(%i1) batch("temp/diffeq.sub_sin_cos.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sub_sin_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_tmp3,[40],convfloat)
(%i190) completearray(array_tmp4_g,[40],convfloat)
(%i191) completearray(array_tmp4,[40],convfloat)
(%i192) completearray(array_tmp5,[40],convfloat)
(%i193) completearray(array_m1,[40],convfloat)
(%i194) completearray(array_y_higher,[2,40],convfloat)
(%i195) completearray(array_y_higher_work,[2,40],convfloat)
(%i196) completearray(array_y_higher_work2,[2,40],convfloat)
(%i197) completearray(array_y_set_initial,[2,40],convfloat)
(%i198) completearray(array_given_rad_poles,[2,3],convfloat)
(%i199) completearray(array_given_ord_poles,[2,3],convfloat)
(%i200) completearray(array_rad_test_poles,[2,4],convfloat)
(%i201) completearray(array_ord_test_poles,[2,4],convfloat)
(%i202) completearray(array_fact_2,[40,40],convfloat)
(%i203) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i204) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i205) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i206) 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))
(%i207) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i208) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i209) 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)
(%i210) 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)
(%i211) 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)
(%i212) 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)
(%i213) 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)
(%i214) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i215) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i216) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i217) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i218) log_revs(file,revs):=printf(file,revs)
(%i219) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i220) 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)
(%i221) logstart(file):=(printf(file,""),0)
(%i222) logend(file):=(printf(file,"
~%"),0)
(%i223) 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)
(%i224) 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)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) c(in_val):=(ret:in_val,ret)
(%i229) 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)
(%i230) 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)
(%i231) 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)
(%i232) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i233) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i234) 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)
(%i235) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i236) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i237) 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)
(%i238) log10(x):=log(x)/glob_log_10
(%i239) c(x):=x
(%i240) 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
(%i241) 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)
(%i242) exact_soln_y(x):=block(cos(c(x))-sin(c(x)))
(%o242) exact_soln_y(x) := block(cos(c(x)) - sin(c(x)))
(%i243) 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)
(%i244) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i245) 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)
(%i246) 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)
(%i247) 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))
(%i248) 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))
(%i249) 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(25)
*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)
(%i250) 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)
(%i251) 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)
(%i252) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),array_tmp1[1]:sin(array_x[1]),
array_tmp1_g[1]:cos(array_x[1]),
array_tmp2[1]:neg(array_tmp1[1]),
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
array_tmp4[1]:cos(array_x[1]),
array_tmp4_g[1]:sin(array_x[1]),
array_tmp5[1]:array_tmp3[1]-array_tmp4[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp5[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_tmp1_g[1]*array_x[2]/c(1),
array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1),
array_tmp2[2]:neg(array_tmp1[2]),
array_tmp3[2]:array_tmp2[2],
array_tmp4[2]:neg(array_tmp4_g[1])*array_x[2]/c(1),
array_tmp4_g[2]:array_tmp4[1]*array_x[2]/c(1),
array_tmp5[2]:array_tmp3[2]-array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp5[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_tmp1_g[2]*array_x[2]/c(2),
array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2),
array_tmp2[3]:neg(array_tmp1[3]),
array_tmp3[3]:array_tmp2[3],
array_tmp4[3]:neg(array_tmp4_g[2])*array_x[2]/c(2),
array_tmp4_g[3]:array_tmp4[2]*array_x[2]/c(2),
array_tmp5[3]:array_tmp3[3]-array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp5[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_tmp1_g[3]*array_x[2]/c(3),
array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3),
array_tmp2[4]:neg(array_tmp1[4]),
array_tmp3[4]:array_tmp2[4],
array_tmp4[4]:neg(array_tmp4_g[3])*array_x[2]/c(3),
array_tmp4_g[4]:array_tmp4[3]*array_x[2]/c(3),
array_tmp5[4]:array_tmp3[4]-array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp5[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_tmp1_g[4]*array_x[2]/c(4),
array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4),
array_tmp2[5]:neg(array_tmp1[5]),
array_tmp3[5]:array_tmp2[5],
array_tmp4[5]:neg(array_tmp4_g[4])*array_x[2]/c(4),
array_tmp4_g[5]:array_tmp4[4]*array_x[2]/c(4),
array_tmp5[5]:array_tmp3[5]-array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp5[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp1_g[kkk]
:neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1),
array_tmp2[kkk]:neg(array_tmp1[kkk]),
array_tmp3[kkk]:array_tmp2[kkk],
array_tmp4[kkk]
:neg(array_tmp4_g[kkk-1])*array_x[2]/c(kkk-1),
array_tmp4_g[kkk]
:array_tmp4[kkk-1]*array_x[2]/c(kkk-1),
array_tmp5[kkk]:array_tmp3[kkk]-array_tmp4[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_tmp5[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)
(%i253) exact_soln_y(x):=block(cos(c(x))-sin(c(x)))
(%o253) exact_soln_y(x) := block(cos(c(x)) - sin(c(x)))
(%i254) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp4_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1_g),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4_g),
zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5),
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/sub_sin_cospostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = neg ( sin ( x ) ) - 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(0.1),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,""),
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," (cos(c(x)) - 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(0.1),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:3,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = neg ( sin ( x ) ) - 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,
"2015-04-24T22:51:24-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sub_sin_cos"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = neg ( sin ( x ) ) - 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,
"sub_sin_cos diffeq.max"),
logitem_str(html_log_file,
"sub_sin_cos maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i255) main():=(glob_iolevel:2,compile(all),main_prog())
(%i256) 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_tmp2 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp4_g in translation.
warning: encountered undefined variable array_tmp5 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/sub_sin_cospostode.ode#################"
"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
""
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (cos(c(x)) - sin(c(x))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = 0.8951707486311977 " "
y[1] (numeric) = 0.8951707486311977 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = 0.8841777971195219 " "
y[1] (numeric) = 0.884177797119522 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.255655851393289400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = 0.8730964285649468 " "
y[1] (numeric) = 0.8730964285649468 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (closed_form) = 0.8619277510950932 " "
y[1] (numeric) = 0.861927751095093 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.576139411254829700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (closed_form) = 0.8506728815684006 " "
y[1] (numeric) = 0.8506728815684006 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (closed_form) = 0.839332945462443 " "
y[1] (numeric) = 0.839332945462443 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (closed_form) = 0.8279090767613809 " "
y[1] (numeric) = 0.8279090767613809 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (closed_form) = 0.8164024178425646 " "
y[1] (numeric) = 0.8164024178425646 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (closed_form) = 0.8048141193622972 " "
y[1] (numeric) = 0.8048141193622972 " "
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] = 0.19000000000000009 " "
y[1] (closed_form) = 0.7931453401407697 " "
y[1] (numeric) = 0.7931453401407698 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.399772486122292400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = 0.7813972470461803 " "
y[1] (numeric) = 0.7813972470461803 " "
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] = 0.2100000000000001 " "
y[1] (closed_form) = 0.7695710148780486 " "
y[1] (numeric) = 0.7695710148780485 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.442651819210069900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = 0.757667826249736 " "
y[1] (numeric) = 0.757667826249736 " "
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] = 0.23000000000000012 " "
y[1] (closed_form) = 0.7456888714701863 " "
y[1] (numeric) = 0.7456888714701864 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.488855563093306700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = 0.7336353484248949 " "
y[1] (numeric) = 0.7336353484248949 " "
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] = 0.2500000000000001 " "
y[1] (closed_form) = 0.7215084624561217 " "
y[1] (numeric) = 0.7215084624561218 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.538752602908901300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = 0.709309426242358 " "
y[1] (numeric) = 0.709309426242358 " "
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] = 0.27000000000000013 " "
y[1] (closed_form) = 0.6970394596770593 " "
y[1] (numeric) = 0.6970394596770593 " "
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] = 0.28000000000000014 " "
y[1] (closed_form) = 0.684699789746657 " "
y[1] (numeric) = 0.6846997897466571 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.621474171966586500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (closed_form) = 0.6722916504078613 " "
y[1] (numeric) = 0.6722916504078618 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 6.60560352907321700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (closed_form) = 0.6598162824642663 " "
y[1] (numeric) = 0.6598162824642665 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.36524894620278800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (closed_form) = 0.6472749334422697 " "
y[1] (numeric) = 0.6472749334422698 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.715226354774600500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (closed_form) = 0.6346688574663228 " "
y[1] (numeric) = 0.6346688574663231 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.49858989160837400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (closed_form) = 0.6219993151335184 " "
y[1] (numeric) = 0.6219993151335187 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.35477932666293700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (closed_form) = 0.6092675733875317 " "
y[1] (numeric) = 0.6092675733875317 " "
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] = 0.3500000000000002 " "
y[1] (closed_form) = 0.5964749053919274 " "
y[1] (numeric) = 0.5964749053919275 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.861307180887449800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (closed_form) = 0.5836225904028447 " "
y[1] (numeric) = 0.5836225904028448 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.902296180582774600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (closed_form) = 0.5707119136410721 " "
y[1] (numeric) = 0.5707119136410723 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.89066006189381800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (closed_form) = 0.5577441661635272 " "
y[1] (numeric) = 0.5577441661635275 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.97167890932083300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (closed_form) = 0.5447206447341513 " "
y[1] (numeric) = 0.5447206447341515 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 4.076302359228541300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (closed_form) = 0.5316426516942343 " "
y[1] (numeric) = 0.5316426516942344 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.08828810308410600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (closed_form) = 0.5185114948321818 " "
y[1] (numeric) = 0.5185114948321818 " "
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] = 0.42000000000000026 " "
y[1] (closed_form) = 0.5053284872527377 " "
y[1] (numeric) = 0.5053284872527376 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.197032331703642200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (closed_form) = 0.492094947245674 " "
