(%i1) batch("temp/diffeq.mult_lin_sin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.mult_lin_sin.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,30,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[30],convfloat)
(%i173) completearray(array_norms,[30],convfloat)
(%i174) completearray(array_fact_1,[30],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[30],convfloat)
(%i184) completearray(array_x,[30],convfloat)
(%i185) completearray(array_tmp0,[30],convfloat)
(%i186) completearray(array_tmp1,[30],convfloat)
(%i187) completearray(array_tmp2,[30],convfloat)
(%i188) completearray(array_tmp3_g,[30],convfloat)
(%i189) completearray(array_tmp3,[30],convfloat)
(%i190) completearray(array_tmp4,[30],convfloat)
(%i191) completearray(array_tmp5,[30],convfloat)
(%i192) completearray(array_m1,[30],convfloat)
(%i193) completearray(array_y_higher,[2,30],convfloat)
(%i194) completearray(array_y_higher_work,[2,30],convfloat)
(%i195) completearray(array_y_higher_work2,[2,30],convfloat)
(%i196) completearray(array_y_set_initial,[2,30],convfloat)
(%i197) completearray(array_given_rad_poles,[2,3],convfloat)
(%i198) completearray(array_given_ord_poles,[2,3],convfloat)
(%i199) completearray(array_rad_test_poles,[2,4],convfloat)
(%i200) completearray(array_ord_test_poles,[2,4],convfloat)
(%i201) completearray(array_fact_2,[30,30],convfloat)
(%i202) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i203) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i204) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i205) 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))
(%i206) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i207) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i208) 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)
(%i209) 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)
(%i210) 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)
(%i211) 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)
(%i212) 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)
(%i213) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i214) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i215) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i216) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i217) log_revs(file,revs):=printf(file,revs)
(%i218) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i219) 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)
(%i220) logstart(file):=(printf(file,""),0)
(%i221) logend(file):=(printf(file,"
~%"),0)
(%i222) 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)
(%i223) 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)
(%i224) 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)
(%i225) 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)
(%i226) 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)
(%i227) c(in_val):=(ret:in_val,ret)
(%i228) 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)
(%i229) 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)
(%i230) 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)
(%i231) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i232) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i233) 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)
(%i234) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i235) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i236) 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)
(%i237) log10(x):=log(x)/glob_log_10
(%i238) c(x):=x
(%i239) 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
(%i240) 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)
(%i241) exact_soln_y(x):=block(
-c(0.3)*cos(c(x))-c(0.2)*cos(c(x))*c(x)+c(0.2)*sin(c(x)))
(%o241) exact_soln_y(x) := block(- c(0.3) cos(c(x)) - c(0.2) cos(c(x)) c(x)
+ c(0.2) sin(c(x)))
(%i242) 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)
(%i243) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i244) 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)
(%i245) 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)
(%i246) 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))
(%i247) 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))
(%i248) 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)
(%i249) 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)
(%i250) 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)
(%i251) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D2[1]*array_x[1],
array_tmp2[1]:array_const_0D3[1]+array_tmp1[1],
array_tmp3[1]:sin(array_x[1]),
array_tmp3_g[1]:cos(array_x[1]),
array_tmp4[1]:array_tmp2[1]*array_tmp3[1],
array_tmp5[1]:array_tmp4[1]+array_const_0D0[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_const_0D2[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:array_tmp3_g[1]*array_x[2]/c(1),
array_tmp3_g[2]:neg(array_tmp3[1])*array_x[2]/c(1),
array_tmp4[2]:array_tmp3[2]*array_tmp2[1]
+array_tmp3[1]*array_tmp2[2],
array_tmp5[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_tmp3[3]:array_tmp3_g[2]*array_x[2]/c(2),
array_tmp3_g[3]:neg(array_tmp3[2])*array_x[2]/c(2),
array_tmp4[3]:array_tmp3[3]*array_tmp2[1]
+array_tmp3[2]*array_tmp2[2],
array_tmp5[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_tmp3[4]:array_tmp3_g[3]*array_x[2]/c(3),
array_tmp3_g[4]:neg(array_tmp3[3])*array_x[2]/c(3),
array_tmp4[4]:array_tmp3[4]*array_tmp2[1]
+array_tmp3[3]*array_tmp2[2],
array_tmp5[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_tmp3[5]:array_tmp3_g[4]*array_x[2]/c(4),
array_tmp3_g[5]:neg(array_tmp3[4])*array_x[2]/c(4),
array_tmp4[5]:array_tmp3[5]*array_tmp2[1]
+array_tmp3[4]*array_tmp2[2],
array_tmp5[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_tmp3[kkk]
:array_tmp3_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp3_g[kkk]
:neg(array_tmp3[kkk-1])*array_x[2]/c(kkk-1),
array_tmp4[kkk]
:array_tmp3[kkk]*array_tmp2[1]
+array_tmp3[kkk-1]*array_tmp2[2],
array_tmp5[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)
(%i252) exact_soln_y(x):=block(
-c(0.3)*cos(c(x))-c(0.2)*cos(c(x))*c(x)+c(0.2)*sin(c(x)))
(%o252) exact_soln_y(x) := block(- c(0.3) cos(c(x)) - c(0.2) cos(c(x)) c(x)
+ c(0.2) sin(c(x)))
(%i253) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:30,
glob_html_log:true,term:1,
while term <= 30 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 30 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3_g[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 30 do
(term:1,
while term <= 30 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3_g),
zero_ats_ar(array_tmp3),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_const_0D2),array_const_0D2[1]:c(0.2),
zero_ats_ar(array_const_0D3),array_const_0D3[1]:c(0.3),
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,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/mult_lin_sinpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(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,""),
omniout_str(always,
" (c(0.2) * sin(c(x)) - c(0.2) * cos(c(x)) * c(x) - c(0.3) * cos(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
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 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T22:08:14-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"mult_lin_sin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"mult_lin_sin diffeq.max"),
logitem_str(html_log_file,
"mult_lin_sin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i254) main():=(glob_iolevel:2,compile(all),main_prog())
(%i255) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D3 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp3_g in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_const_0D0 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/mult_lin_sinpostode.ode#################"
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* 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("
""
" (c(0.2) * sin(c(x)) - c(0.2) * cos(c(x)) * c(x) - c(0.3) * cos(c(x))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = -0.29843464955960264 " "
y[1] (numeric) = -0.29843464955960264 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = -0.2980982033746214 " "
y[1] (numeric) = -0.29809820337462145 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.862176645241189500000000000000E-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) = -0.2977275565588688 " "
y[1] (numeric) = -0.2977275565588688 " "
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) = -0.2973223488270819 " "
y[1] (numeric) = -0.2973223488270819 " "
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] = 0.14000000000000004 " "
y[1] (closed_form) = -0.2968822238288977 " "
