833269096274837 " "
y[1] (numeric) = 1.783326909627483 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.73534325747510600000000000000E-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) = 1.789503739689951 " "
y[1] (numeric) = 1.78950373968995 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.96326663085940800000000000000E-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) = 1.7956016200363665 " "
y[1] (numeric) = 1.7956016200363658 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.70980849728573200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = 1.8016199408837776 " "
y[1] (numeric) = 1.8016199408837767 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.92988781676357800000000000000E-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) = 1.8075581004051147 " "
y[1] (numeric) = 1.8075581004051136 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.14211529010508900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = 1.8134155047893743 " "
y[1] (numeric) = 1.8134155047893727 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 8.57118641795086300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = 1.8191915683009987 " "
y[1] (numeric) = 1.819191568300997 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 9.76453975685060300000000000000E-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) = 1.8248857133384506 " "
y[1] (numeric) = 1.824885713338449 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 8.51731274520066500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = 1.830497370491971 " "
y[1] (numeric) = 1.8304973704919698 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.0651440560483790000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (closed_form) = 1.8360259786005209 " "
y[1] (numeric) = 1.83602597860052 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.837504643464380400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (closed_form) = 1.8414709848078967 " "
y[1] (numeric) = 1.8414709848078958 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.82320072934942560000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0099999999999996 " "
y[1] (closed_form) = 1.846831844618015 " "
y[1] (numeric) = 1.8468318446180148 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.20230006631143710000000000000E-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) = 1.8521080219493622 " "
y[1] (numeric) = 1.8521080219493624 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.198875023991997600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999974 " "
y[1] (closed_form) = 1.857298989188602 " "
y[1] (numeric) = 1.857298989188603 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.78209714682579830000000000000E-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) = 1.8624042272433365 " "
y[1] (numeric) = 1.8624042272433379 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 7.15348263315618800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = 1.8674232255940146 " "
y[1] (numeric) = 1.8674232255940164 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 9.51234200718052800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = 1.8723554823449833 " "
y[1] (numeric) = 1.872355482344986 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.4230926147438880000000000000E-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) = 1.8772005042746782 " "
y[1] (numeric) = 1.8772005042746815 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.77427454674714690000000000000E-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) = 1.8819578068849436 " "
y[1] (numeric) = 1.8819578068849474 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.00576137781409260000000000000E-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) = 1.886626914449483 " "
y[1] (numeric) = 1.8866269144494872 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.23618536408225320000000000000E-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) = 1.8912073600614305 " "
y[1] (numeric) = 1.8912073600614352 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 2.4655872232192430000000000000E-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) = 1.8956986856800424 " "
y[1] (numeric) = 1.895698685680048 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 2.9282686985323490000000000000E-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) = 1.9001004421764995 " "
y[1] (numeric) = 1.9001004421765055 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.15520390390970350000000000000E-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) = 1.90441218937882 " "
y[1] (numeric) = 1.9044121893788262 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 3.26465508495238900000000000000E-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) = 1.908633496115877 " "
y[1] (numeric) = 1.9086334961158837 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 3.49010858360546960000000000000E-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) = 1.9127639402605146 " "
y[1] (numeric) = 1.9127639402605217 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.7147434704531584000000000000E-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) = 1.9168031087717603 " "
y[1] (numeric) = 1.9168031087717678 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 3.9385978314113890000000000000E-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) = 1.9207505977361286 " "
y[1] (numeric) = 1.9207505977361365 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.1617093789910575000000000000E-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) = 1.924606012408013 " "
y[1] (numeric) = 1.9246060124080215 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.3841154671413410000000000000E-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) = 1.9283689672491593 " "
y[1] (numeric) = 1.928368967249168 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.490706778189570400000000000E-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) = 1.9320390859672187 " "
y[1] (numeric) = 1.9320390859672278 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.7120313807568330000000000000E-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) = 1.9356160015533779 " "
y[1] (numeric) = 1.9356160015533874 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.9327542261036880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = 1.9390993563190595 " "
y[1] (numeric) = 1.939099356319069 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.9238931366059050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = 1.9424888019316893 " "
y[1] (numeric) = 1.9424888019316993 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.1439201151069470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = 1.9457839994495307 " "
y[1] (numeric) = 1.9457839994495412 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 5.3634403584513390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = 1.9489846193555778 " "
y[1] (numeric) = 1.9489846193555886 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 5.5824892270950890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = 1.952090341590507 " "
y[1] (numeric) = 1.9520903415905184 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 5.8011018291038230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = 1.9551008555846836 " "
y[1] (numeric) = 1.9551008555846954 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 6.0193130330901860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = 1.9580158602892164 " "
y[1] (numeric) = 1.9580158602892288 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 6.3505603442686450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = 1.960835064206064 " "
y[1] (numeric) = 1.960835064206077 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 6.6811492357115980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = 1.9635581854171842 " "
y[1] (numeric) = 1.9635581854171975 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 6.7849663913429180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = 1.9661849516127254 " "
y[1] (numeric) = 1.966184951612739 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 6.8888335704721540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = 1.9687151001182568 " "
y[1] (numeric) = 1.9687151001182703 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 6.8799801960239470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = 1.9711483779210361 " "
y[1] (numeric) = 1.97114837792105 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 6.9841345580852220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = 1.9734845416953108 " "
y[1] (numeric) = 1.973484541695325 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.2008948714613420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = 1.9757233578266509 " "
y[1] (numeric) = 1.975723357826665 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.192735085560931000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = 1.9778646024353082 " "
y[1] (numeric) = 1.9778646024353224 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.1849482000458690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = 1.9799080613986062 " "
y[1] (numeric) = 1.9799080613986209 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 7.4018305247465990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = 1.981853530372352 " "
y[1] (numeric) = 1.9818535303723668 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.5066034406599160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = 1.983700814811269 " "
y[1] (numeric) = 1.983700814811284 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.6115475792344540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = 1.9854497299884528 " "
y[1] (numeric) = 1.985449729988468 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.6048428257057620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = 1.9871001010138434 " "
y[1] (numeric) = 1.9871001010138585 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.5985266807637990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = 1.9886517628517129 " "
y[1] (numeric) = 1.9886517628517284 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 7.8159095700412930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = 1.9901045603371712 " "
y[1] (numeric) = 1.9901045603371867 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 7.8102038729657590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = 1.99145834819168 " "