y[1] (numeric) = 0.4920949472456739 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.256115472916830300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (closed_form) = 0.4788121981539634 " "
y[1] (numeric) = 0.47881219815396336 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.159351233015330500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (closed_form) = 0.4654815682414463 " "
y[1] (numeric) = 0.4654815682414463 " "
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] = 0.4600000000000003 " "
y[1] (closed_form) = 0.45210439056000506 " "
y[1] (numeric) = 0.45210439056000506 " "
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] = 0.4700000000000003 " "
y[1] (closed_form) = 0.4386820028162603 " "
y[1] (numeric) = 0.4386820028162602 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.530815072188334000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (closed_form) = 0.42521574723780087 " "
y[1] (numeric) = 0.42521574723780087 " "
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] = 0.4900000000000003 " "
y[1] (closed_form) = 0.41170697043896304 " "
y[1] (numeric) = 0.4117069704389631 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.348317012268985800000000000000E-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) = 0.39815702328616925 " "
y[1] (numeric) = 0.3981570232861693 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.394202487578877500000000000000E-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) = 0.38456726076284325 " "
y[1] (numeric) = 0.38456726076284337 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.88694108391565400000000000000E-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) = 0.37093904183391274 " "
y[1] (numeric) = 0.3709390418339128 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.49650333264495900000000000000E-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) = 0.3572737293099135 " "
y[1] (numeric) = 0.35727372930991363 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.10748575544468500000000000000E-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) = 0.34357268971071053 " "
y[1] (numeric) = 0.3435726897107106 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.615703252723562400000000000000E-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) = 0.32983729312884613 " "
y[1] (numeric) = 0.3298372931288461 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.682985896005798300000000000000E-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) = 0.31606891309253216 " "
y[1] (numeric) = 0.3160689130925322 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.75629898834772200000000000000E-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) = 0.30226892642829895 " "
y[1] (numeric) = 0.30226892642829895 " "
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] = 0.5800000000000004 " "
y[1] (closed_form) = 0.2884387131233128 " "
y[1] (numeric) = 0.2884387131233129 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.92453886061840100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = 0.2745796561873791 " "
y[1] (numeric) = 0.27457965618737923 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.04335499592699700000000000000E-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) = 0.2606931415146424 " "
y[1] (numeric) = 0.2606931415146424 " "
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] = 0.6100000000000004 " "
y[1] (closed_form) = 0.24678055774499763 " "
y[1] (numeric) = 0.24678055774499774 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.49882695286055800000000000000E-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) = 0.23284329612522825 " "
y[1] (numeric) = 0.23284329612522833 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.57608435512371600000000000000E-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) = 0.2188827503698818 " "
y[1] (numeric) = 0.21888275036988183 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.268056782397233300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = 0.20490031652189988 " "
y[1] (numeric) = 0.20490031652190008 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 9.48212441090283200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = 0.19089739281301565 " "
y[1] (numeric) = 0.19089739281301582 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 8.72371545990118800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = 0.17687537952393062 " "
y[1] (numeric) = 0.17687537952393084 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.25537316455617530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = 0.16283567884428896 " "
y[1] (numeric) = 0.16283567884428915 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.19316006595330150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = 0.14877969473245867 " "
y[1] (numeric) = 0.14877969473245897 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 2.05210349652175660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = 0.134708832775138 " "
y[1] (numeric) = 0.13470883277513818 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.23624746991727370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = 0.12062450004679659 " "
y[1] (numeric) = 0.1206245000467969 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 2.5310888886873867000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = 0.1065281049689708 " "
y[1] (numeric) = 0.106528104968971 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.82382883245688350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = 9.24210571694210600E-2 " "
y[1] (numeric) = 9.24210571694213500E-2 " "
absolute error = 2.9143354396410360000000000000000E-16 " "
relative error = 3.1533240680190890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = 7.83047673411717500E-2 " "
y[1] (numeric) = 7.83047673411720400E-2 " "
absolute error = 2.9143354396410360000000000000000E-16 " "
relative error = 3.72178545265750560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = 6.418064710144200E-2 " "
y[1] (numeric) = 6.41806471014423900E-2 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 6.0544428292321520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = 5.005010885048589000E-2 " "
y[1] (numeric) = 5.00501088504862600E-2 " "
absolute error = 3.81639164714897560000000000000000E-16 " "
relative error = 7.6251415527379540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = 3.591456563035300E-2 " "
y[1] (numeric) = 3.591456563035338000E-2 " "
absolute error = 3.74700270810990330000000000000000E-16 " "
relative error = 1.0433100449203662000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = 2.17754309835858080E-2 " "
y[1] (numeric) = 2.177543098358615300E-2 " "
absolute error = 3.4347524824340780000000000000000E-16 " "
relative error = 1.5773522393302683000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = 7.634118811866375000E-3 " "
y[1] (numeric) = 7.634118811866708000E-3 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.362872986333826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = -6.5079567653726360000E-3 " "
y[1] (numeric) = -6.5079567653721780000E-3 " "
absolute error = 4.5709963591988867000000000000000E-16 " "
relative error = 7.023704250034547000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = -2.06493815523581810E-2 " "
y[1] (numeric) = -2.064938155235780700E-2 " "
absolute error = 3.74700270810990330000000000000000E-16 " "
relative error = 1.814583501500553000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = -3.478874141839627400E-2 " "
y[1] (numeric) = -3.47887414183959700E-2 " "
absolute error = 3.05311331771918050000000000000000E-16 " "
relative error = 8.7761534141177510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = -4.892462243928319400E-2 " "
y[1] (numeric) = -4.89246224392828100E-2 " "
absolute error = 3.81639164714897560000000000000000E-16 " "
relative error = 7.8005541113479670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = -6.3055611038696500E-2 " "
y[1] (numeric) = -6.30556110386961100E-2 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 6.1624659918106080000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = -7.71802941295520700E-2 " "
y[1] (numeric) = -7.7180294129551700E-2 " "
absolute error = 3.74700270810990330000000000000000E-16 " "
relative error = 4.8548696922822280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = -9.12972592553115100E-2 " "
y[1] (numeric) = -9.129725925531100E-2 " "
absolute error = 5.1347814888913490000000000000000E-16 " "
relative error = 5.6242449453296330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = -0.10540509473122606 " "
y[1] (numeric) = -0.10540509473122558 " "
absolute error = 4.7184478546569153000000000000000E-16 " "
relative error = 4.47648936390461270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = -0.11950238978550487 " "
y[1] (numeric) = -0.11950238978550434 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 4.41293214004759000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = -0.1335877347003901 " "
y[1] (numeric) = -0.1335877347003896 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 3.73986700352260400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = -0.14765972095312796 " "
y[1] (numeric) = -0.14765972095312752 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.0075176018450630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = -0.1617169413568199 " "
y[1] (numeric) = -0.16171694135681952 " "
absolute error = 3.8857805861880480000000000000000E-16 " "
relative error = 2.402828394839770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = -0.1757579902011398 " "
y[1] (numeric) = -0.17575799020113944 " "
absolute error = 3.6082248300317590000000000000000E-16 " "
relative error = 2.05295066580043260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = -0.18978146339290425 " "
y[1] (numeric) = -0.18978146339290372 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.77875366365557650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = -0.20378595859647985 " "
y[1] (numeric) = -0.20378595859647944 " "
absolute error = 4.1633363423443370000000000000000E-16 " "
relative error = 2.04299470435459800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = -0.21777007537401705 " "
y[1] (numeric) = -0.21777007537401655 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.29416443110130680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = -0.23173241532549127 " "
y[1] (numeric) = -0.23173241532549077 " "
absolute error = 4.9960036108132044000000000000000E-16 " "
relative error = 2.15593645101218150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = -0.24567158222854268 " "
y[1] (numeric) = -0.24567158222854216 " "
absolute error = 5.2735593669694940000000000000000E-16 " "
relative error = 2.14658908414715240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = -0.2595861821780968 " "
y[1] (numeric) = -0.25958618217809626 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 2.13844784670290170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = -0.27347482372575427 " "
y[1] (numeric) = -0.27347482372575366 " "
absolute error = 6.1062266354383610000000000000000E-16 " "
relative error = 2.23282953518302660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (closed_form) = -0.287336118018934 " "
y[1] (numeric) = -0.28733611801893333 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 2.31830867406372850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (closed_form) = -0.30116867893975763 " "
y[1] (numeric) = -0.3011686789397572 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.47455310231278470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0099999999999996 " "
y[1] (closed_form) = -0.31497112324365917 " "
y[1] (numeric) = -0.31497112324366006 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.81987253483246270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999985 " "
y[1] (closed_form) = -0.3287420706977112 " "
y[1] (numeric) = -0.3287420706977137 " "
absolute error = 2.4980018054066022000000000000000E-15 " "
relative error = 7.5986678556380890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999974 " "
y[1] (closed_form) = -0.3424801442186445 " "
y[1] (numeric) = -0.3424801442186484 " "
absolute error = 3.941291737419305700000000000000E-15 " "
relative error = 1.1508088290523279000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = -0.3561839700105549 " "
y[1] (numeric) = -0.3561839700105604 " "
absolute error = 5.495603971894525000000000000000E-15 " "
relative error = 1.5429116508897556000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = -0.36985217770228335 " "
y[1] (numeric) = -0.36985217770229034 " "
absolute error = 6.994405055138486000000000000000E-15 " "
relative error = 1.8911352904804876000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = -0.3834834004844506 " "
y[1] (numeric) = -0.3834834004844591 " "
absolute error = 8.493206138382448000000000000000E-15 " "
relative error = 2.2147519625759726000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = -0.3970762752461379 " "
y[1] (numeric) = -0.3970762752461479 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 2.5163949207070120000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = -0.41062944271119645 " "
y[1] (numeric) = -0.410629442711208 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 2.811858638257066000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = -0.4241415475741739 " "
y[1] (numeric) = -0.4241415475741869 " "
absolute error = 1.298960938811433200000000000000E-14 " "
relative error = 3.0625647174644470000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = -0.43761123863584406 " "
y[1] (numeric) = -0.43761123863585855 " "
absolute error = 1.448841047135829300000000000000E-14 " "