y[1] (numeric) = -0.29688222382889773 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.869803806887764500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (closed_form) = -0.2964068292241741 " "
y[1] (numeric) = -0.29640682922417416 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.872802707567660000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (closed_form) = -0.2958958167578589 " "
y[1] (numeric) = -0.29589581675785903 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.75207408063388700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (closed_form) = -0.295348842334394 " "
y[1] (numeric) = -0.2953488423343942 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 5.638534161079402000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (closed_form) = -0.29476556609164395 " "
y[1] (numeric) = -0.29476556609164406 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.76646105359532800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = -0.29414565247433727 " "
y[1] (numeric) = -0.2941456524743373 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.887199445727007500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = -0.29348877030700987 " "
y[1] (numeric) = -0.29348877030701 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.78284669448778300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = -0.2927945928664388 " "
y[1] (numeric) = -0.2927945928664389 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.791815326082869600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = -0.29206279795355444 " "
y[1] (numeric) = -0.29206279795355455 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.80131612928569800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = -0.291293067964822 " "
y[1] (numeric) = -0.2912930679648221 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.81136095129882200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = -0.29048508996307937 " "
y[1] (numeric) = -0.2904850899630795 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.82196216943962900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = -0.28963855574782105 " "
y[1] (numeric) = -0.2896385557478212 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 5.74969907800426900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = -0.2887531619249176 " "
y[1] (numeric) = -0.28875316192491773 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.844886120810132600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = -0.287828609975759 " "
y[1] (numeric) = -0.28782860997575915 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 5.78585477335970800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (closed_form) = -0.2868646063258117 " "
y[1] (numeric) = -0.28686460632581184 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 5.805298040310700000000000000E-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) = -0.28586086241257846 " "
y[1] (numeric) = -0.2858608624125787 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 7.76757626248807300000000000000E-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) = -0.28481709475295025 " "
y[1] (numeric) = -0.28481709475295036 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.898021028506598600000000000000E-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) = -0.2837330250099395 " "
y[1] (numeric) = -0.28373302500993963 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.912914348219647700000000000000E-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) = -0.2826083800587849 " "
y[1] (numeric) = -0.282608380058785 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 3.9284858587499100000000000000E-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) = -0.28144289205241596 " "
y[1] (numeric) = -0.281442892052416 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.972377089591568800000000000000E-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) = -0.2802362984862685 " "
y[1] (numeric) = -0.2802362984862686 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.980869413816421000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (closed_form) = -0.2789883422624399 " "
y[1] (numeric) = -0.27898834226243996 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.989730136431269400000000000000E-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) = -0.2776987717531737 " "
y[1] (numeric) = -0.27769877175317376 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.998969994746597800000000000000E-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) = -0.27636734086366443 " "
y[1] (numeric) = -0.2763673408636645 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.008600258546547600000000000000E-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) = -0.27499380909417126 " "
y[1] (numeric) = -0.27499380909417137 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.03726552347570200000000000000E-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) = -0.273577941601432 " "
y[1] (numeric) = -0.2735779416014321 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.058159872562420000000000000000E-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) = -0.27211950925936623 " "
y[1] (numeric) = -0.27211950925936623 " "
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] = 0.41000000000000025 " "
y[1] (closed_form) = -0.2706182887190585 " "
y[1] (numeric) = -0.2706182887190586 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.051271238688769600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (closed_form) = -0.26907406246801224 " "
y[1] (numeric) = -0.26907406246801235 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.12608712427323170000000000000E-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) = -0.26748661888866343 " "
y[1] (numeric) = -0.2674866188886635 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.07528703536244400000000000000E-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) = -0.2658557523161458 " "
y[1] (numeric) = -0.26585575231614583 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.088017684313485700000000000000E-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) = -0.2641812630952979 " "
y[1] (numeric) = -0.2641812630952978 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.10125239696629600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = -0.26246295763690186 " "
y[1] (numeric) = -0.2624629576369018 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.11500897997398200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = -0.26070064847314595 " "
y[1] (numeric) = -0.26070064847314584 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.25861243969831400000000000000E-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) = -0.25889415431229984 " "
y[1] (numeric) = -0.25889415431229984 " "
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) = -0.2570433000925967 " "
y[1] (numeric) = -0.2570433000925966 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.159603117889500300000000000000E-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) = -0.25514791703530837 " "
y[1] (numeric) = -0.2551479170353083 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.175645871472114400000000000000E-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) = -0.25320784269701047 " "
y[1] (numeric) = -0.25320784269701035 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.38463126892026800000000000000E-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) = -0.2512229210210231 " "
y[1] (numeric) = -0.25122292102102306 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.20963720211709820000000000000E-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) = -0.24919300238802347 " "
y[1] (numeric) = -0.24919300238802342 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.22763683969023680000000000000E-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) = -0.24711794366581752 " "
y[1] (numeric) = -0.24711794366581746 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.24634239051157900000000000000E-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) = -0.24499760825826544 " "
y[1] (numeric) = -0.24499760825826536 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.39867509070173100000000000000E-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) = -0.24283186615335062 " "
y[1] (numeric) = -0.2428318661533506 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.142995606602183200000000000000E-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) = -0.2406205939703853 " "
y[1] (numeric) = -0.24062059397038524 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.306999177222957600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = -0.23836367500634295 " "
y[1] (numeric) = -0.23836367500634287 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.49326409926642500000000000000E-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) = -0.23606099928131147 " "