y[1] (numeric) = 1.9914583481916954 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 7.6933960249478890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = 1.9927129910375827 " "
y[1] (numeric) = 1.9927129910375976 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4656955602175400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = 1.9938683634116394 " "
y[1] (numeric) = 1.9938683634116545 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.5727331914062250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = 1.9949243497775757 " "
y[1] (numeric) = 1.9949243497775913 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 7.7913342159993050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = 1.9958808445376355 " "
y[1] (numeric) = 1.995880844537651 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 7.7876003406169770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = 1.996737752043139 " "
y[1] (numeric) = 1.9967377520431544 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 7.6730545732157570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = 1.9974949866040506 " "
y[1] (numeric) = 1.9974949866040663 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 7.8924688449304430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = 1.9981524724975448 " "
y[1] (numeric) = 1.9981524724975603 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 7.7787468967893250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = 1.9987101439755801 " "
y[1] (numeric) = 1.9987101439755954 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 7.665482554339981000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = 1.9991679452714737 " "
y[1] (numeric) = 1.999167945271489 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 7.6637271901369250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = 1.9995258306054773 " "
y[1] (numeric) = 1.9995258306054924 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.5513068667534980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = 1.9997837641893557 " "
y[1] (numeric) = 1.9997837641893708 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.5503328936280090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = 1.9999417202299656 " "
y[1] (numeric) = 1.9999417202299805 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4387110281725850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = 1.9999996829318345 " "
y[1] (numeric) = 1.9999996829318496 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 7.5495177643069390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = 1.9999576464987405 " "
y[1] (numeric) = 1.9999576464987554 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4386517914625570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = 1.999815615134292 " "
y[1] (numeric) = 1.999815615134307 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4391801011005090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = 1.9995736030415072 " "
y[1] (numeric) = 1.999573603041522 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4400804788321060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = 1.9992316344213932 " "
y[1] (numeric) = 1.9992316344214078 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 7.3302881330673940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = 1.9987897434705273 " "
y[1] (numeric) = 1.998789743470542 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 7.3319087077195420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = 1.9982479743776365 " "
y[1] (numeric) = 1.9982479743776513 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4450161945544350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = 1.9976063813191784 " "
y[1] (numeric) = 1.9976063813191933 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4474073917168000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = 1.9968650284539244 " "
y[1] (numeric) = 1.996865028453939 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 7.3389757025284160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = 1.996023989916543 " "
y[1] (numeric) = 1.996023989916558 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 7.4533114857998920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = 1.9950833498101874 " "
y[1] (numeric) = 1.9950833498102019 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.2342337584543440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = 1.994043202198084 " "
y[1] (numeric) = 1.9940432021980985 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.2380073331496960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = 1.9929036510941276 " "
y[1] (numeric) = 1.992903651094142 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.2421460576898470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = 1.9916648104524786 " "
y[1] (numeric) = 1.9916648104524928 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.1351638290850240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = 1.9903268041561688 " "
y[1] (numeric) = 1.990326804156183 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 7.1399604755998480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = 1.9888897660047131 " "
y[1] (numeric) = 1.988889766004727 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 7.0334768418954310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = 1.987353839700729 " "
y[1] (numeric) = 1.9873538397007429 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 6.9271838916340370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = 1.9857191788355673 " "
y[1] (numeric) = 1.985719178835581 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 6.9328864081500290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 1.9839859468739514 " "
y[1] (numeric) = 1.9839859468739653 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 7.0508614903841980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 1.9821543171376341 " "
y[1] (numeric) = 1.9821543171376477 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 6.8333331987927200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 1.9802244727880622 " "
y[1] (numeric) = 1.980224472788076 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 6.9521237084647210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 1.9781966068080625 " "
y[1] (numeric) = 1.978196606808076 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 6.8470044149363500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 1.976070921982543 " "
y[1] (numeric) = 1.9760709219825567 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 6.9667365438180160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 1.9738476308782151 " "
y[1] (numeric) = 1.9738476308782285 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 6.7495971254753240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 1.9715269558223363 " "
y[1] (numeric) = 1.9715269558223496 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 6.7575420443312710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 1.9691091288804785 " "
y[1] (numeric) = 1.9691091288804914 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 6.5403115026813340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 1.9665943918333209 " "
y[1] (numeric) = 1.9665943918333335 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 6.4357665888225990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 1.9639829961524726 " "
y[1] (numeric) = 1.963982996152485 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 6.331265545659750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 1.9612752029753255 " "
y[1] (numeric) = 1.9612752029753378 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 6.2267922688004150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 1.958471283078941 " "
y[1] (numeric) = 1.958471283078953 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 6.1223306001716780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 1.955571516852972 " "
y[1] (numeric) = 1.9555715168529832 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 5.7907751026156940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 1.9525761942716247 " "
y[1] (numeric) = 1.9525761942716355 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 5.5722207785008890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 1.949485614864661 " "
y[1] (numeric) = 1.9494856148646713 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.239357371334350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 1.9463000876874463 " "
y[1] (numeric) = 1.9463000876874565 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 5.2479326755246490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 1.9430199312900438 " "
y[1] (numeric) = 1.9430199312900538 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.1425140116768330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 1.9396454736853594 " "
y[1] (numeric) = 1.939645473685369 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 4.922506788642740400000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 1.9361770523163417 " "
y[1] (numeric) = 1.936177052316351 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 4.8166428765873065000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 1.9326150140222376 " "
y[1] (numeric) = 1.9326150140222464 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 4.5957338282890187000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 1.9289597150039077 " "
y[1] (numeric) = 1.9289597150039162 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 4.374220426440630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 1.9252115207882081 " "
y[1] (numeric) = 1.925211520788216 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.0367310752401440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = 1.9213708061914367 " "
y[1] (numeric) = 1.921370806191444 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 3.8136688342062570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = 1.9174379552818526 " "
y[1] (numeric) = 1.9174379552818592 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 3.47408276205305460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = 1.9134133613412692 " "
y[1] (numeric) = 1.9134133613412756 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.3653436695519240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = 1.9092974268257272 " "
y[1] (numeric) = 1.9092974268257332 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.1400054537040245000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 1.9050905633252477 " "