relative error = 3.31079487732598000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = -0.4510371689383254 " "
y[1] (numeric) = -0.45103716893834134 " "
absolute error = 1.593170040337099600000000000000E-14 " "
relative error = 3.5322366981133410000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = -0.46441799589977606 " "
y[1] (numeric) = -0.4644179958997934 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 3.729286835794813000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = -0.4777523814486504 " "
y[1] (numeric) = -0.47775238144866916 " "
absolute error = 1.876276911616514600000000000000E-14 " "
relative error = 3.927299966411952000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = -0.49103899215750557 " "
y[1] (numeric) = -0.49103899215752583 " "
absolute error = 2.026157019940910700000000000000E-14 " "
relative error = 4.126265026405482000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = -0.5042764993763428 " "
y[1] (numeric) = -0.5042764993763644 " "
absolute error = 2.164934898019055300000000000000E-14 " "
relative error = 4.2931504852923136000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = -0.5174635793654715 " "
y[1] (numeric) = -0.5174635793654945 " "
absolute error = 2.29816166097407400000000000000E-14 " "
relative error = 4.4412046617699064000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = -0.5305989134278817 " "
y[1] (numeric) = -0.5305989134279062 " "
absolute error = 2.45359288442159600000000000000E-14 " "
relative error = 4.62419507904832000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = -0.5436811880411136 " "
y[1] (numeric) = -0.5436811880411394 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 4.737551112280870600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = -0.5567090949886074 " "
y[1] (numeric) = -0.5567090949886346 " "
absolute error = 2.720046410331633500000000000000E-14 " "
relative error = 4.8859385176513000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = -0.5696813314905251 " "
y[1] (numeric) = -0.569681331490554 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 5.067007999845992000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = -0.5825966003340266 " "
y[1] (numeric) = -0.5825966003340569 " "
absolute error = 3.030908857226677400000000000000E-14 " "
relative error = 5.202414252827655000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = -0.5954536100029904 " "
y[1] (numeric) = -0.5954536100030221 " "
absolute error = 3.17523785042794770000000000000E-14 " "
relative error = 5.332468889410212000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = -0.6082510748071634 " "
y[1] (numeric) = -0.6082510748071965 " "
absolute error = 3.308464613382966500000000000000E-14 " "
relative error = 5.439307467614198000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = -0.62098771501073 " "
y[1] (numeric) = -0.6209877150107647 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 5.578042452531667000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = -0.6336622569602837 " "
y[1] (numeric) = -0.6336622569603196 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 5.676719041214673000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = -0.6462734332121913 " "
y[1] (numeric) = -0.6462734332122287 " "
absolute error = 3.741451592986777500000000000000E-14 " "
relative error = 5.789270300638127000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = -0.6588199826593371 " "
y[1] (numeric) = -0.658819982659376 " "
absolute error = 3.896882816434299500000000000000E-14 " "
relative error = 5.914943260683246000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = -0.6713006506572319 " "
y[1] (numeric) = -0.6713006506572723 " "
absolute error = 4.0412118096355700000000000000E-14 " "
relative error = 6.019973026510628000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = -0.6837141891494763 " "
y[1] (numeric) = -0.6837141891495181 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 6.105531578602292000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = -0.6960593567925657 " "
y[1] (numeric) = -0.6960593567926089 " "
absolute error = 4.31876756579185900000000000000E-14 " "
relative error = 6.204596667865647000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = -0.7083349190800234 " "
y[1] (numeric) = -0.708334919080068 " "
absolute error = 4.45199432874687800000000000000E-14 " "
relative error = 6.285154393530497000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = -0.7205396484658502 " "
y[1] (numeric) = -0.7205396484658961 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 6.3790012551488210000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = -0.7326723244872781 " "
y[1] (numeric) = -0.7326723244873254 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 6.455205044373542000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = -0.7447317338868157 " "
y[1] (numeric) = -0.7447317338868644 " "
absolute error = 4.87387907810443700000000000000E-14 " "
relative error = 6.5444761601164280000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = -0.7567166707335722 " "
y[1] (numeric) = -0.7567166707336221 " "
absolute error = 4.996003610813204400000000000000E-14 " "
relative error = 6.602211638829109000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = -0.7686259365438506 " "
y[1] (numeric) = -0.7686259365439018 " "
absolute error = 5.118128143521972000000000000000E-14 " "
relative error = 6.658802286240544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = -0.7804583404009939 " "
y[1] (numeric) = -0.7804583404010466 " "
absolute error = 5.26245713672324200000000000000E-14 " "
relative error = 6.742777755465371000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = -0.7922126990744771 " "
y[1] (numeric) = -0.7922126990745308 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 6.7828746565959660000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = -0.8038878371382279 " "
y[1] (numeric) = -0.8038878371382828 " "
absolute error = 5.49560397189452500000000000000E-14 " "
relative error = 6.836282025933377000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = -0.8154825870881691 " "
y[1] (numeric) = -0.8154825870882253 " "
absolute error = 5.61772850460329200000000000000E-14 " "
relative error = 6.888839312513620000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = -0.8269957894589681 " "
y[1] (numeric) = -0.8269957894590255 " "
absolute error = 5.73985303731205900000000000000E-14 " "
relative error = 6.940607328928663000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = -0.8384262929399822 " "
y[1] (numeric) = -0.8384262929400408 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 6.991643295757722000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = -0.8497729544903883 " "
y[1] (numeric) = -0.8497729544904482 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 7.055066063583054000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = -0.8610346394534873 " "
y[1] (numeric) = -0.8610346394535484 " "
absolute error = 6.10622663543836100000000000000E-14 " "
relative error = 7.0917316860957900000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = -0.8722102216701675 " "
y[1] (numeric) = -0.8722102216702299 " "
absolute error = 6.2394533983933800000000000000E-14 " "
relative error = 7.15361187403382100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = -0.88329858359152 " "
y[1] (numeric) = -0.8832985835915836 " "
absolute error = 6.36157793110214700000000000000E-14 " "
relative error = 7.202069661694428000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = -0.8942986163905932 " "
y[1] (numeric) = -0.894298616390658 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 7.25004192668805000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = -0.9052092200732738 " "
y[1] (numeric) = -0.9052092200733397 " "
absolute error = 6.5947247662734300000000000000E-14 " "
relative error = 7.285304457835292000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = -0.9160293035882854 " "
y[1] (numeric) = -0.9160293035883528 " "
absolute error = 6.739053759474700000000000000E-14 " "
relative error = 7.35681023857683000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = -0.9267577849362933 " "
y[1] (numeric) = -0.926757784936362 " "
absolute error = 6.86117829218346700000000000000E-14 " "
relative error = 7.40342126465667000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = -0.9373935912781035 " "
y[1] (numeric) = -0.9373935912781732 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 7.437858184137605000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = -0.9479356590419444 " "
y[1] (numeric) = -0.9479356590420153 " "
absolute error = 7.08322289710849900000000000000E-14 " "
relative error = 7.472261254806408000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = -0.958382934029825 " "
y[1] (numeric) = -0.9583829340298968 " "
absolute error = 7.18314296932476300000000000000E-14 " "
relative error = 7.495065609235089000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = -0.9687343715229524 " "
y[1] (numeric) = -0.9687343715230254 " "
absolute error = 7.3052675020335300000000000000E-14 " "
relative error = 7.541042949213086000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = -0.9789889363862034 " "
y[1] (numeric) = -0.9789889363862777 " "
absolute error = 7.42739203474229700000000000000E-14 " "
relative error = 7.586798745815704000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = -0.9891456031716371 " "
y[1] (numeric) = -0.9891456031717126 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 7.632361245143268000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = -0.9992033562210392 " "
y[1] (numeric) = -0.9992033562211156 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 7.644424292477416000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = -1.0091611897674857 " "
y[1] (numeric) = -1.0091611897675632 " "
absolute error = 7.74935671188359300000000000000E-14 " "
relative error = 7.679007863618964000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = -1.0190181080359204 " "
y[1] (numeric) = -1.019018108035999 " "
absolute error = 7.86037901434610800000000000000E-14 " "
relative error = 7.71367942567418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = -1.0287731253427304 " "
y[1] (numeric) = -1.02877312534281 " "
absolute error = 7.97140131680862400000000000000E-14 " "
relative error = 7.74845407645441100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = -1.0384252661943143 " "
y[1] (numeric) = -1.0384252661943951 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 7.783346459675534000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = -1.0479735653846303 " "
y[1] (numeric) = -1.047973565384712 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 7.797182802260971000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = -1.0574170680917163 " "
y[1] (numeric) = -1.057417068091799 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 7.811543384785536000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = -1.0667548299731708 " "
y[1] (numeric) = -1.0667548299732548 " "
absolute error = 8.39328606616618300000000000000E-14 " "
relative error = 7.86805536786487000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = -1.0759859172605877 " "
y[1] (numeric) = -1.075985917260672 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 7.841826599955124000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = -1.0851094068529306 " "
y[1] (numeric) = -1.0851094068530156 " "
absolute error = 8.50430836862869900000000000000E-14 " "
relative error = 7.837281950483841000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = -1.0941243864088428 " "
y[1] (numeric) = -1.094124386408929 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 7.874178455494104000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = -1.1030299544378814 " "
y[1] (numeric) = -1.103029954437969 " "
absolute error = 8.74855743404623400000000000000E-14 " "
relative error = 7.931386993478897000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = -1.111825220390665 " "
y[1] (numeric) = -1.1118252203907535 " "
absolute error = 8.85957973650874900000000000000E-14 " "
relative error = 7.968500420772733000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = -1.1205093047479273 " "
y[1] (numeric) = -1.120509304748017 " "
absolute error = 8.97060203897126500000000000000E-14 " "
relative error = 8.005825566070881000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = -1.1290813391084695 " "
y[1] (numeric) = -1.1290813391085601 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 8.023708803915455000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = -1.1375404662759991 " "
y[1] (numeric) = -1.1375404662760902 " "
absolute error = 9.10382880192628400000000000000E-14 " "
relative error = 8.003081272114887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = -1.1458858403448482 " "
y[1] (numeric) = -1.14588584034494 " "
absolute error = 9.17044218340379300000000000000E-14 " "
relative error = 8.002928267831635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = -1.1541166267845644 " "
y[1] (numeric) = -1.1541166267846572 " "
absolute error = 9.28146448586630900000000000000E-14 " "
relative error = 8.04205075159952000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = -1.162232002523363 " "
y[1] (numeric) = -1.1622320025234565 " "
absolute error = 9.34807786734381800000000000000E-14 " "
relative error = 8.043211550747076000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = -1.1702311560304326 " "
y[1] (numeric) = -1.1702311560305267 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 8.0451551817823010000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = -1.1781132873970885 " "