y[1] (numeric) = -0.23606099928131138 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.52733942075957400000000000000E-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) = -0.23371246358305772 " "
y[1] (numeric) = -0.23371246358305767 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.3751900253933200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = -0.231317971510696 " "
y[1] (numeric) = -0.23131797151069594 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.39977684694036100000000000000E-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) = -0.22887743351745327 " "
y[1] (numeric) = -0.22887743351745318 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.63804878301980600000000000000E-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) = -0.2263907669525227 " "
y[1] (numeric) = -0.22639076695252258 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 4.90401194169718900000000000000E-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) = -0.2238578961019987 " "
y[1] (numeric) = -0.2238578961019986 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 3.719624292767723700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = -0.221278752228886 " "
y[1] (numeric) = -0.22127875222888588 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.01730515669559500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = -0.2186532736121748 " "
y[1] (numeric) = -0.21865327361217476 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.269387608843166300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = -0.21598140558497653 " "
y[1] (numeric) = -0.21598140558497647 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.570181959919568500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = -0.21326310057171072 " "
y[1] (numeric) = -0.2132631005717107 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.301471072174343000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = -0.210498318124339 " "
y[1] (numeric) = -0.2104983181243389 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 5.274260785159148000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = -0.20768702495763652 " "
y[1] (numeric) = -0.20768702495763647 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.672827117754749000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = -0.20482919498349714 " "
y[1] (numeric) = -0.20482919498349708 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.71011909389822560000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = -0.20192480934426257 " "
y[1] (numeric) = -0.20192480934426252 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 2.749100093818417400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = -0.19897385644507243 " "
y[1] (numeric) = -0.1989738564450724 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.394935802698831500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = -0.19597633198522618 " "
y[1] (numeric) = -0.19597633198522615 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.416271818870519800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = -0.19293223898855236 " "
y[1] (numeric) = -0.19293223898855236 " "
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] = 0.7600000000000006 " "
y[1] (closed_form) = -0.18984158783277869 " "
y[1] (numeric) = -0.18984158783277869 " "
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] = 0.7700000000000006 " "
y[1] (closed_form) = -0.18670439627789676 " "
y[1] (numeric) = -0.18670439627789678 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.48660535953939900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = -0.18352068949351624 " "
y[1] (numeric) = -0.18352068949351627 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.512394907202520800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = -0.18029050008520234 " "
y[1] (numeric) = -0.18029050008520245 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 6.15796741425911800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = -0.1770138681197913 " "
y[1] (numeric) = -0.17701386811979145 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 7.83994381639233300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = -0.17369084114967845 " "
y[1] (numeric) = -0.17369084114967853 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.793961863258608400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = -0.1703214742360733 " "
y[1] (numeric) = -0.17032147423607338 " "
absolute error = 8.32667268468867400000000000000000E-17 " "
relative error = 4.88879791701868850000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = -0.16690582997121767 " "
y[1] (numeric) = -0.1669058299712178 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 8.31474119879912700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = -0.1634439784995601 " "
y[1] (numeric) = -0.16344397849956022 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 6.79268232954904900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = -0.1599359975378828 " "
y[1] (numeric) = -0.15993599753788296 " "
absolute error = 1.66533453693773480000000000000000E-16 " "
relative error = 1.04125060184983060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = -0.15638197239437684 " "
y[1] (numeric) = -0.15638197239437698 " "
absolute error = 1.38777878078144570000000000000000E-16 " "
relative error = 8.87428876572570400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = -0.15278199598665926 " "
y[1] (numeric) = -0.15278199598665948 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.4533427416697708000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = -0.14913616885873004 " "
y[1] (numeric) = -0.14913616885873027 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.48887159046819930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = -0.14544459919686206 " "
y[1] (numeric) = -0.14544459919686228 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.52666105273864200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = -0.14170740284442201 " "
y[1] (numeric) = -0.14170740284442224 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.56692311388142550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = -0.13792470331561682 " "
y[1] (numeric) = -0.13792470331561701 " "
absolute error = 1.9428902930940240000000000000000E-16 " "
relative error = 1.40866012134755550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = -0.1340966318081625 " "
y[1] (numeric) = -0.13409663180816278 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 2.06981899853650340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = -0.13022332721487123 " "
y[1] (numeric) = -0.13022332721487148 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.91824449492435900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = -0.1263049361341528 " "
y[1] (numeric) = -0.12630493613415306 " "
absolute error = 2.4980018054066022000000000000000E-16 " "
relative error = 1.97775469578907740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = -0.12234161287942787 " "
y[1] (numeric) = -0.12234161287942813 " "
absolute error = 2.6367796834847470000000000000000E-16 " "
relative error = 2.15525986737103880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = -0.1183335194874487 " "
y[1] (numeric) = -0.11833351948744898 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 2.34553791147679550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = -0.1142808257255247 " "
y[1] (numeric) = -0.11428082572552498 " "
absolute error = 2.77555756156289140000000000000000E-16 " "
relative error = 2.42871675448786050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = -0.11018370909764934 " "
y[1] (numeric) = -0.11018370909764963 " "
absolute error = 2.9143354396410360000000000000000E-16 " "
relative error = 2.644978521333160000000000000E-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) = -0.10604235484952622 " "
y[1] (numeric) = -0.10604235484952644 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.0939237462249110000000000000E-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) = -0.10185695597249028 " "
y[1] (numeric) = -0.1018569559724905 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.17996505790926550000000000000E-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) = -9.76277132063235600E-2 " "
y[1] (numeric) = -9.76277132063233500E-2 " "
absolute error = 2.08166817117216850000000000000000E-16 " "
relative error = 2.13225128685830380000000000000E-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) = -9.33548350409594500E-2 " "
y[1] (numeric) = -9.33548350409587500E-2 " "
absolute error = 7.0776717819853730000000000000000E-16 " "