y[1] (numeric) = 1.9050905633252533 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 2.9138326702099490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 1.9007931915226757 " "
y[1] (numeric) = 1.9007931915226808 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 2.68678672464341850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 1.8964057411516098 " "
y[1] (numeric) = 1.8964057411516144 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 2.4588286157550052000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 1.891928650953431 " "
y[1] (numeric) = 1.8919286509534354 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.34728307341963150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 1.8873623686334282 " "
y[1] (numeric) = 1.8873623686334327 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.3529620873579870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 1.8827073508160286 " "
y[1] (numeric) = 1.8827073508160326 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.12290183438133100000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 1.877964062999134 " "
y[1] (numeric) = 1.8779640629991377 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.8917900234612420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 1.8731329795075742 " "
y[1] (numeric) = 1.8731329795075768 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.42250191964526320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 1.8682145834456718 " "
y[1] (numeric) = 1.8682145834456736 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 9.50831266997176600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 1.8632093666489344 " "
y[1] (numeric) = 1.8632093666489358 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 7.1503914342505200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 1.858117829634871 " "
y[1] (numeric) = 1.8581178296348722 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.97498719897284800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 1.8529404815529402 " "
y[1] (numeric) = 1.8529404815529409 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.595009237516418000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 1.8476778401336353 " "
y[1] (numeric) = 1.8476778401336353 " "
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] = 2.1399999999998753 " "
y[1] (closed_form) = 1.842330431636713 " "
y[1] (numeric) = 1.842330431636712 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.02618838380063100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 1.8368987907985665 " "
y[1] (numeric) = 1.8368987907985652 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 7.25280911623336000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 1.8313834607787536 " "
y[1] (numeric) = 1.831383460778752 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 8.48709332459671600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 1.8257849931056802 " "
y[1] (numeric) = 1.825784993105678 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.21615965605748010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 1.820103947621448 " "
y[1] (numeric) = 1.8201039476214451 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.5859423126891478000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 1.8143408924258715 " "
y[1] (numeric) = 1.8143408924258677 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.0805121570503088000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 1.8084964038196674 " "
y[1] (numeric) = 1.8084964038196634 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.21001428601629720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 1.8025710662468262 " "
y[1] (numeric) = 1.8025710662468215 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 2.58682544657418860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 1.7965654722361672 " "
y[1] (numeric) = 1.796565472236162 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 2.9662545565721630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 1.790480222342087 " "
y[1] (numeric) = 1.790480222342081 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.34837785872532770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 1.7843159250845042 " "
y[1] (numeric) = 1.784315925084497 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.98215767606540500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 1.7780731968880072 " "
y[1] (numeric) = 1.7780731968879993 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 4.4956561919338170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 1.7717526620202135 " "
y[1] (numeric) = 1.7717526620202049 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 4.8876684526620595000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 1.7653549525293428 " "
y[1] (numeric) = 1.7653549525293335 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 5.2827185793369810000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 1.7588807081810132 " "
y[1] (numeric) = 1.7588807081810032 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 5.6808896562177160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = 1.7523305763942636 " "
y[1] (numeric) = 1.7523305763942532 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 5.9555523210412860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = 1.7457052121768148 " "
y[1] (numeric) = 1.7457052121768035 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 6.4869342041178550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = 1.7390052780595675 " "
y[1] (numeric) = 1.7390052780595553 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 7.0226660177269450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = 1.73223144403035 " "
y[1] (numeric) = 1.7322314440303366 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 7.6910486421515710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = 1.72538438746692 " "
y[1] (numeric) = 1.725384387466906 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 8.1076484822111400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = 1.718464793069228 " "
y[1] (numeric) = 1.7184647930692138 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 8.2695058825272780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = 1.7114733527909483 " "
y[1] (numeric) = 1.7114733527909334 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 8.6925037458028610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = 1.7044107657702818 " "
y[1] (numeric) = 1.704410765770266 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 9.2496288255679970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = 1.6972777382600452 " "
y[1] (numeric) = 1.697277738260029 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 9.5501495094987320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = 1.6900749835570457 " "
y[1] (numeric) = 1.6900749835570288 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 9.9849948306940180000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = 1.682803221930751 " "
y[1] (numeric) = 1.6828032219307332 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.0555939139230798000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = 1.6754631805512639 " "
y[1] (numeric) = 1.6754631805512452 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.1132292866958615000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = 1.668055593416606 " "
y[1] (numeric) = 1.6680555934165864 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.1714193046395997000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = 1.6605812012793173 " "
y[1] (numeric) = 1.6605812012792966 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.243549441732747900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = 1.6530407515723835 " "
y[1] (numeric) = 1.6530407515723617 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 1.3163844425465285000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = 1.6454349983344911 " "
y[1] (numeric) = 1.6454349983344687 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 1.362952965029203000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = 1.6377647021346262 " "
y[1] (numeric) = 1.637764702134603 " "
absolute error = 2.331468351712828700000000000000E-14 " "
relative error = 1.4235673468075385000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = 1.6300306299960163 " "
y[1] (numeric) = 1.6300306299959928 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 1.4439439166925863000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = 1.622233555319431 " "
y[1] (numeric) = 1.6222335553194065 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 1.5056344052101660000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = 1.6143742578058395 " "
y[1] (numeric) = 1.6143742578058144 " "
absolute error = 2.509104035652854000000000000000E-14 " "
relative error = 1.5542269851744770000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = 1.6064535233784447 " "
y[1] (numeric) = 1.6064535233784185 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 1.6310003993175756000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = 1.598472144104088 " "
y[1] (numeric) = 1.5984721441040612 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 1.6808173539356502000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = 1.5904309181140464 " "
y[1] (numeric) = 1.5904309181140186 " "
absolute error = 2.775557561562891400000000000000E-14 " "
relative error = 1.7451607171056407000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = 1.5823306495242173 " "
y[1] (numeric) = 1.582330649524189 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.7961928146275860000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = 1.5741721483547098 " "
y[1] (numeric) = 1.57417214835468 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.8901348935090995000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = 1.565956230448842 " "
y[1] (numeric) = 1.5659562304488117 " "
absolute error = 3.01980662698042600000000000000E-14 " "
relative error = 1.928410621103295000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = 1.5576837173915579 " "
y[1] (numeric) = 1.5576837173915268 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 1.995671158555879000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = 1.5493554364272695 " "
y[1] (numeric) = 1.5493554364272373 " "
absolute error = 3.21964677141295400000000000000E-14 " "
relative error = 2.0780556195919037000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = 1.540972220377133 " "