y[1] (numeric) = -1.1781132873971836 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 8.066719213216155000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = -1.1858776084167628 " "
y[1] (numeric) = -1.1858776084168587 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 8.088800112827699000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = -1.1935233426638234 " "
y[1] (numeric) = -1.19352334266392 " "
absolute error = 9.65894031423886200000000000000E-14 " "
relative error = 8.092795481218727000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = -1.201049725571217 " "
y[1] (numeric) = -1.2010497255713144 " "
absolute error = 9.74775815620887400000000000000E-14 " "
relative error = 8.116032124792220000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = -1.2084560045069248 " "
y[1] (numeric) = -1.2084560045070232 " "
absolute error = 9.83657599817888700000000000000E-14 " "
relative error = 8.13978825997262000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = -1.2157414388492256 " "
y[1] (numeric) = -1.215741438849325 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 8.182330537369376000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = -1.2229053000607557 " "
y[1] (numeric) = -1.2229053000608565 " "
absolute error = 1.00808250635964210000000000000E-13 " "
relative error = 8.243340725643752000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = -1.2299468717613644 " "
y[1] (numeric) = -1.2299468717614657 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 8.232253129829445000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = -1.236865449799749 " "
y[1] (numeric) = -1.2368654497998512 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 8.258013697613685000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = -1.2436603423238717 " "
y[1] (numeric) = -1.243660342323974 " "
absolute error = 1.02362562870439430000000000000E-13 " "
relative error = 8.230749135183275000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = -1.250330869850142 " "
y[1] (numeric) = -1.2503308698502453 " "
absolute error = 1.03250741290139560000000000000E-13 " "
relative error = 8.257873478123006000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = -1.2568763653313662 " "
y[1] (numeric) = -1.2568763653314703 " "
absolute error = 1.04138919709839680000000000000E-13 " "
relative error = 8.285534089296381000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = -1.263296174223451 " "
y[1] (numeric) = -1.2632961742235558 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 8.296158546434174000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = -1.2695896545508565 " "
y[1] (numeric) = -1.2695896545509622 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 8.324991588065993000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = -1.275756176970795 " "
y[1] (numeric) = -1.2757561769709014 " "
absolute error = 1.06359365759090000000000000E-13 " "
relative error = 8.336966551996934000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = -1.281795124836163 " "
y[1] (numeric) = -1.2817951248362702 " "
absolute error = 1.07247544178790120000000000000E-13 " "
relative error = 8.366980190574398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = -1.2877058942572064 " "
y[1] (numeric) = -1.2877058942573145 " "
absolute error = 1.08135722598490250000000000000E-13 " "
relative error = 8.397548157599038000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = -1.2934878941619088 " "
y[1] (numeric) = -1.2934878941620176 " "
absolute error = 1.08801856413265340000000000000E-13 " "
relative error = 8.411509447002706000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = -1.299140546355098 " "
y[1] (numeric) = -1.2991405463552077 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 8.443276991139614000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = -1.3046632855762654 " "
y[1] (numeric) = -1.3046632855763753 " "
absolute error = 1.0991207943789050000000000000E-13 " "
relative error = 8.424555259048522000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = -1.310055559556091 " "
y[1] (numeric) = -1.3100555595562011 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 8.406828492078169000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = -1.3153168290716701 " "
y[1] (numeric) = -1.315316829071781 " "
absolute error = 1.10800257857590620000000000000E-13 " "
relative error = 8.423845525932463000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = -1.3204465680004358 " "
y[1] (numeric) = -1.320446568000547 " "
absolute error = 1.11244347067440690000000000000E-13 " "
relative error = 8.42475188041110900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = -1.32544426337277 " "
y[1] (numeric) = -1.325444263372882 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 8.443243067606977000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = -1.3303094154233004 " "
y[1] (numeric) = -1.3303094154234123 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 8.412364791585437000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = -1.3350415376408757 " "
y[1] (numeric) = -1.3350415376409883 " "
absolute error = 1.12576614696990870000000000000E-13 " "
relative error = 8.43244285087359000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = -1.339640156817218 " "
y[1] (numeric) = -1.3396401568173313 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 8.453221406919719000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = -1.3441048130942415 " "
y[1] (numeric) = -1.3441048130943558 " "
absolute error = 1.14352971536391120000000000000E-13 " "
relative error = 8.50774213605716000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = -1.3484350600100394 " "
y[1] (numeric) = -1.348435060010154 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 8.496887951019542000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = -1.3526304645435283 " "
y[1] (numeric) = -1.3526304645436438 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 8.536196513951917000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = -1.3566906071577514 " "
y[1] (numeric) = -1.356690607157867 " "
absolute error = 1.1568523916594131000000000000E-13 " "
relative error = 8.527017033625696000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = -1.3606150818418303 " "
y[1] (numeric) = -1.3606150818419465 " "
absolute error = 1.16129328375791370000000000000E-13 " "
relative error = 8.535061085651795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = -1.3644034961515672 " "
y[1] (numeric) = -1.364403496151684 " "
absolute error = 1.16795462190566470000000000000E-13 " "
relative error = 8.560184910109029000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = -1.368055471248688 " "
y[1] (numeric) = -1.368055471248805 " "
absolute error = 1.1701750679549150000000000000E-13 " "
relative error = 8.553564475619118000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = -1.3715706419387266 " "
y[1] (numeric) = -1.3715706419388443 " "
absolute error = 1.1768364061026660000000000000E-13 " "
relative error = 8.58020994412069000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = -1.374948656707543 " "
y[1] (numeric) = -1.374948656707661 " "
absolute error = 1.17905685215191620000000000000E-13 " "
relative error = 8.575279130606156000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = -1.3781891777564754 " "
y[1] (numeric) = -1.3781891777565938 " "
absolute error = 1.18349774425041690000000000000E-13 " "
relative error = 8.587338830921654000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = -1.3812918810361192 " "
y[1] (numeric) = -1.381291881036238 " "
absolute error = 1.18793863634891750000000000000E-13 " "
relative error = 8.600199948021372000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = -1.3842564562787323 " "
y[1] (numeric) = -1.3842564562788517 " "
absolute error = 1.19459997449666840000000000000E-13 " "
relative error = 8.62990357804135900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = -1.3870826070292608 " "
y[1] (numeric) = -1.3870826070293802 " "
absolute error = 1.19459997449666840000000000000E-13 " "
relative error = 8.612320336531104000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = -1.3897700506749846 " "
y[1] (numeric) = -1.3897700506751045 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 8.627620562213281000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = -1.392318518473779 " "
y[1] (numeric) = -1.392318518473899 " "
absolute error = 1.20126131264441940000000000000E-13 " "
relative error = 8.627776594979207000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = -1.3947277555809874 " "
y[1] (numeric) = -1.394727755581108 " "
absolute error = 1.205702204742920000000000000E-13 " "
relative error = 8.644713636179652000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = -1.396997521074907 " "
y[1] (numeric) = -1.396997521075028 " "
absolute error = 1.21014309684142060000000000000E-13 " "
relative error = 8.662457009302973000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = -1.39912758798088 " "
y[1] (numeric) = -1.3991275879810015 " "
absolute error = 1.21458398893992130000000000000E-13 " "
relative error = 8.681009504592224000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = -1.4011177432939905 " "
y[1] (numeric) = -1.4011177432941122 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 8.684526627494537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = -1.402967788000366 " "
y[1] (numeric) = -1.402967788000488 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.704728202122868000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = -1.4046775370970774 " "
y[1] (numeric) = -1.4046775370971993 " "
absolute error = 1.2190248810384219000000000000E-13 " "
relative error = 8.678325443700571000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = -1.4062468196106397 " "
y[1] (numeric) = -1.4062468196107618 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.684430855643175000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = -1.4076754786141097 " "
y[1] (numeric) = -1.4076754786142318 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.675616970255229000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = -1.408963371242777 " "
y[1] (numeric) = -1.4089633712428995 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 8.699205701174868000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = -1.4101103687084526 " "
y[1] (numeric) = -1.410110368708575 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 8.676383071046548000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = -1.4111163563123452 " "
y[1] (numeric) = -1.4111163563124676 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 8.67019766062518100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = -1.4119812334565331 " "
y[1] (numeric) = -1.4119812334566555 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 8.664886927299137000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = -1.4127049136540224 " "
y[1] (numeric) = -1.4127049136541447 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 8.660448203385769000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = -1.4132873245373965 " "
y[1] (numeric) = -1.4132873245375193 " "
absolute error = 1.22790666523542310000000000000E-13 " "
relative error = 8.688301691500326000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = -1.4137284078660524 " "
y[1] (numeric) = -1.4137284078661754 " "
absolute error = 1.23012711128467340000000000000E-13 " "
relative error = 8.701297253702956000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = -1.4140281195320248 " "
y[1] (numeric) = -1.4140281195321476 " "
absolute error = 1.22790666523542310000000000000E-13 " "
relative error = 8.683749978337073000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = -1.4141864295643969 " "
y[1] (numeric) = -1.4141864295645197 " "
absolute error = 1.22790666523542310000000000000E-13 " "
relative error = 8.682777882500595000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = -1.4142033221322974 " "
y[1] (numeric) = -1.41420332213242 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 8.666973128998993000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = -1.4140787955464837 " "
y[1] (numeric) = -1.4140787955466059 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.636331517973937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = -1.41381286225951 " "
y[1] (numeric) = -1.4138128622596324 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 8.653661356437364000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = -1.413405548864484 " "
y[1] (numeric) = -1.4134055488646065 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 8.656155157448211000000000000E-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) = -1.412856896092406 " "
y[1] (numeric) = -1.412856896092528 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.643800589184358000000000000E-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) = -1.4121669588080952 " "
y[1] (numeric) = -1.4121669588082177 " "
absolute error = 1.22568621918617280000000000000E-13 " "
relative error = 8.679471018219284000000000000E-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) = -1.4113358060047057 " "
y[1] (numeric) = -1.4113358060048278 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.65311658566111900000000000E-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) = -1.410363520796825 " "
y[1] (numeric) = -1.410363520796947 " "
absolute error = 1.2190248810384219000000000000E-13 " "
relative error = 8.643338139869776000000000000E-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) = -1.4092502004121634 " "
y[1] (numeric) = -1.4092502004122855 " "
absolute error = 1.22124532708767220000000000000E-13 " "
relative error = 8.665922678105666000000000000E-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) = -1.407995956181832 " "