relative error = 7.581473181201640000000000000E-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) = -8.90385377170778300E-2 " "
y[1] (numeric) = -8.9038537717076700E-2 " "
absolute error = 1.124100812432971000000000000000E-15 " "
relative error = 1.2624879532555100000000000000E-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) = -8.46790452255853900E-2 " "
y[1] (numeric) = -8.46790452255837400E-2 " "
absolute error = 1.6514567491299204000000000000000E-15 " "
relative error = 1.9502543335608372000000000000E-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) = -8.0276589305979500E-2 " "
y[1] (numeric) = -8.02765893059773900E-2 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 2.6276947800405300000000000000E-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) = -7.58314094435954800E-2 " "
y[1] (numeric) = -7.58314094435928900E-2 " "
absolute error = 2.5951463200613034000000000000000E-15 " "
relative error = 3.4222577941026020000000000000E-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) = -7.13437528657333800E-2 " "
y[1] (numeric) = -7.13437528657302600E-2 " "
absolute error = 3.1225022567582530000000000000000E-15 " "
relative error = 4.376700315491814000000000000E-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) = -6.68138745366640400E-2 " "
y[1] (numeric) = -6.68138745366604300E-2 " "
absolute error = 3.608224830031759000000000000000E-15 " "
relative error = 5.4004124967363620000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = -6.22420371515126200E-2 " "
y[1] (numeric) = -6.224203715150851000E-2 " "
absolute error = 4.107825191113079000000000000000E-15 " "
relative error = 6.599760192799617000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = -5.76285111290179500E-2 " "
y[1] (numeric) = -5.76285111290133300E-2 " "
absolute error = 4.614364446098307000000000000000E-15 " "
relative error = 8.007085999094666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = -5.29735746031668200E-2 " "
y[1] (numeric) = -5.29735746031616400E-2 " "
absolute error = 5.176414852314792000000000000000E-15 " "
relative error = 9.771692567647382000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = -4.82775134137020800E-2 " "
y[1] (numeric) = -4.82775134136964160E-2 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 1.172831205507215600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = -4.354062109550406000E-2 " "
y[1] (numeric) = -4.354062109549785600E-2 " "
absolute error = 6.2103100439969690000000000000000E-15 " "
relative error = 1.42632555249383800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = -3.8763198866843496E-2 " "
y[1] (numeric) = -3.87631988668367700E-2 " "
absolute error = 6.7307270867900120000000000000000E-15 " "
relative error = 1.736370393452540000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = -3.39455556165068200E-2 " "
y[1] (numeric) = -3.39455556164995600E-2 " "
absolute error = 7.258083023486961000000000000000E-15 " "
relative error = 2.138154138787331500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = -2.908800788979218300E-2 " "
y[1] (numeric) = -2.90880078897844200E-2 " "
absolute error = 7.764622278472189000000000000000E-15 " "
relative error = 2.669355119776703000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = -2.419087987337667500E-2 " "
y[1] (numeric) = -2.41908798733683600E-2 " "
absolute error = 8.316264343832813000000000000000E-15 " "
relative error = 3.43776844305084400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = -1.925450337905404400E-2 " "
y[1] (numeric) = -1.925450337904518500E-2 " "
absolute error = 8.86096751528953100000000000000E-15 " "
relative error = 4.60202340244667600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = -1.42792178263434900E-2 " "
y[1] (numeric) = -1.427921782633408000E-2 " "
absolute error = 9.409140133698202000000000000000E-15 " "
relative error = 6.58939463500545200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = -9.2653702239691990E-3 " "
y[1] (numeric) = -9.265370223959244000E-3 " "
absolute error = 9.955578028630896000000000000000E-15 " "
relative error = 1.07449327851747920000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = -4.213315150211255400E-3 " "
y[1] (numeric) = -4.213315150200722000E-3 " "
absolute error = 1.053324094613117300000000000000E-14 " "
relative error = 2.49998886164568950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = 8.7658526787191830000E-4 " "
y[1] (numeric) = 8.7658526788298570000E-4 " "
absolute error = 1.10674273565147810000000000000E-14 " "
relative error = 1.262561414405597000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = 6.003961376348412000E-3 " "
y[1] (numeric) = 6.0039613763600430000E-3 " "
absolute error = 1.162958618294851500000000000000E-14 " "
relative error = 1.93698550906095030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = 1.116843601744507700E-2 " "
y[1] (numeric) = 1.116843601745728700E-2 " "
absolute error = 1.220898382392476800000000000000E-14 " "
relative error = 1.0931686231495939000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = 1.636962455370548400E-2 " "
y[1] (numeric) = 1.636962455371824300E-2 " "
absolute error = 1.276062588928539300000000000000E-14 " "
relative error = 7.79530761223039400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = 2.160713489327277500E-2 " "
y[1] (numeric) = 2.16071348932861100E-2 " "
absolute error = 1.33330846363577400000000000000E-14 " "
relative error = 6.17068607301049300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = 2.6880567516296500E-2 " "
y[1] (numeric) = 2.68805675163104300E-2 " "
absolute error = 1.392982951209376000000000000000E-14 " "
relative error = 5.18211883125187700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = 3.21895155024616600E-2 " "
y[1] (numeric) = 3.218951550247619600E-2 " "
absolute error = 1.453698272868564300000000000000E-14 " "
relative error = 4.5160613640096400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = 3.75335645596386300E-2 " "
y[1] (numeric) = 3.753356455965372600E-2 " "
absolute error = 1.509209424099822200000000000000E-14 " "
relative error = 4.02095948468144300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = 4.29122930536521730E-2 " "
y[1] (numeric) = 4.29122930536678900E-2 " "
absolute error = 1.571659469234987200000000000000E-14 " "
relative error = 3.66249239412580600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = 4.832527203916830000E-2 " "
y[1] (numeric) = 4.83252720391845800E-2 " "
absolute error = 1.628558399247026500000000000000E-14 " "
relative error = 3.36999323651413200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = 5.37720652916958300E-2 " "
y[1] (numeric) = 5.37720652917127200E-2 " "
absolute error = 1.688926776211019400000000000000E-14 " "
relative error = 3.14089995809003300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = 5.925222934070198000E-2 " "
y[1] (numeric) = 5.92522293407194800E-2 " "
absolute error = 1.749295153175012300000000000000E-14 " "
relative error = 2.95228580028021600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = 6.47653135038385600E-2 " "
y[1] (numeric) = 6.47653135038566800E-2 " "
absolute error = 1.81243908770056800000000000000E-14 " "
relative error = 2.798471882010032000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = 7.03108599222770400E-2 " "
y[1] (numeric) = 7.03108599222957900E-2 " "
absolute error = 1.87488913283573300000000000000E-14 " "
relative error = 2.66657118816107700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = 7.58884035971495700E-2 " "
y[1] (numeric) = 7.5888403597168910E-2 " "
absolute error = 1.933175841628553800000000000000E-14 " "
relative error = 2.54739294805928100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = 8.14974724270934300E-2 " "
y[1] (numeric) = 8.14974724271133600E-2 " "
absolute error = 1.99285032920215600000000000000E-14 " "
relative error = 2.445290964066319800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = 8.71375872468960800E-2 " "
y[1] (numeric) = 8.71375872469166300E-2 " "
absolute error = 2.05530037433732100000000000000E-14 " "
relative error = 2.358684052742730200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = 9.28082618672375800E-2 " "
y[1] (numeric) = 9.28082618672587600E-2 " "
absolute error = 2.116362640691704700000000000000E-14 " "
relative error = 2.280360172803543900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = 9.85090031155275200E-2 " "
y[1] (numeric) = 9.85090031155493300E-2 " "
absolute error = 2.181588243388432600000000000000E-14 " "
relative error = 2.214607979364029400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = 0.10423931087783275 " "
y[1] (numeric) = 0.10423931087785523 " "
absolute error = 2.24820162486594200000000000000E-14 " "