y[1] (numeric) = 1.5409722203771001 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 2.132588835434161000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = 1.5325349075557677 " "
y[1] (numeric) = 1.5325349075557337 " "
absolute error = 3.39728245535297900000000000000E-14 " "
relative error = 2.21677329410479000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = 1.5240443416874245 " "
y[1] (numeric) = 1.52404434168739 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 2.2728314013457487000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = 1.5155013718216144 " "
y[1] (numeric) = 1.515501371821579 " "
absolute error = 3.53050921830799800000000000000E-14 " "
relative error = 2.3295981672813454000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = 1.5069068522482054 " "
y[1] (numeric) = 1.506906852248169 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 2.416560463135189000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = 1.4982616424119926 " "
y[1] (numeric) = 1.4982616424119548 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 2.519425297205565000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = 1.4895666068267552 " "
y[1] (numeric) = 1.4895666068267166 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 2.5937585523121900000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = 1.480822614988806 " "
y[1] (numeric) = 1.4808226149887664 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 2.6690529491241155000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = 1.472030541290042 " "
y[1] (numeric) = 1.4720305412900014 " "
absolute error = 4.06341627012807300000000000000E-14 " "
relative error = 2.760415736053289000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = 1.4631912649305066 " "
y[1] (numeric) = 1.463191264930465 " "
absolute error = 4.152234112098085500000000000000E-14 " "
relative error = 2.8377931249441224000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = 1.4543056698304695 " "
y[1] (numeric) = 1.4543056698304266 " "
absolute error = 4.28546087505310400000000000000E-14 " "
relative error = 2.9467401275776270000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = 1.4453746445420361 " "
y[1] (numeric) = 1.4453746445419922 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 3.04176027586856970000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = 1.436399082160293 " "
y[1] (numeric) = 1.4363990821602486 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 3.091684026852539000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = 1.4273798802339983 " "
y[1] (numeric) = 1.4273798802339528 " "
absolute error = 4.55191440096314200000000000000E-14 " "
relative error = 3.1889999740061636000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = 1.4183179406758293 " "
y[1] (numeric) = 1.4183179406757829 " "
absolute error = 4.640732242933154300000000000000E-14 " "
relative error = 3.271997138188806300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = 1.4092141696721896 " "
y[1] (numeric) = 1.4092141696721423 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 3.356161317909081000000000000E-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) = 1.4000694775925933 " "
y[1] (numeric) = 1.4000694775925453 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 3.425661042641709000000000000E-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) = 1.390884778898628 " "
y[1] (numeric) = 1.390884778898579 " "
absolute error = 4.90718576884319200000000000000E-14 " "
relative error = 3.5281037245435576000000000000E-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) = 1.3816609920525091 " "
y[1] (numeric) = 1.381660992052459 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 3.6320111084926643000000000000E-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) = 1.3723990394252346 " "
y[1] (numeric) = 1.3723990394251837 " "
absolute error = 5.08482145278321700000000000000E-14 " "
relative error = 3.705060486571571400000000000E-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) = 1.3630998472043492 " "
y[1] (numeric) = 1.363099847204297 " "
absolute error = 5.21804821573823600000000000000E-14 " "
relative error = 3.828074829910806400000000000E-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) = 1.3537643453013255 " "
y[1] (numeric) = 1.3537643453012724 " "
absolute error = 5.30686605770824800000000000000E-14 " "
relative error = 3.920081124995967000000000000E-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) = 1.3443934672585742 " "
y[1] (numeric) = 1.3443934672585205 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 3.9969544408327956000000000000E-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) = 1.3349881501560907 " "
y[1] (numeric) = 1.334988150156036 " "
absolute error = 5.48450174164827300000000000000E-14 " "
relative error = 4.1082774712322423000000000000E-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) = 1.3255493345177478 " "
y[1] (numeric) = 1.3255493345176916 " "
absolute error = 5.61772850460329200000000000000E-14 " "
relative error = 4.238038040769787600000000000E-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) = 1.3160779642172429 " "
y[1] (numeric) = 1.3160779642171858 " "
absolute error = 5.70654634657330500000000000000E-14 " "
relative error = 4.3360245378527845000000000000E-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) = 1.306574986383714 " "
y[1] (numeric) = 1.3065749863836558 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 4.45253331011445040000000000E-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) = 1.297041351307025 " "
y[1] (numeric) = 1.2970413513069656 " "
absolute error = 5.92859095149833600000000000000E-14 " "
relative error = 4.57085731732771000000000000E-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) = 1.2874780123427387 " "
y[1] (numeric) = 1.2874780123426783 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 4.691041863286633000000000000E-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) = 1.2778859258167827 " "
y[1] (numeric) = 1.277885925816721 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 4.830509431403585000000000000E-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) = 1.2682660509298156 " "
y[1] (numeric) = 1.2682660509297528 " "
absolute error = 6.28386231937838600000000000000E-14 " "
relative error = 4.95468779186468000000000000E-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) = 1.2586193496613098 " "
y[1] (numeric) = 1.258619349661246 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 5.080872643155966000000000000E-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) = 1.2489467866733535 " "
y[1] (numeric) = 1.2489467866732884 " "
absolute error = 6.50590692430341700000000000000E-14 " "
relative error = 5.209114586564813000000000000E-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) = 1.2392493292141846 " "
y[1] (numeric) = 1.2392493292141185 " "
absolute error = 6.61692922676593300000000000000E-14 " "
relative error = 5.3394656513243920000000000000E-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) = 1.2295279470214682 " "
y[1] (numeric) = 1.2295279470214011 " "
absolute error = 6.70574706873594600000000000000E-14 " "
relative error = 5.453920006438748000000000000E-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) = 1.2197836122253223 " "
y[1] (numeric) = 1.2197836122252543 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 5.570303488755877000000000000E-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) = 1.2100172992511062 " "
y[1] (numeric) = 1.2100172992510372 " "
absolute error = 6.90558721316847400000000000000E-14 " "
relative error = 5.707015277750509000000000000E-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) = 1.2002299847219788 " "
y[1] (numeric) = 1.2002299847219084 " "
absolute error = 7.03881397612349200000000000000E-14 " "
relative error = 5.864554348518431000000000000E-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) = 1.1904226473612372 " "
y[1] (numeric) = 1.1904226473611657 " "
absolute error = 7.14983627858600800000000000000E-14 " "
relative error = 6.006132607133078000000000000E-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) = 1.1805962678944444 " "
y[1] (numeric) = 1.1805962678943716 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 6.1689700701240880000000000000E-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) = 1.1707518289513583 " "
y[1] (numeric) = 1.1707518289512846 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 6.296706698390578000000000000E-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) = 1.1608903149676701 " "
y[1] (numeric) = 1.160890314967595 " "
absolute error = 7.50510764646605800000000000000E-14 " "
relative error = 6.464958445858918000000000000E-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) = 1.1510127120865599 " "
y[1] (numeric) = 1.1510127120864837 " "
absolute error = 7.61612994892857400000000000000E-14 " "
relative error = 6.616894730139015000000000000E-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) = 1.1411200080600845 " "
y[1] (numeric) = 1.1411200080600072 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 6.771550929623367000000000000E-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) = 1.1312131921504025 " "
y[1] (numeric) = 1.1312131921503241 " "
absolute error = 7.83817455385360500000000000000E-14 " "
relative error = 6.9289985373609990000000000000E-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) = 1.1212932550308496 " "
y[1] (numeric) = 1.1212932550307704 " "
absolute error = 7.92699239582361800000000000000E-14 " "
relative error = 7.069508676929949000000000000E-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) = 1.111361188686871 " "
y[1] (numeric) = 1.111361188686791 " "
absolute error = 8.0158102377936300000000000000E-14 " "
relative error = 7.212605874121546000000000000E-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) = 1.1014179863168245 " "
y[1] (numeric) = 1.1014179863167428 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 7.41883786423902100000000000E-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) = 1.091464642232661 " "
y[1] (numeric) = 1.0914646422325782 " "
absolute error = 8.28226376370366800000000000000E-14 " "
relative error = 7.588210779564756000000000000E-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) = 1.0815021517604944 " "
y[1] (numeric) = 1.0815021517604104 " "
absolute error = 8.39328606616618300000000000000E-14 " "
relative error = 7.760766867179504000000000000E-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) = 1.0715315111410701 " "