y[1] (numeric) = -1.407995956181954 " "
absolute error = 1.2190248810384219000000000000E-13 " "
relative error = 8.657872032133834000000000000E-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) = -1.4066009135292088 " "
y[1] (numeric) = -1.4066009135293305 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 8.650672861687319000000000000E-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) = -1.4050652119573959 " "
y[1] (numeric) = -1.4050652119575175 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 8.660127833455087000000000000E-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) = -1.403389005035271 " "
y[1] (numeric) = -1.4033890050353925 " "
absolute error = 1.21458398893992130000000000000E-13 " "
relative error = 8.65464945629523000000000000E-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) = -1.40157246038213 " "
y[1] (numeric) = -1.4015724603822515 " "
absolute error = 1.21458398893992130000000000000E-13 " "
relative error = 8.665866541133183000000000000E-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) = -1.3996157596509233 " "
y[1] (numeric) = -1.3996157596510448 " "
absolute error = 1.21458398893992130000000000000E-13 " "
relative error = 8.677981657214615000000000000E-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) = -1.3975190985100947 " "
y[1] (numeric) = -1.3975190985102157 " "
absolute error = 1.21014309684142060000000000000E-13 " "
relative error = 8.659224035875882000000000000E-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) = -1.3952826866240104 " "
y[1] (numeric) = -1.3952826866241308 " "
absolute error = 1.20348175869366970000000000000E-13 " "
relative error = 8.625361514415281000000000000E-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) = -1.3929067476319952 " "
y[1] (numeric) = -1.3929067476321153 " "
absolute error = 1.20126131264441940000000000000E-13 " "
relative error = 8.62413305619071900000000000E-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) = -1.3903915191259686 " "
y[1] (numeric) = -1.3903915191260887 " "
absolute error = 1.20126131264441940000000000000E-13 " "
relative error = 8.639734176453833000000000000E-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) = -1.3877372526266853 " "
y[1] (numeric) = -1.3877372526268053 " "
absolute error = 1.1990408665951690000000000000E-13 " "
relative error = 8.640258552731397000000000000E-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) = -1.3849442135585832 " "
y[1] (numeric) = -1.3849442135587027 " "
absolute error = 1.19459997449666840000000000000E-13 " "
relative error = 8.625618005415326000000000000E-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) = -1.3820126812232416 " "
y[1] (numeric) = -1.3820126812233606 " "
absolute error = 1.19015908239816780000000000000E-13 " "
relative error = 8.6117811983080990000000000E-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) = -1.378942948771451 " "
y[1] (numeric) = -1.3789429487715696 " "
absolute error = 1.18571819029966720000000000000E-13 " "
relative error = 8.598747260400189000000000000E-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) = -1.375735323173899 " "
y[1] (numeric) = -1.3757353231740168 " "
absolute error = 1.17905685215191620000000000000E-13 " "
relative error = 8.57037565504799000000000000E-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) = -1.3723901251904713 " "
y[1] (numeric) = -1.372390125190589 " "
absolute error = 1.1768364061026660000000000000E-13 " "
relative error = 8.57508651877931000000000000E-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) = -1.3689076893381795 " "
y[1] (numeric) = -1.3689076893382968 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 8.564459993434463000000000000E-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) = -1.3652883638577065 " "
y[1] (numeric) = -1.3652883638578237 " "
absolute error = 1.17239551400416530000000000000E-13 " "
relative error = 8.58716403830974900000000000E-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) = -1.3615325106785843 " "
y[1] (numeric) = -1.3615325106787006 " "
absolute error = 1.1635137298071640000000000000E-13 " "
relative error = 8.545618416612555000000000000E-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) = -1.357640505383001 " "
y[1] (numeric) = -1.357640505383117 " "
absolute error = 1.16129328375791370000000000000E-13 " "
relative error = 8.553761317178025000000000000E-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) = -1.3536127371682425 " "
y[1] (numeric) = -1.3536127371683584 " "
absolute error = 1.15907283770866340000000000000E-13 " "
relative error = 8.562809774776821000000000000E-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) = -1.3494496088077743 " "
y[1] (numeric) = -1.3494496088078896 " "
absolute error = 1.15241149956091250000000000000E-13 " "
relative error = 8.539863156350513000000000000E-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) = -1.3451515366109628 " "
y[1] (numeric) = -1.3451515366110776 " "
absolute error = 1.14797060746241190000000000000E-13 " "
relative error = 8.53413594095623100000000000E-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) = -1.3407189503814463 " "
y[1] (numeric) = -1.3407189503815606 " "
absolute error = 1.14352971536391120000000000000E-13 " "
relative error = 8.529227658328892000000000000E-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) = -1.3361522933741534 " "
y[1] (numeric) = -1.3361522933742673 " "
absolute error = 1.13908882326541060000000000000E-13 " "
relative error = 8.525142148197021000000000000E-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) = -1.3314520222509798 " "
y[1] (numeric) = -1.3314520222510935 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 8.538560595628129000000000000E-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) = -1.326618607035121 " "
y[1] (numeric) = -1.3266186070352337 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 8.50271952343644900000000000E-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) = -1.3216525310640703 " "
y[1] (numeric) = -1.3216525310641827 " "
absolute error = 1.12354570092065840000000000000E-13 " "
relative error = 8.501067220868447000000000000E-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) = -1.3165542909412868 " "
y[1] (numeric) = -1.3165542909413985 " "
absolute error = 1.11688436277290750000000000000E-13 " "
relative error = 8.483390092286867000000000000E-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) = -1.311324396486534 " "
y[1] (numeric) = -1.3113243964866452 " "
absolute error = 1.11244347067440690000000000000E-13 " "
relative error = 8.483358302911208000000000000E-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) = -1.3059633706848994 " "
y[1] (numeric) = -1.3059633706850098 " "
absolute error = 1.10356168647740560000000000000E-13 " "
relative error = 8.450173345203807000000000000E-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) = -1.3004717496344955 " "
y[1] (numeric) = -1.3004717496346052 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 8.434634190538505000000000000E-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) = -1.2948500824928508 " "
y[1] (numeric) = -1.2948500824929603 " "
absolute error = 1.09467990228040430000000000000E-13 " "
relative error = 8.4541053600037000000000000E-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) = -1.2890989314219952 " "
y[1] (numeric) = -1.289098931422104 " "
absolute error = 1.08801856413265340000000000000E-13 " "
relative error = 8.440147901856287000000000000E-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) = -1.283218871532243 " "
y[1] (numeric) = -1.283218871532351 " "
absolute error = 1.07913677993565220000000000000E-13 " "
relative error = 8.409608086943858000000000000E-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) = -1.2772104908246829 " "
y[1] (numeric) = -1.2772104908247899 " "
absolute error = 1.07025499573865090000000000000E-13 " "
relative error = 8.379628913379793000000000000E-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) = -1.2710743901323789 " "
y[1] (numeric) = -1.2710743901324855 " "
absolute error = 1.06581410364015030000000000000E-13 " "
relative error = 8.385143402418396000000000000E-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) = -1.264811183060287 " "
y[1] (numeric) = -1.2648111830603928 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 8.356443503969008000000000000E-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) = -1.2584214959238949 " "
y[1] (numeric) = -1.2584214959239999 " "
absolute error = 1.05027098129539810000000000000E-13 " "
relative error = 8.345939613216166000000000000E-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) = -1.2519059676865913 " "
y[1] (numeric) = -1.2519059676866962 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 8.371639422590581000000000000E-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) = -1.2452652498957708 " "
y[1] (numeric) = -1.2452652498958752 " "
absolute error = 1.04360964314764710000000000000E-13 " "
relative error = 8.380621263100353000000000000E-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) = -1.2385000066176781 " "
y[1] (numeric) = -1.2385000066177823 " "
absolute error = 1.04138919709839680000000000000E-13 " "
relative error = 8.408471469793629000000000000E-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) = -1.2316109143710037 " "
y[1] (numeric) = -1.2316109143711074 " "
absolute error = 1.03694830499989620000000000000E-13 " "
relative error = 8.419447188233765000000000000E-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) = -1.2245986620592313 " "
y[1] (numeric) = -1.2245986620593339 " "
absolute error = 1.02584607475364460000000000000E-13 " "
relative error = 8.376998167127073000000000000E-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) = -1.2174639509017484 " "
y[1] (numeric) = -1.2174639509018503 " "
absolute error = 1.01918473660589370000000000000E-13 " "
relative error = 8.37137506906061900000000000E-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) = -1.2102074943637253 " "
y[1] (numeric) = -1.2102074943638261 " "
absolute error = 1.00808250635964210000000000000E-13 " "
relative error = 8.329831959019955000000000000E-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) = -1.2028300180847686 " "
y[1] (numeric) = -1.2028300180848688 " "
absolute error = 1.00142116821189120000000000000E-13 " "
relative error = 8.325541873376465000000000000E-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) = -1.1953322598063587 " "
y[1] (numeric) = -1.1953322598064577 " "
absolute error = 9.90318937965639600000000000000E-14 " "
relative error = 8.284884222283678000000000000E-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) = -1.187714969298075 " "
y[1] (numeric) = -1.1877149692981734 " "
absolute error = 9.83657599817888700000000000000E-14 " "
relative error = 8.281933167847655000000000000E-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) = -1.1799789082826206 " "
y[1] (numeric) = -1.1799789082827181 " "
absolute error = 9.74775815620887400000000000000E-14 " "
relative error = 8.260959655962052000000000000E-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) = -1.1721248503596504 " "
y[1] (numeric) = -1.172124850359747 " "
absolute error = 9.65894031423886200000000000000E-14 " "
relative error = 8.240538805465261000000000000E-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) = -1.1641535809284118 " "
y[1] (numeric) = -1.1641535809285075 " "
absolute error = 9.5701224722688490000000000000E-14 " "
relative error = 8.220670046504245000000000000E-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) = -1.1560658971092053 " "
y[1] (numeric) = -1.1560658971093 " "
absolute error = 9.48130463029883700000000000000E-14 " "
relative error = 8.201353101070852000000000000E-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) = -1.1478626076636727 " "
y[1] (numeric) = -1.1478626076637664 " "
absolute error = 9.37028232783632100000000000000E-14 " "
relative error = 8.163243810954284000000000000E-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) = -1.1395445329139229 " "
y[1] (numeric) = -1.139544532914016 " "
absolute error = 9.30366894635881200000000000000E-14 " "
relative error = 8.164375044271812000000000000E-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) = -1.131112504660499 " "
y[1] (numeric) = -1.1311125046605912 " "
absolute error = 9.21485110438879900000000000000E-14 " "
relative error = 8.146714908040573000000000000E-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) = -1.1225673660991995 " "
y[1] (numeric) = -1.1225673660992908 " "
absolute error = 9.12603326241878700000000000000E-14 " "
relative error = 8.129608554478799000000000000E-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) = -1.11390997173676 " "
y[1] (numeric) = -1.1139099717368501 " "
absolute error = 9.01501095995627100000000000000E-14 " "
relative error = 8.09312349174903000000000000E-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) = -1.105141187305402 " "
y[1] (numeric) = -1.1051411873054913 " "
absolute error = 8.92619311798625900000000000000E-14 " "
relative error = 8.07697081650757000000000000E-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) = -1.0962618896762613 " "
y[1] (numeric) = -1.0962618896763494 " "
absolute error = 8.81517081552374300000000000000E-14 " "
relative error = 8.041117636705372000000000000E-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) = -1.0872729667717016 " "
y[1] (numeric) = -1.0872729667717889 " "
absolute error = 8.7263529735537300000000000000E-14 " "
relative error = 8.025908157602554000000000000E-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) = -1.0781753174765225 " "
y[1] (numeric) = -1.0781753174766089 " "
absolute error = 8.63753513158371800000000000000E-14 " "