relative error = 2.156769462435153800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = 0.10999867814189315 " "
y[1] (numeric) = 0.10999867814191627 " "
absolute error = 2.312039448781888500000000000000E-14 " "
relative error = 2.10187930240349400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = 0.1157865910412208 " "
y[1] (numeric) = 0.11578659104124454 " "
absolute error = 2.374489493917053600000000000000E-14 " "
relative error = 2.050746526488304300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = 0.1216025289002799 " "
y[1] (numeric) = 0.12160252890030429 " "
absolute error = 2.439715096613781500000000000000E-14 " "
relative error = 2.006302926984741300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = 0.12744596428074279 " "
y[1] (numeric) = 0.12744596428076785 " "
absolute error = 2.50632847809129100000000000000E-14 " "
relative error = 1.966581281907252800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = 0.13331636302881839 " "
y[1] (numeric) = 0.13331636302884406 " "
absolute error = 2.567390744445674500000000000000E-14 " "
relative error = 1.925788167421499000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = 0.13921318432364854 " "
y[1] (numeric) = 0.13921318432367488 " "
absolute error = 2.63400412592318400000000000000E-14 " "
relative error = 1.892065136445369200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = 0.1451358807267685 " "
y[1] (numeric) = 0.14513588072679542 " "
absolute error = 2.692290834716004600000000000000E-14 " "
relative error = 1.855013950536798500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = 0.15108389823262616 " "
y[1] (numeric) = 0.15108389823265372 " "
absolute error = 2.75612865863195100000000000000E-14 " "
relative error = 1.824237189318677600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = 0.15705667632015657 " "
y[1] (numeric) = 0.15705667632018477 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 1.795508824342785800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = 0.16305364800540598 " "
y[1] (numeric) = 0.16305364800543481 " "
absolute error = 2.88380430646384400000000000000E-14 " "
relative error = 1.76862299110795300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = 0.16907423989520062 " "
y[1] (numeric) = 0.16907423989523016 " "
absolute error = 2.953193245502916400000000000000E-14 " "
relative error = 1.746684324787401400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = 0.17511787224185607 " "
y[1] (numeric) = 0.17511787224188624 " "
absolute error = 3.01703106941886300000000000000E-14 " "
relative error = 1.722857313645307400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = 0.18118395899892065 " "
y[1] (numeric) = 0.18118395899895148 " "
absolute error = 3.08364445089637230000000000000E-14 " "
relative error = 1.701941202705887800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = 0.18727190787794848 " "
y[1] (numeric) = 0.18727190787797995 " "
absolute error = 3.14748227481231900000000000000E-14 " "
relative error = 1.680701772346785100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = 0.19338112040629626 " "
y[1] (numeric) = 0.1933811204063284 " "
absolute error = 3.21409565628982800000000000000E-14 " "
relative error = 1.66205245348510300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = 0.19951099198593858 " "
y[1] (numeric) = 0.19951099198597136 " "
absolute error = 3.27793348020577470000000000000E-14 " "
relative error = 1.642983901577112800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = 0.20566091195329497 " "
y[1] (numeric) = 0.20566091195332856 " "
absolute error = 3.358424649491098500000000000000E-14 " "
relative error = 1.632991226963822800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = 0.21183026364006444 " "
y[1] (numeric) = 0.21183026364009871 " "
absolute error = 3.42781358853017100000000000000E-14 " "
relative error = 1.618188794002828300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = 0.2180184244350595 " "
y[1] (numeric) = 0.21801842443509442 " "
absolute error = 3.491651412446117300000000000000E-14 " "
relative error = 1.601539604505382300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = 0.22422476584703507 " "
y[1] (numeric) = 0.22422476584707063 " "
absolute error = 3.55548923636206400000000000000E-14 " "
relative error = 1.585680878261056800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = 0.23044865356850502 " "
y[1] (numeric) = 0.2304486535685413 " "
absolute error = 3.62765373296269900000000000000E-14 " "
relative error = 1.57417007076776580000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = 0.2366894475405404 " "
y[1] (numeric) = 0.2366894475405773 " "
absolute error = 3.691491556878645500000000000000E-14 " "
relative error = 1.559635038755313700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = 0.24294650201854195 " "
y[1] (numeric) = 0.2429465020185796 " "
absolute error = 3.763656053479280700000000000000E-14 " "
relative error = 1.549170711332997200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = 0.2492191656389816 " "
y[1] (numeric) = 0.24921916563901997 " "
absolute error = 3.83582055007991600000000000000E-14 " "
relative error = 1.53913545944394900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = 0.25550678148710415 " "
y[1] (numeric) = 0.25550678148714323 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.529503453464225700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = 0.26180868716558353 " "
y[1] (numeric) = 0.2618086871656233 " "
absolute error = 3.974598428158060400000000000000E-14 " "
relative error = 1.51813084248204700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = 0.26812421486412635 " "
y[1] (numeric) = 0.2681242148641669 " "
absolute error = 4.052314039881821400000000000000E-14 " "
relative error = 1.51135698129143510000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = 0.2744526914300146 " "
y[1] (numeric) = 0.27445269143005596 " "
absolute error = 4.13558076672870800000000000000E-14 " "
relative error = 1.506846496997563700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = 0.280793438439581 " "
y[1] (numeric) = 0.2807934384396231 " "
absolute error = 4.21329637845246900000000000000E-14 " "
relative error = 1.500496735916090300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = 0.2871457722706087 " "
y[1] (numeric) = 0.28714577227065147 " "
absolute error = 4.274358644806852700000000000000E-14 " "
relative error = 1.488567500404867000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = 0.2935090041756484 " "
y[1] (numeric) = 0.29350900417569187 " "
absolute error = 4.34652314140748800000000000000E-14 " "
relative error = 1.480882385061802800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = 0.29988244035624423 " "
y[1] (numeric) = 0.29988244035628836 " "
absolute error = 4.41313652288499700000000000000E-14 " "
relative error = 1.47162218556125800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = 0.306265382038061 " "
y[1] (numeric) = 0.3062653820381058 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.46451452973167700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 0.31265712554690483 " "
y[1] (numeric) = 0.31265712554695035 " "
absolute error = 4.55191440096314200000000000000E-14 " "
relative error = 1.45588058900012580000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 0.31905696238562836 " "
y[1] (numeric) = 0.31905696238567455 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 1.447555868365118200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 0.32546417931191246 " "
y[1] (numeric) = 0.3254641793119593 " "
absolute error = 4.685141163918160600000000000000E-14 " "
relative error = 1.439525902304628300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 0.33187805841691637 " "
y[1] (numeric) = 0.331878058416964 " "
absolute error = 4.762856775641921600000000000000E-14 " "
relative error = 1.435122526135385600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 0.3382978772047873 " "
y[1] (numeric) = 0.33829787720483556 " "
absolute error = 4.82391904199630500000000000000E-14 " "
relative error = 1.425938312665250300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 0.3447229086730203 " "
y[1] (numeric) = 0.3447229086730693 " "
absolute error = 4.90163465372006600000000000000E-14 " "
relative error = 1.42190569016386700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 0.3511524213936607 " "
y[1] (numeric) = 0.3511524213937105 " "
absolute error = 4.97935026544382700000000000000E-14 " "
relative error = 1.418002543078496500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 0.3575856795953394 " "
y[1] (numeric) = 0.3575856795953898 " "
absolute error = 5.04041253179821100000000000000E-14 " "
relative error = 1.40956778176972200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 0.3640219432461312 " "