y[1] (numeric) = 1.0715315111409849 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 7.957314125126707000000000000E-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) = 1.061553717430141 " "
y[1] (numeric) = 1.0615537174300549 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 8.115774576106815000000000000E-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) = 1.0515697683987635 " "
y[1] (numeric) = 1.0515697683986764 " "
absolute error = 8.70414851306122700000000000000E-14 " "
relative error = 8.277290556113198000000000000E-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) = 1.0415806624335209 " "
y[1] (numeric) = 1.0415806624334327 " "
absolute error = 8.81517081552374300000000000000E-14 " "
relative error = 8.463262744268136000000000000E-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) = 1.0315873984366852 " "
y[1] (numeric) = 1.0315873984365957 " "
absolute error = 8.94839757847876200000000000000E-14 " "
relative error = 8.674395976569289000000000000E-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) = 1.0215909757263286 " "
y[1] (numeric) = 1.0215909757262382 " "
absolute error = 9.03721542044877400000000000000E-14 " "
relative error = 8.846216964694225000000000000E-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) = 1.0115923939363918 " "
y[1] (numeric) = 1.0115923939363005 " "
absolute error = 9.12603326241878700000000000000E-14 " "
relative error = 9.021453025073481000000000000E-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) = 1.0015926529167218 " "
y[1] (numeric) = 1.0015926529166295 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 9.222367534328674000000000000E-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) = 0.9915927526330872 " "
y[1] (numeric) = 0.9915927526329938 " "
absolute error = 9.33697563709756700000000000000E-14 " "
relative error = 9.416139450700955000000000000E-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) = 0.9815936930671832 " "
y[1] (numeric) = 0.9815936930670889 " "
absolute error = 9.4368957093138310000000000000E-14 " "
relative error = 9.613851205406982000000000000E-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) = 0.9715964741166342 " "
y[1] (numeric) = 0.9715964741165386 " "
absolute error = 9.55902024202259800000000000000E-14 " "
relative error = 9.838467405631091000000000000E-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) = 0.9616020954950039 " "
y[1] (numeric) = 0.9616020954949072 " "
absolute error = 9.67004254448511300000000000000E-14 " "
relative error = 1.005617873524627400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 0.9516115566318258 " "
y[1] (numeric) = 0.9516115566317281 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 1.026675490499673600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 0.9416258565726611 " "
y[1] (numeric) = 0.9416258565725623 " "
absolute error = 9.88098491916389300000000000000E-14 " "
relative error = 1.049353610055781500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 0.9316459938791941 " "
y[1] (numeric) = 0.9316459938790943 " "
absolute error = 9.98090499138015700000000000000E-14 " "
relative error = 1.071319477242809300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 0.9216729665293778 " "
y[1] (numeric) = 0.9216729665292769 " "
absolute error = 1.00919272938426730000000000000E-13 " "
relative error = 1.094957502317173300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 0.9117077718176362 " "
y[1] (numeric) = 0.9117077718175342 " "
absolute error = 1.02029495963051890000000000000E-13 " "
relative error = 1.119103062592519700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 0.9017514062551362 " "
y[1] (numeric) = 0.9017514062550329 " "
absolute error = 1.03250741290139560000000000000E-13 " "
relative error = 1.145002276391531400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 0.891804865470137 " "
y[1] (numeric) = 0.8918048654700328 " "
absolute error = 1.0424994201230220000000000000E-13 " "
relative error = 1.16897704922639390000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 0.8818691441084286 " "
y[1] (numeric) = 0.8818691441083233 " "
absolute error = 1.05360165036927360000000000000E-13 " "
relative error = 1.194736948682411100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 0.8719452357338674 " "
y[1] (numeric) = 0.8719452357337609 " "
absolute error = 1.06470388061552510000000000000E-13 " "
relative error = 1.221067375543859200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 0.8620341327290207 " "
y[1] (numeric) = 0.8620341327289133 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 1.246697603997289300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 0.8521368261959301 " "
y[1] (numeric) = 0.8521368261958213 " "
absolute error = 1.08801856413265340000000000000E-13 " "
relative error = 1.276812045537024400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 0.8422543058570009 " "
y[1] (numeric) = 0.842254305856891 " "
absolute error = 1.0991207943789050000000000000E-13 " "
relative error = 1.304974978145751800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 0.8323875599560316 " "
y[1] (numeric) = 0.8323875599559207 " "
absolute error = 1.10911280160053140000000000000E-13 " "
relative error = 1.332447594073987400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 0.8225375751593903 " "
y[1] (numeric) = 0.8225375751592784 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 1.360551593774058400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 0.8127053364573481 " "
y[1] (numeric) = 0.8127053364572353 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 1.387940428613584400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 0.8028918270655818 " "
y[1] (numeric) = 0.8028918270654679 " "
absolute error = 1.13908882326541060000000000000E-13 " "
relative error = 1.418732617354650800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 0.7930980283268527 " "
y[1] (numeric) = 0.7930980283267377 " "
absolute error = 1.15019105351166220000000000000E-13 " "
relative error = 1.450250804352830600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 0.7833249196128731 " "
y[1] (numeric) = 0.783324919612757 " "
absolute error = 1.16129328375791370000000000000E-13 " "
relative error = 1.482517987978521600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 0.7735734782263703 " "
y[1] (numeric) = 0.7735734782262532 " "
absolute error = 1.17128529097954020000000000000E-13 " "
relative error = 1.51412286479240880000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 0.7638446793033568 " "
y[1] (numeric) = 0.7638446793032386 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 1.546488874254537700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 0.7541394957156173 " "
y[1] (numeric) = 0.7541394957154982 " "
absolute error = 1.1912693054227930000000000000E-13 " "
relative error = 1.579640520342161200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 0.7444588979734234 " "
y[1] (numeric) = 0.744458897973303 " "
absolute error = 1.20348175869366970000000000000E-13 " "
relative error = 1.616585901477979300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 0.7348038541284818 " "
y[1] (numeric) = 0.7348038541283605 " "
absolute error = 1.2134737659152961000000000000E-13 " "
relative error = 1.651425423393489700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 0.7251753296771313 " "
y[1] (numeric) = 0.7251753296770089 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 1.687130991730847200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 0.7155742874637934 " "
y[1] (numeric) = 0.71557428746367 " "
absolute error = 1.2334577803585489000000000000E-13 " "
relative error = 1.723731277056205800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 0.7060016875846884 " "
y[1] (numeric) = 0.706001687584564 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 1.76125611233899100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 0.6964584872918271 " "
y[1] (numeric) = 0.6964584872917019 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 1.798142451600894300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 0.6869456408972863 " "
y[1] (numeric) = 0.6869456408971601 " "
absolute error = 1.26121335597417780000000000000E-13 " "
relative error = 1.835972573210865600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 0.6774640996777779 " "
y[1] (numeric) = 0.6774640996776509 " "
absolute error = 1.2700951401711790000000000000E-13 " "
relative error = 1.8747785170834502000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 0.6680148117795227 " "
y[1] (numeric) = 0.6680148117793946 " "
absolute error = 1.28119737041743060000000000000E-13 " "
relative error = 1.917917608749501700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 0.6585987221234362 " "
y[1] (numeric) = 0.658598722123307 " "
absolute error = 1.29229960066368220000000000000E-13 " "
relative error = 1.962195730500485800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 0.6492167723106372 " "
y[1] (numeric) = 0.649216772310507 " "
absolute error = 1.30229160788530860000000000000E-13 " "
relative error = 2.005942642625055700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 0.6398699005282886 " "
y[1] (numeric) = 0.6398699005281575 " "
absolute error = 1.311173392082310000000000000E-13 " "
relative error = 2.049124972122896600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 0.63055904145578 " "
y[1] (numeric) = 0.6305590414556478 " "
absolute error = 1.32227562232856140000000000000E-13 " "
relative error = 2.096989394166494000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 0.6212851261712593 " "
y[1] (numeric) = 0.6212851261711259 " "
absolute error = 1.33448807559943820000000000000E-13 " "
relative error = 2.147947889600019300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 0.6120490820585267 " "
y[1] (numeric) = 0.6120490820583921 " "
absolute error = 1.34559030584568970000000000000E-13 " "
relative error = 2.19850065181050080000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 0.602851832714297 " "
y[1] (numeric) = 0.6028518327141613 " "
absolute error = 1.35669253609194130000000000000E-13 " "
relative error = 2.25045767876914400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 0.5936942978558402 " "
y[1] (numeric) = 0.5936942978557033 " "
absolute error = 1.3689049893628180000000000000E-13 " "
relative error = 2.305740503667786700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 0.5845773932290106 " "
y[1] (numeric) = 0.5845773932288727 " "