relative error = 8.011252893267797000000000000E-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) = -1.0689698515480723 " "
y[1] (numeric) = -1.0689698515481578 " "
absolute error = 8.54871728961370500000000000000E-14 " "
relative error = 7.997154716041366000000000000E-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) = -1.0596574895252726 " "
y[1] (numeric) = -1.0596574895253572 " "
absolute error = 8.45989944764369300000000000000E-14 " "
relative error = 7.983616905717086000000000000E-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) = -1.0502391626365652 " "
y[1] (numeric) = -1.050239162636649 " "
absolute error = 8.3710816056736800000000000000E-14 " "
relative error = 7.970643167274928000000000000E-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) = -1.0407158127067908 " "
y[1] (numeric) = -1.0407158127068734 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 7.936901892292414000000000000E-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) = -1.0310883920630058 " "
y[1] (numeric) = -1.0310883920630876 " "
absolute error = 8.17124146124115200000000000000E-14 " "
relative error = 7.924869995764475000000000000E-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) = -1.021357863439252 " "
y[1] (numeric) = -1.0213578634393328 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 7.913410087288043000000000000E-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) = -1.011525199880283 " "
y[1] (numeric) = -1.0115251998803625 " "
absolute error = 7.94919685631612100000000000000E-14 " "
relative error = 7.858624636595244000000000000E-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) = -1.001591384644261 " "
y[1] (numeric) = -1.0015913846443392 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 7.803551641108744000000000000E-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) = -0.9915574111044312 " "
y[1] (numeric) = -0.9915574111045083 " "
absolute error = 7.71605002114483800000000000000E-14 " "
relative error = 7.781748121422877000000000000E-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) = -0.981424282649786 " "
y[1] (numeric) = -0.981424282649862 " "
absolute error = 7.60502771868232200000000000000E-14 " "
relative error = 7.74897040263688000000000000E-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) = -0.9711930125847268 " "
y[1] (numeric) = -0.9711930125848017 " "
absolute error = 7.49400541621980700000000000000E-14 " "
relative error = 7.716288440209542000000000000E-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) = -0.960864624027734 " "
y[1] (numeric) = -0.9608646240278076 " "
absolute error = 7.36077865326478800000000000000E-14 " "
relative error = 7.6605782637829000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = -0.9504401498090561 " "
y[1] (numeric) = -0.9504401498091287 " "
absolute error = 7.26085858104852400000000000000E-14 " "
relative error = 7.639469547353649000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = -0.9399206323674283 " "
y[1] (numeric) = -0.9399206323674997 " "
absolute error = 7.13873404833975700000000000000E-14 " "
relative error = 7.595039200660002000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = -0.9293071236458282 " "
y[1] (numeric) = -0.9293071236458986 " "
absolute error = 7.03881397612349200000000000000E-14 " "
relative error = 7.574260217127187000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = -0.9186006849862838 " "
y[1] (numeric) = -0.918600684986353 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 7.541679194115145000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = -0.9078023870237387 " "
y[1] (numeric) = -0.9078023870238068 " "
absolute error = 6.8056671409522100000000000000E-14 " "
relative error = 7.496859711136938000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = -0.8969133095789906 " "
y[1] (numeric) = -0.8969133095790576 " "
absolute error = 6.69464483848969400000000000000E-14 " "
relative error = 7.464093538351155000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = -0.8859345415507099 " "
y[1] (numeric) = -0.8859345415507757 " "
absolute error = 6.57252030578092700000000000000E-14 " "
relative error = 7.418742579193953000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = -0.8748671808065507 " "
y[1] (numeric) = -0.8748671808066151 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 7.360309866566769000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = -0.8637123340733642 " "
y[1] (numeric) = -0.8637123340734274 " "
absolute error = 6.31716901011714100000000000000E-14 " "
relative error = 7.313973369263657000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = -0.8524711168265283 " "
y[1] (numeric) = -0.8524711168265903 " "
absolute error = 6.19504447740837300000000000000E-14 " "
relative error = 7.267160558436867000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = -0.8411446531784001 " "
y[1] (numeric) = -0.8411446531784609 " "
absolute error = 6.07291994469960600000000000000E-14 " "
relative error = 7.2198282682438790000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = -0.8297340757659056 " "
y[1] (numeric) = -0.829734075765965 " "
absolute error = 5.93969318174458700000000000000E-14 " "
relative error = 7.158550378037460000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = -0.8182405256372772 " "
y[1] (numeric) = -0.8182405256373355 " "
absolute error = 5.82867087928207200000000000000E-14 " "
relative error = 7.123419943961439000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = -0.80666515213795 " "
y[1] (numeric) = -0.8066651521380069 " "
absolute error = 5.69544411632705300000000000000E-14 " "
relative error = 7.060481168960997000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = -0.7950091127956277 " "
y[1] (numeric) = -0.7950091127956835 " "
absolute error = 5.584421813864537000000000000000E-14 " "
relative error = 7.024349436985787000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = -0.7832735732045313 " "
y[1] (numeric) = -0.7832735732045856 " "
absolute error = 5.428990590417015000000000000000E-14 " "
relative error = 6.931155060173819000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = -0.77145970690884 " "
y[1] (numeric) = -0.7714597069088932 " "
absolute error = 5.317968287954500000000000000E-14 " "
relative error = 6.893384372935113000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = -0.7595686952853391 " "
y[1] (numeric) = -0.7595686952853908 " "
absolute error = 5.173639294753230000000000000000E-14 " "
relative error = 6.8112855714909410000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = -0.7476017274252814 " "
y[1] (numeric) = -0.7476017274253317 " "
absolute error = 5.02931030155195900000000000000E-14 " "
relative error = 6.7272588024545610000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = -0.7355600000154805 " "
y[1] (numeric) = -0.7355600000155295 " "
absolute error = 4.896083538596940300000000000000E-14 " "
relative error = 6.656266706310698000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = -0.7234447172186427 " "
y[1] (numeric) = -0.7234447172186903 " "
absolute error = 4.762856775641921600000000000000E-14 " "
relative error = 6.583580835247802000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = -0.7112570905529517 " "
y[1] (numeric) = -0.7112570905529979 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 6.4934716908763260000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = -0.6989983387709177 " "
y[1] (numeric) = -0.6989983387709625 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 6.416754905844773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = -0.6866696877375031 " "
y[1] (numeric) = -0.6866696877375466 " "
absolute error = 4.34097202628436200000000000000E-14 " "
relative error = 6.321776108375136000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = -0.6742723703075378 " "
y[1] (numeric) = -0.6742723703075797 " "
absolute error = 4.1855408028368400000000000000E-14 " "
relative error = 6.207492679742760000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = -0.6618076262024335 " "
y[1] (numeric) = -0.661807626202474 " "
absolute error = 4.052314039881821400000000000000E-14 " "
relative error = 6.1230996432221540000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = -0.6492767018862133 " "
y[1] (numeric) = -0.6492767018862525 " "
absolute error = 3.919087276926802600000000000000E-14 " "
relative error = 6.0360817900002650000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = -0.636680850440867 " "
y[1] (numeric) = -0.6366808504409047 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 5.9288076296180680000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = -0.6240213314410419 " "
y[1] (numeric) = -0.6240213314410782 " "
absolute error = 3.63042929052426200000000000000E-14 " "
relative error = 5.817796776498927000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = -0.6112994108280889 " "
y[1] (numeric) = -0.6112994108281237 " "
absolute error = 3.4749980670767400000000000000E-14 " "
relative error = 5.6846088929962780000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = -0.5985163607834675 " "
y[1] (numeric) = -0.5985163607835009 " "
absolute error = 3.34177130412172100000000000000E-14 " "
relative error = 5.5834251544056190000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = -0.5856734596015298 " "
y[1] (numeric) = -0.5856734596015618 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 5.459428387101356000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = -0.5727719915616916 " "
y[1] (numeric) = -0.5727719915617222 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 5.34979990835567000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = -0.5598132468000054 " "
y[1] (numeric) = -0.559813246800035 " "
absolute error = 2.953193245502916400000000000000E-14 " "
relative error = 5.27531862167233000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = -0.5467985211801489 " "
y[1] (numeric) = -0.546798521180177 " "
absolute error = 2.80886425230164600000000000000E-14 " "
relative error = 5.136927302289163000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = -0.5337291161638382 " "
y[1] (numeric) = -0.5337291161638651 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 5.033901352251005000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = -0.5206063386806841 " "
y[1] (numeric) = -0.5206063386807095 " "
absolute error = 2.542410726391608500000000000000E-14 " "
relative error = 4.883556994013102000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = -0.507431500997499 " "
y[1] (numeric) = -0.507431500997523 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 4.725922077120232600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = -0.4942059205870723 " "
y[1] (numeric) = -0.49420592058709484 " "
absolute error = 2.253752739989067800000000000000E-14 " "
relative error = 4.560351558135547500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = -0.4809309199964238 " "
y[1] (numeric) = -0.480930919996445 " "
absolute error = 2.12052597703404900000000000000E-14 " "
relative error = 4.40921115458706000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = -0.4676078267145502 " "
y[1] (numeric) = -0.46760782671456985 " "
absolute error = 1.96509475358652700000000000000E-14 " "
relative error = 4.202441963799962000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = -0.45423797303967695 " "
y[1] (numeric) = -0.4542379730396952 " "
absolute error = 1.826316875508382500000000000000E-14 " "
relative error = 4.020616909869965000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = -0.4408226959460301 " "
y[1] (numeric) = -0.440822695946047 " "
absolute error = 1.693090112553363700000000000000E-14 " "
relative error = 3.840750778314392000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = -0.4273633369501398 " "
y[1] (numeric) = -0.4273633369501551 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 3.5850238930567550000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = -0.41386124197668933 " "
y[1] (numeric) = -0.41386124197670315 " "
absolute error = 1.382227665658320000000000000000E-14 " "
relative error = 3.339833561259582000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = -0.4003177612239244 " "
y[1] (numeric) = -0.4003177612239368 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 3.1061569283822790000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = -0.3867342490286342 " "
y[1] (numeric) = -0.38673424902864506 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 2.813349391385544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = -0.3731120637307185 " "
y[1] (numeric) = -0.37311206373072786 " "
absolute error = 9.381384558082573000000000000000E-15 " "
relative error = 2.5143610914851800000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = -0.35945256753735555 " "
y[1] (numeric) = -0.35945256753736327 " "
absolute error = 7.716050021144838000000000000000E-15 " "
relative error = 2.1466114636510306000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = -0.34575712638678147 " "
y[1] (numeric) = -0.34575712638678785 " "
absolute error = 6.38378239159465000000000000000E-15 " "
relative error = 1.846319831005717700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = -0.3320271098116989 " "
y[1] (numeric) = -0.33202710981170364 " "
absolute error = 4.718447854656915300000000000000E-15 " "
relative error = 1.4211031916438593000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = -0.3182638908023234 " "
y[1] (numeric) = -0.3182638908023267 " "
absolute error = 3.2751579226442120000000000000000E-15 " "
relative error = 1.029069906230249000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = -0.30446884566908683 " "
y[1] (numeric) = -0.3044688456690885 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 5.4696385545722140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = -0.2906433539050064 " "