y[1] (numeric) = 0.36402194324618237 " "
absolute error = 5.118128143521972000000000000000E-14 " "
relative error = 1.405994401843347300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 0.37046046813722927 " "
y[1] (numeric) = 0.37046046813728123 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.402536627287595300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 0.37690050596742375 " "
y[1] (numeric) = 0.37690050596747626 " "
absolute error = 5.251354906476990000000000000000E-14 " "
relative error = 1.39330004161121400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 0.3833413044283762 " "
y[1] (numeric) = 0.38334130442842945 " "
absolute error = 5.323519403077626000000000000000E-14 " "
relative error = 1.388715314937390700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 0.3897821072906814 " "
y[1] (numeric) = 0.3897821072907353 " "
absolute error = 5.39013278455513500000000000000E-14 " "
relative error = 1.382857931068504400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 0.3962221544907044 " "
y[1] (numeric) = 0.3962221544907591 " "
absolute error = 5.46784839627889600000000000000E-14 " "
relative error = 1.37999562475428800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 0.4026606822181857 " "
y[1] (numeric) = 0.4026606822182411 " "
absolute error = 5.54001289287953100000000000000E-14 " "
relative error = 1.375851464404369300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 0.4090969230046019 " "
y[1] (numeric) = 0.40909692300465805 " "
absolute error = 5.61772850460329200000000000000E-14 " "
relative error = 1.373202336342212000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 0.4155301058122745 " "
y[1] (numeric) = 0.41553010581233146 " "
absolute error = 5.69544411632705300000000000000E-14 " "
relative error = 1.37064536038698100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 0.42195945612421465 " "
y[1] (numeric) = 0.4219594561242724 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 1.36817877743006100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 0.42838419603469435 " "
y[1] (numeric) = 0.4283841960347528 " "
absolute error = 5.84532422465144900000000000000E-14 " "
relative error = 1.364505105173871300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 0.4348035443405339 " "
y[1] (numeric) = 0.4348035443405932 " "
absolute error = 5.92859095149833600000000000000E-14 " "
relative error = 1.363510263121296400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 0.44121671663309525 " "
y[1] (numeric) = 0.44121671663315515 " "
absolute error = 5.9896532178527200000000000000E-14 " "
relative error = 1.35753088948204200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 0.4476229253909693 " "
y[1] (numeric) = 0.44762292539103 " "
absolute error = 6.0673688295764800000000000000E-14 " "
relative error = 1.35546427258546510000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = 0.45402138007334913 " "
y[1] (numeric) = 0.4540213800734105 " "
absolute error = 6.1339822110539900000000000000E-14 " "
relative error = 1.351033779524439500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = 0.460411287214075 " "
y[1] (numeric) = 0.46041128721413715 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 1.350368488036236300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = 0.4667918505163433 " "
y[1] (numeric) = 0.4667918505164062 " "
absolute error = 6.28941343450151200000000000000E-14 " "
relative error = 1.347370016752532700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = 0.4731622709480664 " "
y[1] (numeric) = 0.4731622709481299 " "
absolute error = 6.35047570085589500000000000000E-14 " "
relative error = 1.342134842689711200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 0.479521746837873 " "
y[1] (numeric) = 0.47952174683793725 " "
absolute error = 6.4226401974565310000000000000E-14 " "
relative error = 1.339384551338822500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 0.4858694739717383 " "
y[1] (numeric) = 0.4858694739718032 " "
absolute error = 6.4892535789340400000000000000E-14 " "
relative error = 1.335596065726801000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 0.4922046456902313 " "
y[1] (numeric) = 0.4922046456902969 " "
absolute error = 6.56141807553467500000000000000E-14 " "
relative error = 1.33306707545058400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 0.4985264529863698 " "
y[1] (numeric) = 0.498526452986436 " "
absolute error = 6.62248034188905900000000000000E-14 " "
relative error = 1.328411020562258000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 0.504834084604069 " "
y[1] (numeric) = 0.5048340846041358 " "
absolute error = 6.68354260824344200000000000000E-14 " "
relative error = 1.323908747858260600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 0.5111267271371748 " "
y[1] (numeric) = 0.5111267271372423 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.320642343930757400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 0.5174035651290684 " "
y[1] (numeric) = 0.5174035651291368 " "
absolute error = 6.83897383169096400000000000000E-14 " "
relative error = 1.321787148873811000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 0.5236637811728309 " "
y[1] (numeric) = 0.5236637811728999 " "
absolute error = 6.90558721316847400000000000000E-14 " "
relative error = 1.318706288546876400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 0.5299065560119556 " "
y[1] (numeric) = 0.5299065560120252 " "
absolute error = 6.96109836439973200000000000000E-14 " "
relative error = 1.31364639395831100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 0.5361310686415974 " "
y[1] (numeric) = 0.5361310686416678 " "
absolute error = 7.03881397612349200000000000000E-14 " "
relative error = 1.312890520215109200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 0.5423364964103454 " "
y[1] (numeric) = 0.5423364964104164 " "
absolute error = 7.0943251273547500000000000000E-14 " "
relative error = 1.308103949173836400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 0.5485220151225078 " "
y[1] (numeric) = 0.5485220151225793 " "
absolute error = 7.14983627858600800000000000000E-14 " "
relative error = 1.303472984031306700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 0.5546867991408959 " "
y[1] (numeric) = 0.5546867991409681 " "
absolute error = 7.21644966006351800000000000000E-14 " "
relative error = 1.300995385367097500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = 0.560830021490097 " "
y[1] (numeric) = 0.56083002149017 " "
absolute error = 7.3052675020335300000000000000E-14 " "
relative error = 1.302581392241414500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 0.5669508539602206 " "
y[1] (numeric) = 0.5669508539602942 " "
absolute error = 7.36077865326478800000000000000E-14 " "
relative error = 1.298309827359612500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 0.5730484672111078 " "
y[1] (numeric) = 0.5730484672111821 " "
absolute error = 7.42739203474229700000000000000E-14 " "
relative error = 1.296119344126277500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 0.5791220308769911 " "
y[1] (numeric) = 0.5791220308770659 " "
absolute error = 7.48290318597355500000000000000E-14 " "
relative error = 1.29211164262596800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 0.5851707136715903 " "
y[1] (numeric) = 0.5851707136716658 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 1.29013916641221500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 0.5911936834936348 " "
y[1] (numeric) = 0.5911936834937109 " "
absolute error = 7.61612994892857400000000000000E-14 " "
relative error = 1.288263078847759000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 0.5971901075327952 " "
y[1] (numeric) = 0.5971901075328724 " "
absolute error = 7.71605002114483800000000000000E-14 " "
relative error = 1.292059249444466600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 0.6031591523760174 " "
y[1] (numeric) = 0.6031591523760951 " "
absolute error = 7.77156117237609600000000000000E-14 " "
relative error = 1.288476041814450000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 0.6090999841142378 " "
y[1] (numeric) = 0.6090999841143161 " "
absolute error = 7.82707232360735400000000000000E-14 " "
relative error = 1.285022578844686200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 0.6150117684494769 " "
y[1] (numeric) = 0.6150117684495559 " "
absolute error = 7.89368570508486300000000000000E-14 " "
relative error = 1.283501570219680600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 0.6208936708022887 " "
y[1] (numeric) = 0.6208936708023685 " "
absolute error = 7.97140131680862400000000000000E-14 " "