absolute error = 1.37889699658444440000000000000E-13 " "
relative error = 2.35879288620430120000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 0.5755020305166739 " "
y[1] (numeric) = 0.575502030516535 " "
absolute error = 1.38888900380607080000000000000E-13 " "
relative error = 2.413352047705469600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 0.5664691172475385 " "
y[1] (numeric) = 0.5664691172473986 " "
absolute error = 1.39888101102769720000000000000E-13 " "
relative error = 2.4694744487128100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 0.5574795567054036 " "
y[1] (numeric) = 0.5574795567052627 " "
absolute error = 1.40887301824932360000000000000E-13 " "
relative error = 2.527219162215545400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 0.5485342478388324 " "
y[1] (numeric) = 0.5485342478386906 " "
absolute error = 1.4177548024463250000000000000E-13 " "
relative error = 2.584624037664249300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 0.5396340851712571 " "
y[1] (numeric) = 0.5396340851711143 " "
absolute error = 1.42774680966795130000000000000E-13 " "
relative error = 2.64576839918265140000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 0.5307799587115278 " "
y[1] (numeric) = 0.5307799587113841 " "
absolute error = 1.43773881688957770000000000000E-13 " "
relative error = 2.70872852920012060000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 0.5219727538649118 " "
y[1] (numeric) = 0.5219727538647673 " "
absolute error = 1.44551037806195380000000000000E-13 " "
relative error = 2.769321516034640000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 0.5132133513445547 " "
y[1] (numeric) = 0.5132133513444093 " "
absolute error = 1.4543921622589550000000000000E-13 " "
relative error = 2.83389385418097500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 0.5045026270834089 " "
y[1] (numeric) = 0.5045026270832624 " "
absolute error = 1.46438416948058150000000000000E-13 " "
relative error = 2.90262942325268900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 0.49584145214664166 " "
y[1] (numeric) = 0.49584145214649444 " "
absolute error = 1.47215573065295760000000000000E-13 " "
relative error = 2.969004959709535000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 0.4872306926445289 " "
y[1] (numeric) = 0.48723069264438085 " "
absolute error = 1.48048240333764620000000000000E-13 " "
relative error = 3.0385655618328800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 0.47867120964584553 " "
y[1] (numeric) = 0.47867120964569637 " "
absolute error = 1.49158463358389780000000000000E-13 " "
relative error = 3.11609431176668500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 0.4701638590917582 " "
y[1] (numeric) = 0.4701638590916082 " "
absolute error = 1.49991130626858650000000000000E-13 " "
relative error = 3.19018843593390900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 0.4617094917102331 " "
y[1] (numeric) = 0.46170949171008213 " "
absolute error = 1.5099033134902130000000000000E-13 " "
relative error = 3.27024533954745230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 0.45330895293096307 " "
y[1] (numeric) = 0.4533089529308112 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 3.35044143264145560000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 0.4449630828008255 " "
y[1] (numeric) = 0.44496308280067276 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 3.43324410705782070000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 0.43667271589987866 " "
y[1] (numeric) = 0.43667271589972506 " "
absolute error = 1.5359935545689040000000000000E-13 " "
relative error = 3.51749376281407100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 0.4284386812579041 " "
y[1] (numeric) = 0.4284386812577494 " "
absolute error = 1.5465406733028430000000000000E-13 " "
relative error = 3.6097129903447805000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 0.420261802271504 " "
y[1] (numeric) = 0.4202618022713485 " "
absolute error = 1.55486734598753170000000000000E-13 " "
relative error = 3.69975890643288230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 0.4121428966217633 " "
y[1] (numeric) = 0.4121428966216069 " "
absolute error = 1.5637491301845330000000000000E-13 " "
relative error = 3.79419163353829500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 0.4040827761924811 " "
y[1] (numeric) = 0.40408277619232386 " "
absolute error = 1.57263091438153420000000000000E-13 " "
relative error = 3.891853370242205000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 0.39608224698898364 " "
y[1] (numeric) = 0.39608224698882555 " "
absolute error = 1.5809575870662230000000000000E-13 " "
relative error = 3.99148812925764540000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 0.3881421090575241 " "
y[1] (numeric) = 0.3881421090573651 " "
absolute error = 1.58983937126322420000000000000E-13 " "
relative error = 4.096023941137507000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 0.38026315640527897 " "
y[1] (numeric) = 0.3802631564051191 " "
absolute error = 1.59872115546022540000000000000E-13 " "
relative error = 4.20424942183021200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 0.3724461769209476 " "
y[1] (numeric) = 0.3724461769207869 " "
absolute error = 1.6070478281449140000000000000E-13 " "
relative error = 4.31484581592580800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 0.3646919522959644 " "
y[1] (numeric) = 0.3646919522958028 " "
absolute error = 1.61592961234191530000000000000E-13 " "
relative error = 4.43094398483055600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 0.35700125794633 " "
y[1] (numeric) = 0.35700125794616755 " "
absolute error = 1.6242562850266040000000000000E-13 " "
relative error = 4.549721461403891700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 0.34937486293507036 " "
y[1] (numeric) = 0.34937486293490716 " "
absolute error = 1.632027846198980000000000000E-13 " "
relative error = 4.67128010437970300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 0.3418135298953314 " "
y[1] (numeric) = 0.34181352989516745 " "
absolute error = 1.63979940737135620000000000000E-13 " "
relative error = 4.79735078910857600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 0.33431801495411606 " "
y[1] (numeric) = 0.3343180149539513 " "
absolute error = 1.64757096854373230000000000000E-13 " "
relative error = 4.928154914923910700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 0.32688906765667214 " "
y[1] (numeric) = 0.3268890676565065 " "
absolute error = 1.65645275274073360000000000000E-13 " "
relative error = 5.06732380074725200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 0.3195274308915387 " "
y[1] (numeric) = 0.3195274308913722 " "
absolute error = 1.66477942542542220000000000000E-13 " "
relative error = 5.210129912102976000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 0.3122338408162574 " "
y[1] (numeric) = 0.31223384081609007 " "
absolute error = 1.6731060981101110000000000000E-13 " "
relative error = 5.35850340160500500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 0.30500902678375796 " "
y[1] (numeric) = 0.3050090267835898 " "
absolute error = 1.68143277079479960000000000000E-13 " "
relative error = 5.51273117561495600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 0.29785371126942284 " "
y[1] (numeric) = 0.297853711269254 " "
absolute error = 1.6886492204548630000000000000E-13 " "
relative error = 5.6693912365839200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 0.2907686097988409 " "
y[1] (numeric) = 0.29076860979867114 " "
absolute error = 1.69753100465186440000000000000E-13 " "
relative error = 5.83808206059879600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 0.28375443087625485 " "
y[1] (numeric) = 0.28375443087608426 " "
absolute error = 1.7058576773365530000000000000E-13 " "
relative error = 6.01173934824114300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 0.2768118759137118 " "
y[1] (numeric) = 0.2768118759135403 " "
absolute error = 1.71529457304586690000000000000E-13 " "
relative error = 6.19660759634662800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 0.2699416391609226 " "
y[1] (numeric) = 0.2699416391607503 " "
absolute error = 1.7230661342182430000000000000E-13 " "
relative error = 6.38310613943874200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 0.26314440763583735 " "
y[1] (numeric) = 0.2631444076356643 " "
absolute error = 1.73028258387830650000000000000E-13 " "
relative error = 6.57541081501084300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 0.2564208610559442 " "
y[1] (numeric) = 0.25642086105577033 " "
absolute error = 1.73860925656299510000000000000E-13 " "
relative error = 6.78029568032562200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 0.24977167177029835 " "
y[1] (numeric) = 0.24977167177012366 " "
absolute error = 1.74693592924768380000000000000E-13 " "
relative error = 6.99413154768907300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 0.24319750469228718 " "
y[1] (numeric) = 0.2431975046921118 " "
absolute error = 1.7538748231515910000000000000E-13 " "
relative error = 7.21173033979412300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 0.23669901723313724 " "
y[1] (numeric) = 0.23669901723296405 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 7.31708960459839100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 0.23027685923618202 " "
y[1] (numeric) = 0.23027685923601096 " "
absolute error = 1.710576125191210000000000000E-13 " "
relative error = 7.42834573506479900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 0.22393167291186933 " "
y[1] (numeric) = 0.2239316729117005 " "
absolute error = 1.68837166469870680000000000000E-13 " "
relative error = 7.53967334206976400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 0.21766409277354415 " "
y[1] (numeric) = 0.2176640927733774 " "
absolute error = 1.6675549829869850000000000000E-13 " "
relative error = 7.66113951887275700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 0.21147474557399726 " "
y[1] (numeric) = 0.21147474557383258 " "
absolute error = 1.64673830127526340000000000000E-13 " "
relative error = 7.78692650418180700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 0.2053642502427908 " "
y[1] (numeric) = 0.2053642502426282 " "
absolute error = 1.6261991753196980000000000000E-13 " "
relative error = 7.91860887860049800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 0.19933321782436586 " "
y[1] (numeric) = 0.1993332178242053 " "
absolute error = 1.60566004936413260000000000000E-13 " "