y[1] (numeric) = -0.2906433539050066 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 7.63976199495702700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = -0.2767887980477376 " "
y[1] (numeric) = -0.27678879804773626 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.813300389853250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = -0.26290656354132047 " "
y[1] (numeric) = -0.26290656354131764 " "
absolute error = 2.831068712794149000000000000000E-15 " "
relative error = 1.0768345508989913000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = -0.24899803859763736 " "
y[1] (numeric) = -0.24899803859763298 " "
absolute error = 4.385380947269368300000000000000E-15 " "
relative error = 1.761211040845114000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = -0.23506461405759205 " "
y[1] (numeric) = -0.23506461405758622 " "
absolute error = 5.828670879282072000000000000000E-15 " "
relative error = 2.479603704985565100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = -0.22110768325202768 " "
y[1] (numeric) = -0.2211076832520202 " "
absolute error = 7.466249840604178000000000000000E-15 " "
relative error = 3.37674825713489000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = -0.20712864186239377 " "
y[1] (numeric) = -0.20712864186238483 " "
absolute error = 8.93729534823251000000000000000E-15 " "
relative error = 4.314852483882946000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = -0.19312888778118031 " "
y[1] (numeric) = -0.19312888778116982 " "
absolute error = 1.04916075827077300000000000000E-14 " "
relative error = 5.432438255738816000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = -0.1791098209721289 " "
y[1] (numeric) = -0.1791098209721169 " "
absolute error = 1.20181642415673200000000000000E-14 " "
relative error = 6.709941518749802000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = -0.16507284333023808 " "
y[1] (numeric) = -0.16507284333022443 " "
absolute error = 1.365574320288942500000000000000E-14 " "
relative error = 8.272555877389411000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = -0.15101935854157433 " "
y[1] (numeric) = -0.15101935854155918 " "
absolute error = 1.515454428613338700000000000000E-14 " "
relative error = 1.003483555517915300000000000E-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) = -0.1369507719429056 " "
y[1] (numeric) = -0.13695077194288885 " "
absolute error = 1.676436767183986400000000000000E-14 " "
relative error = 1.224116332752682900000000000E-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) = -0.12286849038116776 " "
y[1] (numeric) = -0.12286849038114947 " "
absolute error = 1.829092433069945400000000000000E-14 " "
relative error = 1.488658668626641800000000000E-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) = -0.10877392207278191 " "
y[1] (numeric) = -0.10877392207276207 " "
absolute error = 1.984523656517467300000000000000E-14 " "
relative error = 1.824448009872806600000000000E-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) = -9.46684764628333800E-2 " "
y[1] (numeric) = -9.46684764628120200E-2 " "
absolute error = 2.13579154362264500000000000000E-14 " "
relative error = 2.256074697115413600000000000E-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) = -8.05535640841287300E-2 " "
y[1] (numeric) = -8.05535640841058300E-2 " "
absolute error = 2.289834988289385400000000000000E-14 " "
relative error = 2.842624053105734500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = -6.64305964161434600E-2 " "
y[1] (numeric) = -6.64305964161189500E-2 " "
absolute error = 2.45081732686003300000000000000E-14 " "
relative error = 3.68928996438221630000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = -5.230098574387521000E-2 " "
y[1] (numeric) = -5.23009857438491300E-2 " "
absolute error = 2.60833021847872700000000000000E-14 " "
relative error = 4.987153074422081600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = -3.816614501661652600E-2 " "
y[1] (numeric) = -3.81661450165889100E-2 " "
absolute error = 2.76167977375507700000000000000E-14 " "
relative error = 7.2359411005557790000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = -2.4027487706661300E-2 " "
y[1] (numeric) = -2.402748770663204700E-2 " "
absolute error = 2.92509072519209200000000000000E-14 " "
relative error = 1.2173934956924980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = -9.886427667958109000E-3 " "
y[1] (numeric) = -9.886427667927368000E-3 " "
absolute error = 3.074103471778500000000000000E-14 " "
relative error = 3.10941785549259900000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 4.2556210052731025000E-3 " "
y[1] (numeric) = 4.255621005305449000E-3 " "
absolute error = 3.234652129480153300000000000000E-14 " "
relative error = 7.6008933254914490000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 1.83972441199501400E-2 " "
y[1] (numeric) = 1.839724411998407400E-2 " "
absolute error = 3.3934660637058300000000000000E-14 " "
relative error = 1.84455130430428130000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 3.253702752554621400E-2 " "
y[1] (numeric) = 3.2537027525581697E-2 " "
absolute error = 3.548550342458156600000000000000E-14 " "
relative error = 1.09061909225482810000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 4.66735572555038170E-2 " "
y[1] (numeric) = 4.66735572555408540E-2 " "
absolute error = 3.703981565905678500000000000000E-14 " "
relative error = 7.93593157176572300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 6.0805419668630400E-2 " "
y[1] (numeric) = 6.08054196686689700E-2 " "
absolute error = 3.856637231791637500000000000000E-14 " "
relative error = 6.34258796799536300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 7.49312015904611800E-2 " "
y[1] (numeric) = 7.49312015905012200E-2 " "
absolute error = 4.00374178255447100000000000000E-14 " "
relative error = 5.343223780711600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 8.90494904545752200E-2 " "
y[1] (numeric) = 8.9049490454616900E-2 " "
absolute error = 4.167499678686681400000000000000E-14 " "
relative error = 4.67998149951520840000000000E-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) = 0.10315887444385152 " "
y[1] (numeric) = 0.10315887444389477 " "
absolute error = 4.32431868091498500000000000000E-14 " "
relative error = 4.191901767277107500000000000E-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) = 0.11725794263165523 " "
y[1] (numeric) = 0.11725794263169373 " "
absolute error = 3.8496983378877303000000000000E-14 " "
relative error = 3.28310240780947900000000000E-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) = 0.13134528512291033 " "
y[1] (numeric) = 0.1313452851229441 " "
absolute error = 3.37785355242203900000000000000E-14 " "
relative error = 2.571735673085722000000000000E-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) = 0.14541949319510716 " "
y[1] (numeric) = 0.14541949319513628 " "
absolute error = 2.91155988207947300000000000000E-14 " "
relative error = 2.002179912821643600000000000E-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) = 0.15947915943916702 " "
y[1] (numeric) = 0.1594791594391914 " "
absolute error = 2.436939539052218600000000000000E-14 " "
relative error = 1.52806143926397080000000000E-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) = 0.17352287790018173 " "
y[1] (numeric) = 0.17352287790020143 " "
absolute error = 1.97064586870965290000000000000E-14 " "
relative error = 1.135669193916469100000000000E-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) = 0.18754924421800845 " "
y[1] (numeric) = 0.18754924421802338 " "
absolute error = 1.493249968120835500000000000000E-14 " "
relative error = 7.961908747470463000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 0.20155685576770377 " "
y[1] (numeric) = 0.20155685576771404 " "
absolute error = 1.026956297778269800000000000000E-14 " "
relative error = 5.095119656767453000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 0.21554431179978573 " "
y[1] (numeric) = 0.21554431179979144 " "
absolute error = 5.717648576819556000000000000000E-15 " "
relative error = 2.652655748174209000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 0.22951021358030754 " "
y[1] (numeric) = 0.22951021358030846 " "
absolute error = 9.1593399531575410000000000000000E-16 " "
relative error = 3.9908201950030480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 0.24345316453072907 " "
y[1] (numeric) = 0.24345316453072532 " "
absolute error = 3.747002708109903300000000000000E-15 " "
relative error = 1.5391061830444805000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 0.2573717703675745 " "
y[1] (numeric) = 0.2573717703675661 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 3.278407330804229000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 0.27126463924185895 " "
y[1] (numeric) = 0.27126463924184585 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 4.829465324780629000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 0.2851303818782722 " "
y[1] (numeric) = 0.28513038187825457 " "
absolute error = 1.76525460915399900000000000000E-14 " "
relative error = 6.191043541293404000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 0.2989676117141056 " "
y[1] (numeric) = 0.29896761171408326 " "
absolute error = 2.231548279496564600000000000000E-14 " "
relative error = 7.464180707408976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 0.31277494503790626 " "
y[1] (numeric) = 0.3127749450378794 " "
absolute error = 2.686739719592879000000000000000E-14 " "
relative error = 8.590009405220305000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 0.3265510011278481 " "
y[1] (numeric) = 0.32655100112781665 " "
absolute error = 3.14193115968919300000000000000E-14 " "
relative error = 9.621563396950342000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 0.34029440238980213 " "
y[1] (numeric) = 0.340294402389766 " "
absolute error = 3.613775945154884500000000000000E-14 " "
relative error = 1.061955741786007600000000000E-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) = 0.3540037744950948 " "
y[1] (numeric) = 0.3540037744950541 " "
absolute error = 4.06896738525119870000000000000E-14 " "
relative error = 1.149413559517733400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 0.3676777465179401 " "
y[1] (numeric) = 0.3676777465178948 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 1.231978269930356200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 0.3813149510725307 " "
y[1] (numeric) = 0.3813149510724809 " "
absolute error = 4.97935026544382700000000000000E-14 " "
relative error = 1.305836619161753000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 0.3949140244497754 " "
y[1] (numeric) = 0.3949140244497211 " "
absolute error = 5.428990590417015000000000000000E-14 " "
relative error = 1.374727220179405600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 0.4084736067536691 " "
y[1] (numeric) = 0.40847360675361016 " "
absolute error = 5.89528426075958100000000000000E-14 " "
relative error = 1.443247290225717300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 0.42199234203728087 " "
y[1] (numeric) = 0.42199234203721736 " "
absolute error = 6.35047570085589500000000000000E-14 " "
relative error = 1.504879370605939300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 0.435468878438348 " "
y[1] (numeric) = 0.43546887843827997 " "
absolute error = 6.80011602582908400000000000000E-14 " "
relative error = 1.561561884793064300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 0.44890186831446083 " "
y[1] (numeric) = 0.4489018683143882 " "
absolute error = 7.26085858104852400000000000000E-14 " "
relative error = 1.61747123225653630000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 0.4622899683778257 " "
y[1] (numeric) = 0.4622899683777487 " "
absolute error = 7.6993966757754610000000000000E-14 " "
relative error = 1.665490753085692700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 0.4756318398295933 " "
y[1] (numeric) = 0.47563183982951185 " "
absolute error = 8.14348588562552300000000000000E-14 " "
relative error = 1.712140610381156500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 0.48892614849373633 " "
y[1] (numeric) = 0.4889261484936504 " "
absolute error = 8.59312621059871200000000000000E-14 " "
relative error = 1.757550958784279000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 0.5021715649504671 " "
y[1] (numeric) = 0.5021715649503767 " "
absolute error = 9.03721542044877400000000000000E-14 " "
relative error = 1.799627069951716700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 0.5153667646691777 " "
y[1] (numeric) = 0.5153667646690829 " "
absolute error = 9.48130463029883700000000000000E-14 " "
relative error = 1.839719842311725300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 0.5285104281408922 " "
y[1] (numeric) = 0.528510428140793 " "
absolute error = 9.925393840148900000000000000E-14 " "
relative error = 1.87799394518341520000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 0.5416012410102164 " "
y[1] (numeric) = 0.541601241010113 " "
absolute error = 1.03472785895064590000000000000E-13 " "
relative error = 1.91049757755471480000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 0.5546378942067726 " "
y[1] (numeric) = 0.5546378942066648 " "
absolute error = 1.0780265569110270000000000000E-13 " "
relative error = 1.943658318645519500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 0.5676190840761046 " "
y[1] (numeric) = 0.5676190840759924 " "
absolute error = 1.12243547789603330000000000000E-13 " "
relative error = 1.97744492633292200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 0.5805435125100433 " "
y[1] (numeric) = 0.5805435125099266 " "
absolute error = 1.16684439888103950000000000000E-13 " "