relative error = 1.28385932916796600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 0.6267448564195588 " "
y[1] (numeric) = 0.6267448564196391 " "
absolute error = 8.02691246803988200000000000000E-14 " "
relative error = 1.280730489580031400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 0.6325644904826351 " "
y[1] (numeric) = 0.6325644904827159 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 1.277723258399218700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 0.63835173821578 " "
y[1] (numeric) = 0.6383517382158616 " "
absolute error = 8.160139230994901000000000000E-14 " "
relative error = 1.278313936107205500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 0.6441057649949286 " "
y[1] (numeric) = 0.6441057649950107 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 1.275512629869233500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = 0.6498257364567399 " "
y[1] (numeric) = 0.6498257364568227 " "
absolute error = 8.28226376370366800000000000000E-14 " "
relative error = 1.274536125464004700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = 0.6555108186079298 " "
y[1] (numeric) = 0.6555108186080133 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 1.273644447686035400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = 0.6611601779348688 " "
y[1] (numeric) = 0.6611601779349529 " "
absolute error = 8.40438829641243500000000000000E-14 " "
relative error = 1.271157667520676800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = 0.666772981513434 " "
y[1] (numeric) = 0.6667729815135187 " "
absolute error = 8.47100167788994400000000000000E-14 " "
relative error = 1.270447650512556400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = 0.6723483971190996 " "
y[1] (numeric) = 0.6723483971191849 " "
absolute error = 8.53761505936745400000000000000E-14 " "
relative error = 1.269820095645309300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = 0.6778855933372532 " "
y[1] (numeric) = 0.677885593337339 " "
absolute error = 8.5820239803524600000000000000E-14 " "
relative error = 1.265998874249985600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = 0.6833837396737245 " "
y[1] (numeric) = 0.6833837396738109 " "
absolute error = 8.6486373618299700000000000000E-14 " "
relative error = 1.265560893497288400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = 0.6888420066655113 " "
y[1] (numeric) = 0.6888420066655982 " "
absolute error = 8.69304628281497600000000000000E-14 " "
relative error = 1.26197969907432700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = 0.6942595659916908 " "
y[1] (numeric) = 0.6942595659917783 " "
absolute error = 8.74855743404623400000000000000E-14 " "
relative error = 1.260127747977035400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = 0.6996355905844996 " "
y[1] (numeric) = 0.6996355905845878 " "
absolute error = 8.81517081552374300000000000000E-14 " "
relative error = 1.259966035770027600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = 0.7049692547405725 " "
y[1] (numeric) = 0.7049692547406612 " "
absolute error = 8.87068196675500100000000000000E-14 " "
relative error = 1.258307636411661300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = 0.7102597342323209 " "
y[1] (numeric) = 0.7102597342324103 " "
absolute error = 8.9372953482325100000000000000E-14 " "
relative error = 1.258313672799193600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = 0.7155062064194427 " "
y[1] (numeric) = 0.7155062064195329 " "
absolute error = 9.01501095995627100000000000000E-14 " "
relative error = 1.25994867397020300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = 0.7207078503605445 " "
y[1] (numeric) = 0.720707850360635 " "
absolute error = 9.04831765069502600000000000000E-14 " "
relative error = 1.255476493862037700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = 0.7258638469248639 " "
y[1] (numeric) = 0.7258638469249549 " "
absolute error = 9.09272657168003200000000000000E-14 " "
relative error = 1.25267660184503500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = 0.7309733789040799 " "
y[1] (numeric) = 0.7309733789041715 " "
absolute error = 9.15933995315754100000000000000E-14 " "
relative error = 1.253033313865655000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = 0.7360356311241936 " "
y[1] (numeric) = 0.7360356311242858 " "
absolute error = 9.22595333463505100000000000000E-14 " "
relative error = 1.253465585700473700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = 0.7410497905574668 " "
y[1] (numeric) = 0.7410497905575595 " "
absolute error = 9.27036225562005700000000000000E-14 " "
relative error = 1.250976975332018800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = 0.7460150464344051 " "
y[1] (numeric) = 0.7460150464344985 " "
absolute error = 9.33697563709756700000000000000E-14 " "
relative error = 1.251580069560774000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = 0.7509305903557698 " "
y[1] (numeric) = 0.7509305903558635 " "
absolute error = 9.37028232783632100000000000000E-14 " "
relative error = 1.247822694690989100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = 0.7557956164046038 " "
y[1] (numeric) = 0.755795616404698 " "
absolute error = 9.41469124882132700000000000000E-14 " "
relative error = 1.245666294494795600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = 0.7606093212582596 " "
y[1] (numeric) = 0.7606093212583542 " "
absolute error = 9.45910016980633400000000000000E-14 " "
relative error = 1.243621384255237400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = 0.7653709043004133 " "
y[1] (numeric) = 0.7653709043005084 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 1.24168674787526900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = 0.77007956773305 " "
y[1] (numeric) = 0.7700795677331453 " "
absolute error = 9.53681578153009500000000000000E-14 " "
relative error = 1.238419532361369800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = 0.7747345166884065 " "
y[1] (numeric) = 0.7747345166885025 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 1.238143741647608300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = 0.7793349593408591 " "
y[1] (numeric) = 0.7793349593409553 " "
absolute error = 9.62563362350010700000000000000E-14 " "
relative error = 1.235108666450843400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = 0.7838801070187367 " "
y[1] (numeric) = 0.7838801070188336 " "
absolute error = 9.69224700497761700000000000000E-14 " "
relative error = 1.236445078551527400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = 0.7883691743160521 " "
y[1] (numeric) = 0.7883691743161495 " "
absolute error = 9.73665592596262300000000000000E-14 " "
relative error = 1.235037624905823600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = 0.79280137920413 " "
y[1] (numeric) = 0.7928013792042279 " "
absolute error = 9.79216707719388100000000000000E-14 " "
relative error = 1.23513497000017210000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = 0.7971759431431218 " "
y[1] (numeric) = 0.7971759431432202 " "
absolute error = 9.83657599817888700000000000000E-14 " "
relative error = 1.233927852789314200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = 0.8014920911933912 " "
y[1] (numeric) = 0.8014920911934901 " "
absolute error = 9.89208714941014500000000000000E-14 " "
relative error = 1.234208953288759700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = 0.8057490521267554 " "
y[1] (numeric) = 0.805749052126855 " "
absolute error = 9.95870053088765400000000000000E-14 " "
relative error = 1.23595559989824410000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = 0.8099460585375693 " "
y[1] (numeric) = 0.8099460585376694 " "
absolute error = 1.00142116821189120000000000000E-13 " "
relative error = 1.236404767522478700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = 0.814082346953636 " "
y[1] (numeric) = 0.8140823469537366 " "
absolute error = 1.00586206031039180000000000000E-13 " "
relative error = 1.235577781626651800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = 0.8181571579469308 " "
y[1] (numeric) = 0.8181571579470318 " "
absolute error = 1.01030295240889250000000000000E-13 " "
relative error = 1.234851938402798800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = 0.8221697362441232 " "
y[1] (numeric) = 0.8221697362442245 " "
absolute error = 1.01363362148276790000000000000E-13 " "
relative error = 1.232876347545094200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = 0.826119330836883 " "
y[1] (numeric) = 0.8261193308369847 " "
absolute error = 1.01696429055664340000000000000E-13 " "
relative error = 1.231013792555161300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = 0.8300051950919558 " "