relative error = 8.05515541709105900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 0.19338225141693854 " "
y[1] (numeric) = 0.1933822514167799 " "
absolute error = 1.58650870218934870000000000000E-13 " "
relative error = 8.20400367957648400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 0.18751194611219024 " "
y[1] (numeric) = 0.1875119461120336 " "
absolute error = 1.5665246877460960000000000000E-13 " "
relative error = 8.35426606264770300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 0.18172288893575972 " "
y[1] (numeric) = 0.18172288893560498 " "
absolute error = 1.5473733405713120000000000000E-13 " "
relative error = 8.51501618554126600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 0.1760156587885403 " "
y[1] (numeric) = 0.1760156587883875 " "
absolute error = 1.52794443764037170000000000000E-13 " "
relative error = 8.68073015865023800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 0.17039082638879077 " "
y[1] (numeric) = 0.1703908263886399 " "
absolute error = 1.50879309046558770000000000000E-13 " "
relative error = 8.854896254936200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 0.16484895421506385 " "
y[1] (numeric) = 0.16484895421491474 " "
absolute error = 1.49102952207158520000000000000E-13 " "
relative error = 9.044822450777400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 0.15939059644995845 " "
y[1] (numeric) = 0.15939059644981118 " "
absolute error = 1.47271084216527020000000000000E-13 " "
relative error = 9.23963442616036500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 0.1540162989247027 " "
y[1] (numeric) = 0.1540162989245572 " "
absolute error = 1.45494727377126760000000000000E-13 " "
relative error = 9.44670975688475200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 0.14872659906457042 " "
y[1] (numeric) = 0.14872659906442678 " "
absolute error = 1.43635103810879630000000000000E-13 " "
relative error = 9.65766074893702900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 0.14352202583513962 " "
y[1] (numeric) = 0.14352202583499774 " "
absolute error = 1.418865025470950000000000000E-13 " "
relative error = 9.88604374286611000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = 0.13840309968939613 " "
y[1] (numeric) = 0.13840309968925596 " "
absolute error = 1.40165656858926000000000000000E-13 " "
relative error = 1.01273495444455660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 0.13337033251568864 " "
y[1] (numeric) = 0.1333703325155502 " "
absolute error = 1.38444811170757020000000000000E-13 " "
relative error = 1.03804803181750680000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 0.1284242275865407 " "
y[1] (numeric) = 0.12842422758640393 " "
absolute error = 1.36779476633819290000000000000E-13 " "
relative error = 1.06505975705906630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 0.12356527950832352 " "
y[1] (numeric) = 0.12356527950818837 " "
absolute error = 1.351557754603050000000000000E-13 " "
relative error = 1.09380058862895010000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 0.1187939741717956 " "
y[1] (numeric) = 0.11879397417166213 " "
absolute error = 1.33476563135559450000000000000E-13 " "
relative error = 1.12359708534147030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 0.11411078870351476 " "
y[1] (numeric) = 0.1141107887033828 " "
absolute error = 1.31963884264507670000000000000E-13 " "
relative error = 1.15645405455376530000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 0.10951619141812508 " "
y[1] (numeric) = 0.10951619141799464 " "
absolute error = 1.30437327605648080000000000000E-13 " "
relative error = 1.19103235710277370000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 0.10501064177152619 " "
y[1] (numeric) = 0.10501064177139732 " "
absolute error = 1.28869137583365050000000000000E-13 " "
relative error = 1.22720074279469970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 0.10059459031492834 " "
y[1] (numeric) = 0.10059459031480088 " "
absolute error = 1.27467481014775790000000000000E-13 " "
relative error = 1.26714051536685330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 9.62684786497969300E-2 " "
y[1] (numeric) = 9.62684786496709700E-2 " "
absolute error = 1.259548021437240000000000000E-13 " "
relative error = 1.30837013226228760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 9.20327393836936100E-2 " "
y[1] (numeric) = 9.20327393835690400E-2 " "
absolute error = 1.24567023362942560000000000000E-13 " "
relative error = 1.3535077212426580000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 8.78877960870150200E-2 " "
y[1] (numeric) = 8.7887796086891900E-2 " "
absolute error = 1.23123733430929860000000000000E-13 " "
relative error = 1.400919569186020200000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 8.38340632506369100E-2 " "
y[1] (numeric) = 8.38340632505151100E-2 " "
absolute error = 1.21805343589187490000000000000E-13 " "
relative error = 1.45293379404775660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 7.9871946244464700E-2 " "
y[1] (numeric) = 7.98719462443442300E-2 " "
absolute error = 1.2047307595963730000000000000E-13 " "
relative error = 1.50832778746750940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 7.60018412768972400E-2 " "
y[1] (numeric) = 7.6001841276778100E-2 " "
absolute error = 1.1914080833008711000000000000E-13 " "
relative error = 1.56760423600820180000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 7.22241353552063300E-2 " "
y[1] (numeric) = 7.22241353550884100E-2 " "
absolute error = 1.17919563002999440000000000000E-13 " "
relative error = 1.63268916163631340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 6.85392062468359600E-2 " "
y[1] (numeric) = 6.85392062467192500E-2 " "
absolute error = 1.16712195463719580000000000000E-13 " "
relative error = 1.70285303631025760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 6.49474224416262100E-2 " "
y[1] (numeric) = 6.49474224415107000E-2 " "
absolute error = 1.15504827924439720000000000000E-13 " "
relative error = 1.7784359037227962000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 6.14491431149645200E-2 " "
y[1] (numeric) = 6.144914311485016000E-2 " "
absolute error = 1.14366849324198940000000000000E-13 " "
relative error = 1.86116263835007840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 5.804471809186817000E-2 " "
y[1] (numeric) = 5.80447180917550200E-2 " "
absolute error = 1.13152542891015170000000000000E-13 " "
relative error = 1.94940291917564460000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = 5.47344878120027400E-2 " "
y[1] (numeric) = 5.473448781189062000E-2 " "
absolute error = 1.1212558659323690000000000000E-13 " "
relative error = 2.04853632646305430000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 5.151878329563742000E-2 " "
y[1] (numeric) = 5.1518783295526400E-2 " "
absolute error = 1.11015363568611750000000000000E-13 " "
relative error = 2.15485220082851760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 4.839792611054427600E-2 " "
y[1] (numeric) = 4.839792611043427500E-2 " "
absolute error = 1.10002285058641290000000000000E-13 " "
relative error = 2.2728718748689422000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 4.537222833984100E-2 " "
y[1] (numeric) = 4.53722283397320460E-2 " "
absolute error = 1.0895451207915130000000000000E-13 " "
relative error = 2.40134805068586840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 4.2441992550783403E-2 " "
y[1] (numeric) = 4.24419925506753800E-2 " "
absolute error = 1.08024700296027730000000000000E-13 " "
relative error = 2.54523159266785650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 3.960751176450838500E-2 " "
y[1] (numeric) = 3.96075117644013100E-2 " "
absolute error = 1.07074071831192440000000000000E-13 " "
relative error = 2.7033778962893520000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 3.686906942673251500E-2 " "
y[1] (numeric) = 3.68690694266264100E-2 " "
absolute error = 1.06102626684645430000000000000E-13 " "
relative error = 2.87782220529043230000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 3.422693937940768400E-2 " "
y[1] (numeric) = 3.42269393793024460E-2 " "
absolute error = 1.05235264946657030000000000000E-13 " "
relative error = 3.07463263893150900000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 3.168138583333679500E-2 " "
y[1] (numeric) = 3.16813858332323800E-2 " "
absolute error = 1.04416475465995970000000000000E-13 " "
relative error = 3.2958304291134750000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 2.923266334175312000E-2 " "
y[1] (numeric) = 2.923266334164951000E-2 " "
absolute error = 1.03604624879238830000000000000E-13 " "
relative error = 3.5441390908525250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 2.688101677486521000E-2 " "
y[1] (numeric) = 2.688101677476242300E-2 " "
absolute error = 1.02782365951625820000000000000E-13 " "
relative error = 3.82360409996586550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 2.462668129537015600E-2 " "
y[1] (numeric) = 2.462668129526809600E-2 " "
absolute error = 1.02060720985619470000000000000E-13 " "
relative error = 4.14431484947210440000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 2.246988233493718600E-2 " "
y[1] (numeric) = 2.246988233483587500E-2 " "
absolute error = 1.01311320443997490000000000000E-13 " "
relative error = 4.50876061271020030000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 2.04108355716651200E-2 " "
y[1] (numeric) = 2.041083557156447600E-2 " "
absolute error = 1.0064518662922240000000000000E-13 " "
relative error = 4.930968468970510000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 1.84497469085143080E-2 " "
y[1] (numeric) = 1.844974690841435500E-2 " "
absolute error = 9.99547666857836200000000000000E-14 " "
relative error = 5.4176768484371920000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 1.65868124527169800E-2 " "
y[1] (numeric) = 1.658681245261760500E-2 " "
absolute error = 9.93753690448073700000000000000E-14 " "
relative error = 5.991227629063190000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 1.482221849616616200E-2 " "
y[1] (numeric) = 1.482221849606735800E-2 " "
absolute error = 9.880464502121100000000000000E-14 " "
relative error = 6.665982224372640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = 1.31561414967870100E-2 " "
y[1] (numeric) = 1.315614149668877800E-2 " "
absolute error = 9.82339209976146300000000000000E-14 " "
relative error = 7.4667729152658690000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = 1.158874806089116300E-2 " "