relative error = 2.009917213330074400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 0.5934098870765157 " "
y[1] (numeric) = 0.5934098870763947 " "
absolute error = 1.20903287381679550000000000000E-13 " "
relative error = 2.037432978700774400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 0.606216921148787 " "
y[1] (numeric) = 0.6062169211486618 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.065814278829426500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = 0.6189633340341223 " "
y[1] (numeric) = 0.618963334033993 " "
absolute error = 1.29340982368830740000000000000E-13 " "
relative error = 2.089638840573073700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 0.6316478511018554 " "
y[1] (numeric) = 0.6316478511017217 " "
absolute error = 1.33670852164868850000000000000E-13 " "
relative error = 2.116224284333296500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 0.6442692039108495 " "
y[1] (numeric) = 0.6442692039107119 " "
absolute error = 1.3766765505351940000000000000E-13 " "
relative error = 2.136803283749212400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 0.656826130336342 " "
y[1] (numeric) = 0.6568261303362001 " "
absolute error = 1.418865025470950000000000000E-13 " "
relative error = 2.160183585790641200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 0.6693173746961538 " "
y[1] (numeric) = 0.6693173746960079 " "
absolute error = 1.45883305435745570000000000000E-13 " "
relative error = 2.179583422617280300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 0.6817416878762588 " "
y[1] (numeric) = 0.6817416878761087 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 2.201745259218559300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 0.6940978274556922 " "
y[1] (numeric) = 0.6940978274555378 " "
absolute error = 1.54321000422896760000000000000E-13 " "
relative error = 2.223332134442502200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 0.7063845578307929 " "
y[1] (numeric) = 0.7063845578306345 " "
absolute error = 1.58428825614009840000000000000E-13 " "
relative error = 2.242812698235113800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 0.7186006503387623 " "
y[1] (numeric) = 0.7186006503385998 " "
absolute error = 1.62536650805122920000000000000E-13 " "
relative error = 2.261849481050427500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 0.7307448833805297 " "
y[1] (numeric) = 0.730744883380363 " "
absolute error = 1.666444759962360000000000000E-13 " "
relative error = 2.280474072227710600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 0.742816042542911 " "
y[1] (numeric) = 0.7428160425427404 " "
absolute error = 1.70641278884886560000000000000E-13 " "
relative error = 2.29722123798947100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 0.7548129207200494 " "
y[1] (numeric) = 0.7548129207198746 " "
absolute error = 1.74749104075999640000000000000E-13 " "
relative error = 2.315131329618718700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 0.7667343182341242 " "
y[1] (numeric) = 0.7667343182339454 " "
absolute error = 1.7874590696465020000000000000E-13 " "
relative error = 2.331262638358515500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 0.7785790429553188 " "
y[1] (numeric) = 0.7785790429551361 " "
absolute error = 1.82631687550838250000000000000E-13 " "
relative error = 2.345705156121433700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 0.7903459104210315 " "
y[1] (numeric) = 0.7903459104208448 " "
absolute error = 1.86739512741951330000000000000E-13 " "
relative error = 2.362756740810764700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 0.8020337439543214 " "
y[1] (numeric) = 0.8020337439541307 " "
absolute error = 1.90625293328139380000000000000E-13 " "
relative error = 2.376773979462342700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 0.813641374781575 " "
y[1] (numeric) = 0.8136413747813805 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 2.39062417353769180000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = 0.8251676421493828 " "
y[1] (numeric) = 0.8251676421491844 " "
absolute error = 1.98396854500515470000000000000E-13 " "
relative error = 2.404321793129632000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = 0.8366113934406127 " "
y[1] (numeric) = 0.8366113934404107 " "
absolute error = 2.0206059048177850000000000000E-13 " "
relative error = 2.415226377097168300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = 0.8479714842896726 " "
y[1] (numeric) = 0.8479714842894667 " "
absolute error = 2.05946371067966540000000000000E-13 " "
relative error = 2.428694536119730000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = 0.859246778696944 " "
y[1] (numeric) = 0.8592467786967342 " "
absolute error = 2.09832151654154600000000000000E-13 " "
relative error = 2.44204758000218600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = 0.8704361491423822 " "
y[1] (numeric) = 0.8704361491421686 " "
absolute error = 2.13606909937880120000000000000E-13 " "
relative error = 2.454021586170810600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = 0.8815384766982671 " "
y[1] (numeric) = 0.8815384766980496 " "
absolute error = 2.17492690524068170000000000000E-13 " "
relative error = 2.4671945272164400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = 0.892552651141095 " "
y[1] (numeric) = 0.892552651140874 " "
absolute error = 2.21045404202868670000000000000E-13 " "
relative error = 2.476553107766476800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = 0.9034775710626003 " "
y[1] (numeric) = 0.9034775710623755 " "
absolute error = 2.2482016248659420000000000000E-13 " "
relative error = 2.488386758978179700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = 0.9143121439798947 " "
y[1] (numeric) = 0.9143121439796661 " "
absolute error = 2.28594920770319730000000000000E-13 " "
relative error = 2.500184671891948500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = 0.9250552864447152 " "
y[1] (numeric) = 0.9250552864444831 " "
absolute error = 2.32147634449120230000000000000E-13 " "
relative error = 2.509554162339185400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = 0.9357059241517681 " "
y[1] (numeric) = 0.9357059241515325 " "
absolute error = 2.3558932582545822000000000000E-13 " "
relative error = 2.517771019126800500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = 0.946262992046158 " "
y[1] (numeric) = 0.9462629920459188 " "
absolute error = 2.39253061806721230000000000000E-13 " "
relative error = 2.52839922746392940000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = 0.9567254344298932 " "
y[1] (numeric) = 0.9567254344296504 " "
absolute error = 2.42805775485521740000000000000E-13 " "
relative error = 2.537883563534696000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = 0.9670922050674539 " "
y[1] (numeric) = 0.9670922050672077 " "
absolute error = 2.4613644455939720000000000000E-13 " "
relative error = 2.545118689507267500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = 0.9773622672904151 " "
y[1] (numeric) = 0.9773622672901655 " "
absolute error = 2.4957813593573520000000000000E-13 " "
relative error = 2.55358882052661800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = 0.9875345941011132 " "
y[1] (numeric) = 0.9875345941008604 " "
absolute error = 2.52797782707148140000000000000E-13 " "
relative error = 2.55988786840680800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = 0.9976081682753438 " "
y[1] (numeric) = 0.9976081682750877 " "
absolute error = 2.5612845178102360000000000000E-13 " "
relative error = 2.56742536725432200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = 1.0075819824640841 " "
y[1] (numeric) = 1.0075819824638246 " "
absolute error = 2.5957014315736160000000000000E-13 " "
relative error = 2.576168963666578000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = 1.017455039294227 " "
y[1] (numeric) = 1.0174550392939643 " "
absolute error = 2.62678767626312040000000000000E-13 " "
relative error = 2.581723589560509000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = 1.0272263514683166 " "
y[1] (numeric) = 1.0272263514680506 " "
absolute error = 2.6600943670018750000000000000E-13 " "
relative error = 2.589589298599610500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = 1.0368949418632785 " "
y[1] (numeric) = 1.0368949418630093 " "
absolute error = 2.69118061169137950000000000000E-13 " "
relative error = 2.595422644125724400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = 1.04645984362813 " "
y[1] (numeric) = 1.0464598436278578 " "
absolute error = 2.7222668563808840000000000000E-13 " "
relative error = 2.601405943053337600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = 1.055920100280666 " "
y[1] (numeric) = 1.0559201002803902 " "
absolute error = 2.7577939931688890000000000000E-13 " "
relative error = 2.61174495346367700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = 1.065274765803104 " "
y[1] (numeric) = 1.0652747658028252 " "
absolute error = 2.7888802378583930000000000000E-13 " "
relative error = 2.617991458528423000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = 1.0745229047366878 " "
y[1] (numeric) = 1.074522904736406 " "
absolute error = 2.81774603649864730000000000000E-13 " "
relative error = 2.62232291566566200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = 1.0836635922752307 " "
y[1] (numeric) = 1.0836635922749454 " "
absolute error = 2.85327317328665230000000000000E-13 " "
relative error = 2.632987943514829600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = 1.0926959143575958 " "
y[1] (numeric) = 1.0926959143573076 " "
absolute error = 2.88213897192690640000000000000E-13 " "
relative error = 2.637640476235639000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = 1.101618967759102 " "
y[1] (numeric) = 1.1016189677588113 " "
absolute error = 2.906563878468660000000000000E-13 " "
relative error = 2.638447560848695000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = 1.1104318601818448 " "
y[1] (numeric) = 1.1104318601815513 " "
absolute error = 2.9354296771089140000000000000E-13 " "
relative error = 2.643502750928100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = 1.1191337103439265 " "
y[1] (numeric) = 1.1191337103436299 " "
absolute error = 2.96651592179841800000000000000E-13 " "
relative error = 2.650725194299404000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = 1.1277236480675819 " "
y[1] (numeric) = 1.1277236480672825 " "
absolute error = 2.9931612743894220000000000000E-13 " "
relative error = 2.65416201878746900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = 1.136200814366197 " "
y[1] (numeric) = 1.136200814365895 " "
absolute error = 3.0198066269804260000000000000E-13 " "
relative error = 2.657810651777216000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = 1.1445643615302064 " "
y[1] (numeric) = 1.1445643615299015 " "
absolute error = 3.048672425620680000000000000E-13 " "
relative error = 2.663609429132327600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = 1.1528134532118628 " "
y[1] (numeric) = 1.1528134532115553 " "
absolute error = 3.07531777821168360000000000000E-13 " "
relative error = 2.667662985406283000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = 1.160947264508873 " "
y[1] (numeric) = 1.1609472645085626 " "
absolute error = 3.10418357685193770000000000000E-13 " "
relative error = 2.673836850087356000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = 1.1689649820468848 " "
y[1] (numeric) = 1.1689649820465722 " "
absolute error = 3.1263880373444410000000000000E-13 " "
relative error = 2.674492465865027600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = 1.1768658040608262 " "
y[1] (numeric) = 1.1768658040605111 " "
absolute error = 3.15081294388619400000000000000E-13 " "
relative error = 2.677291610491339000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = 1.1846489404750797 " "
y[1] (numeric) = 1.1846489404747622 " "
absolute error = 3.17523785042794770000000000000E-13 " "
relative error = 2.680319664283481500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = 1.1923136129824898 " "
y[1] (numeric) = 1.1923136129821694 " "
absolute error = 3.2041036490682020000000000000E-13 " "
relative error = 2.68729939353234300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = 1.1998590551221928 " "
y[1] (numeric) = 1.19985905512187 " "
absolute error = 3.2285285556099550000000000000E-13 " "
relative error = 2.690756503297101500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = 1.2072845123562628 " "
y[1] (numeric) = 1.2072845123559375 " "
absolute error = 3.25295346215170870000000000000E-13 " "
relative error = 2.694438161724533300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = 1.214589242145164 " "
y[1] (numeric) = 1.2145892421448363 " "
absolute error = 3.2773783686934620000000000000E-13 " "
relative error = 2.698342991170475000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = 1.2217725140220053 " "
y[1] (numeric) = 1.2217725140216746 " "
absolute error = 3.3062441673337160000000000000E-13 " "
relative error = 2.706104556608292000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = 1.2288336096655845 " "
y[1] (numeric) = 1.2288336096652515 " "
absolute error = 3.33066907387546960000000000000E-13 " "
relative error = 2.710431296538088300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = 1.2357718229722214 " "
y[1] (numeric) = 1.2357718229718864 " "
absolute error = 3.35065308831872240000000000000E-13 " "
relative error = 2.71138492238792600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; "
Iterations = 4900
"Total Elapsed Time "= 1 Minutes 52 Seconds
"Elapsed Time(since restart) "= 1 Minutes 52 Seconds
"Time to Timeout "= 1 Minutes 7 Seconds
Percent Done = 100.0204081632654 "%"
(%o256) temp/diffeq.sub_sin_cos.max