y[1] (numeric) = 1.158874806079340800E-2 " "
absolute error = 9.77551373182450300000000000000E-14 " "
relative error = 8.435349254691430000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = 1.012019492651594600E-2 " "
y[1] (numeric) = 1.012019492641868800E-2 " "
absolute error = 9.72590064041156700000000000000E-14 " "
relative error = 9.6103886447174160000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = 8.750628947751027000E-3 " "
y[1] (numeric) = 8.75062894765426100E-3 " "
absolute error = 9.67663449369382500000000000000E-14 " "
relative error = 1.1058215988212812000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = 7.480187080053047000E-3 " "
y[1] (numeric) = 7.480187079956699000E-3 " "
absolute error = 9.63474092174898500000000000000E-14 " "
relative error = 1.2880347534945155000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = 6.308996366550024000E-3 " "
y[1] (numeric) = 6.3089963664540800000E-3 " "
absolute error = 9.59432186475872600000000000000E-14 " "
relative error = 1.5207366286700258000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = 5.237173925337402000E-3 " "
y[1] (numeric) = 5.237173925241763000E-3 " "
absolute error = 9.56387746775533300000000000000E-14 " "
relative error = 1.8261523493587595000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = 4.264826937765975300E-3 " "
y[1] (numeric) = 4.264826937670686000E-3 " "
absolute error = 9.528922789714400000000000000E-14 " "
relative error = 2.234304680767631000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = 3.392052637724352000E-3 " "
y[1] (numeric) = 3.3920526376293225000E-3 " "
absolute error = 9.50294530566164800000000000000E-14 " "
relative error = 2.801532381890438000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = 2.6189383019150636000E-3 " "
y[1] (numeric) = 2.618938301820365000E-3 " "
absolute error = 9.4698554553573900000000000000E-14 " "
relative error = 3.6159139176484933000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = 1.945561241127658000E-3 " "
y[1] (numeric) = 1.9455612410331350000E-3 " "
absolute error = 9.45231306420657400000000000000E-14 " "
relative error = 4.858399141796206000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = 1.371988792506884000E-3 " "
y[1] (numeric) = 1.3719887924125650000E-3 " "
absolute error = 9.43188669527694800000000000000E-14 " "
relative error = 6.8746091416994000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = 8.9827831281974470000E-4 " "
y[1] (numeric) = 8.9827831272554290000E-4 " "
absolute error = 9.42017731181410400000000000000E-14 " "
relative error = 1.04869250179753900000000E-8 "%"
Desired digits = 8
Estimated correct digits = 9
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = 5.2447717271930650000E-4 " "
y[1] (numeric) = 5.2447717262527920000E-4 " "
absolute error = 9.40273249885881200000000000000E-14 " "
relative error = 1.79278202902665400000000E-8 "%"
Desired digits = 8
Estimated correct digits = 9
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = 2.5062275200826710000E-4 " "
y[1] (numeric) = 2.50622751914284240000E-4 " "
absolute error = 9.39828726995162200000000000000E-14 " "
relative error = 3.74997369338662730000000E-8 "%"
Desired digits = 8
Estimated correct digits = 9
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = 7.67424359002788500000E-5 " "
y[1] (numeric) = 7.674243580641801000E-5 " "
absolute error = 9.38608457450029700000000000000E-14 " "
relative error = 1.22306315461458950000000E-7 "%"
Desired digits = 8
Estimated correct digits = 8
Correct digits = 10
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = 2.8536122822497845000000E-6 " "
y[1] (numeric) = 2.8536121883913623000000E-6 " "
absolute error = 9.3858421960224400000000000000E-14 " "
relative error = 3.28910912474159000000E-6 "%"
Desired digits = 8
Estimated correct digits = 7
Correct digits = 9
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = 2.89636699748463400000E-5 " "
y[1] (numeric) = 2.89636698809923300000E-5 " "
absolute error = 9.38540084950527400000000000000E-14 " "
relative error = 3.24040456808687400000000E-7 "%"
Desired digits = 8
Estimated correct digits = 8
Correct digits = 10
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = 1.55069997994083940000E-4 " "
y[1] (numeric) = 1.55069997900209950000E-4 " "
absolute error = 9.38739916963443600000000000000E-14 " "
relative error = 6.0536527317118900000000E-8 "%"
Desired digits = 8
Estimated correct digits = 9
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = 3.81159985812340450000E-4 " "
y[1] (numeric) = 3.8115998571833060000E-4 " "
absolute error = 9.40098693336111100000000000000E-14 " "
relative error = 2.466414965706702800000000E-8 "%"
Desired digits = 8
Estimated correct digits = 9
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = 7.0721102461912540000E-4 " "
y[1] (numeric) = 7.0721102452498020000E-4 " "
absolute error = 9.41452861849545500000000000000E-14 " "
relative error = 1.331219153938632500000000E-8 "%"
Desired digits = 8
Estimated correct digits = 9
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = 1.1331905095822714000E-3 " "
y[1] (numeric) = 1.133190509487986000E-3 " "
absolute error = 9.42854735258569200000000000000E-14 " "
relative error = 8.320355026677149000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = 1.6590558431082147000E-3 " "
y[1] (numeric) = 1.6590558430138336000E-3 " "
absolute error = 9.43811001574701400000000000000E-14 " "
relative error = 5.688844082586676000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = 2.2847544391020325000E-3 " "
y[1] (numeric) = 2.2847544390073907000E-3 " "
absolute error = 9.46417423597356600000000000000E-14 " "
relative error = 4.14231572286307970000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = 3.0102237282253475000E-3 " "
y[1] (numeric) = 3.0102237281304706000E-3 " "
absolute error = 9.48767973907305200000000000000E-14 " "
relative error = 3.1518188000818250000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = 3.8353911641538785000E-3 " "
y[1] (numeric) = 3.8353911640587170000E-3 " "
absolute error = 9.51617257216597100000000000000E-14 " "
relative error = 2.4811478581651586000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = 4.7601742308316375000E-3 " "
y[1] (numeric) = 4.760174230736175000E-3 " "
absolute error = 9.54627002447416800000000000000E-14 " "
relative error = 2.0054455071503474000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = 5.784480450722662000E-3 " "
y[1] (numeric) = 5.784480450626824000E-3 " "
absolute error = 9.58374005155526700000000000000E-14 " "
relative error = 1.6568022198705779000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = 6.908207394058508000E-3 " "
y[1] (numeric) = 6.908207393962265000E-3 " "
absolute error = 9.62433258089312500000000000000E-14 " "
relative error = 1.3931736602422580000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = 8.131242689081164000E-3 " "
y[1] (numeric) = 8.131242688984596000E-3 " "
absolute error = 9.6568586460676900000000000000E-14 " "
relative error = 1.1876239604845593000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = 9.453464033280512000E-3 " "
y[1] (numeric) = 9.45346403318351000E-3 " "
absolute error = 9.7002267329671100000000000000E-14 " "
relative error = 1.0261028866051514000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = 1.087473920562398400E-2 " "
y[1] (numeric) = 1.087473920552643500E-2 " "
absolute error = 9.75504399480797700000000000000E-14 " "
relative error = 8.970370516805639000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = 1.239492607977854500E-2 " "
y[1] (numeric) = 1.23949260796805300E-2 " "
absolute error = 9.80153458396415500000000000000E-14 " "
relative error = 7.9076991027438830000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = 1.401387263832376600E-2 " "
y[1] (numeric) = 1.401387263822519400E-2 " "
absolute error = 9.85721920754301100000000000000E-14 " "
relative error = 7.0339009508238670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = 1.573141698795288400E-2 " "
y[1] (numeric) = 1.57314169878536890E-2 " "
absolute error = 9.91949578033057800000000000000E-14 " "
relative error = 6.3055322911641890000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = 1.754738737566208200E-2 " "
y[1] (numeric) = 1.754738737556233400E-2 " "
absolute error = 9.97465998686664100000000000000E-14 " "
relative error = 5.6844131683679120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = 1.946160220592607600E-2 " "
y[1] (numeric) = 1.94616022058256700E-2 " "
absolute error = 1.0040579478953760000000000000E-13 " "
relative error = 5.1591741382404740000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = 2.147387005885692500E-2 " "
y[1] (numeric) = 2.147387005875583700E-2 " "
absolute error = 1.01089275839072460000000000000E-13 " "
relative error = 4.7075480834148970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = 2.358398970934616500E-2 " "
y[1] (numeric) = 2.358398970924442700E-2 " "
absolute error = 1.01738062419087780000000000000E-13 " "
relative error = 4.3138613810864120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = 2.579175014718737600E-2 " "
y[1] (numeric) = 2.57917501470848200E-2 " "
absolute error = 1.02556851899748840000000000000E-13 " "
relative error = 3.97634326148792960000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = 2.809693059817630600E-2 " "
y[1] (numeric) = 2.809693059807302000E-2 " "
absolute error = 1.03281966312707140000000000000E-13 " "
relative error = 3.67591634081948000000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = 3.04993005461889900E-2 " "
y[1] (numeric) = 3.049930054608491000E-2 " "
absolute error = 1.04076469664704520000000000000E-13 " "
relative error = 3.4124215244571990000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = 3.29986197562325300E-2 " "
y[1] (numeric) = 3.29986197561276700E-2 " "
absolute error = 1.04860564675846040000000000000E-13 " "
relative error = 3.17772577915295300000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = 3.55946382984687600E-2 " "
y[1] (numeric) = 3.55946382983630240E-2 " "
absolute error = 1.05734865307738350000000000000E-13 " "
relative error = 2.9705278761685560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = 3.828709657320683600E-2 " "
y[1] (numeric) = 3.82870965731001300E-2 " "
absolute error = 1.06706310454285360000000000000E-13 " "
relative error = 2.78700450033492600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = cos ( 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.cos.max