y[1] (numeric) = 0.830005195092058 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 1.230600951289206300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = 0.8338265868609928 " "
y[1] (numeric) = 0.8338265868610955 " "
absolute error = 1.02695629777826980000000000000E-13 " "
relative error = 1.231618557096301500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = 0.8375827685901212 " "
y[1] (numeric) = 0.837582768590224 " "
absolute error = 1.0280665208028950000000000000E-13 " "
relative error = 1.227420810642283800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = 0.8412730074292405 " "
y[1] (numeric) = 0.8412730074293436 " "
absolute error = 1.03139718987677040000000000000E-13 " "
relative error = 1.225995819155675500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = 0.8448965753410305 " "
y[1] (numeric) = 0.8448965753411339 " "
absolute error = 1.03472785895064590000000000000E-13 " "
relative error = 1.224679906570804600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = 0.8484527492096554 " "
y[1] (numeric) = 0.8484527492097594 " "
absolute error = 1.04027897407377170000000000000E-13 " "
relative error = 1.226089461131223600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = 0.8519408109491509 " "
y[1] (numeric) = 0.8519408109492556 " "
absolute error = 1.04694031222152260000000000000E-13 " "
relative error = 1.228888555127582300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = 0.8553600476114787 " "
y[1] (numeric) = 0.8553600476115836 " "
absolute error = 1.04916075827077300000000000000E-13 " "
relative error = 1.22657208645700300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = 0.8587097514942348 " "
y[1] (numeric) = 0.8587097514943401 " "
absolute error = 1.05360165036927360000000000000E-13 " "
relative error = 1.226958991132811500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = 0.8619892202479982 " "
y[1] (numeric) = 0.8619892202481039 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 1.226154915416534800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = 0.8651977569833014 " "
y[1] (numeric) = 0.8651977569834075 " "
absolute error = 1.06137321154164970000000000000E-13 " "
relative error = 1.226740595401398700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = 0.8683346703772141 " "
y[1] (numeric) = 0.8683346703773208 " "
absolute error = 1.06692432666477540000000000000E-13 " "
relative error = 1.22870174722067900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = 0.871399274779522 " "
y[1] (numeric) = 0.8713992747796289 " "
absolute error = 1.06914477271402570000000000000E-13 " "
relative error = 1.226928692343170200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = 0.8743908903184858 " "
y[1] (numeric) = 0.8743908903185931 " "
absolute error = 1.07247544178790120000000000000E-13 " "
relative error = 1.226540044804521800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = 0.8773088430061702 " "
y[1] (numeric) = 0.877308843006278 " "
absolute error = 1.0780265569110270000000000000E-13 " "
relative error = 1.22878797530078600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = 0.8801524648433243 " "
y[1] (numeric) = 0.8801524648434322 " "
absolute error = 1.07913677993565220000000000000E-13 " "
relative error = 1.226079370382435900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = 0.8829210939238008 " "
y[1] (numeric) = 0.8829210939239092 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 1.227264451479589700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = 0.8856140745385012 " "
y[1] (numeric) = 0.8856140745386101 " "
absolute error = 1.08912878715727860000000000000E-13 " "
relative error = 1.229800675564952100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = 0.8882307572788302 " "
y[1] (numeric) = 0.8882307572789395 " "
absolute error = 1.09356967925577920000000000000E-13 " "
relative error = 1.231177450560282700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = 0.8907704991396468 " "
y[1] (numeric) = 0.8907704991397564 " "
absolute error = 1.09579012530502950000000000000E-13 " "
relative error = 1.230159874359783400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = 0.8932326636216983 " "
y[1] (numeric) = 0.8932326636218082 " "
absolute error = 1.0991207943789050000000000000E-13 " "
relative error = 1.230497762948360400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = 0.8956166208335222 " "
y[1] (numeric) = 0.8956166208336321 " "
absolute error = 1.0991207943789050000000000000E-13 " "
relative error = 1.227222417283846100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = 0.8979217475928014 " "
y[1] (numeric) = 0.8979217475929117 " "
absolute error = 1.10245146345278040000000000000E-13 " "
relative error = 1.227781225266337300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = 0.9001474275271615 " "
y[1] (numeric) = 0.900147427527272 " "
absolute error = 1.10467190950203080000000000000E-13 " "
relative error = 1.227212205157024600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = 0.9022930511743923 " "
y[1] (numeric) = 0.9022930511745031 " "
absolute error = 1.10800257857590620000000000000E-13 " "
relative error = 1.227985272782240600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = 0.904358016082084 " "
y[1] (numeric) = 0.904358016082195 " "
absolute error = 1.11022302462515650000000000000E-13 " "
relative error = 1.227636627178839700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = 0.9063417269066596 " "
y[1] (numeric) = 0.9063417269067707 " "
absolute error = 1.11133324764978170000000000000E-13 " "
relative error = 1.226174647660499100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = 0.9082435955117941 " "
y[1] (numeric) = 0.9082435955119055 " "
absolute error = 1.1135536936990320000000000000E-13 " "
relative error = 1.226051798440203500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = 0.910063041066204 " "
y[1] (numeric) = 0.9100630410663153 " "
absolute error = 1.1135536936990320000000000000E-13 " "
relative error = 1.223600611661390300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = 0.9117994901407933 " "
y[1] (numeric) = 0.9117994901409051 " "
absolute error = 1.11799458579753260000000000000E-13 " "
relative error = 1.226140832371928800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = 0.9134523768051457 " "
y[1] (numeric) = 0.9134523768052579 " "
absolute error = 1.12243547789603330000000000000E-13 " "
relative error = 1.228783794752188900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = 0.9150211427233442 " "
y[1] (numeric) = 0.9150211427234567 " "
absolute error = 1.12465592394528360000000000000E-13 " "
relative error = 1.229103756660759700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = 0.9165052372491095 " "
y[1] (numeric) = 0.9165052372492223 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 1.23074756932629300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = 0.9179041175202408 " "
y[1] (numeric) = 0.9179041175203535 " "
absolute error = 1.12687636999453390000000000000E-13 " "
relative error = 1.227662397940692300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = 0.9192172485523467 " "
y[1] (numeric) = 0.9192172485524593 " "
absolute error = 1.12687636999453390000000000000E-13 " "
relative error = 1.225908643217068200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = 0.9204441033318516 " "
y[1] (numeric) = 0.9204441033319648 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 1.230305546005959800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = 0.9215841629082688 " "
y[1] (numeric) = 0.9215841629083821 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 1.228783577990345100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = 0.9226369164857189 " "
y[1] (numeric) = 0.9226369164858323 " "
absolute error = 1.134647931166910000000000000E-13 " "
relative error = 1.229788133222255200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = 0.923601861513689 " "
y[1] (numeric) = 0.9236018615138025 " "
absolute error = 1.13575815419153510000000000000E-13 " "
relative error = 1.229705354134024600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = 0.9244785037770145 " "
y[1] (numeric) = 0.9244785037771281 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 1.22974019684764290000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = 0.9252663574850715 " "
y[1] (numeric) = 0.9252663574851854 " "
absolute error = 1.13908882326541060000000000000E-13 " "
relative error = 1.231092878337780600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = 0.9259649453601689 " "
y[1] (numeric) = 0.9259649453602825 " "
absolute error = 1.13575815419153510000000000000E-13 " "
relative error = 1.226567117775461500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = 0.9265737987251232 " "
y[1] (numeric) = 0.9265737987252369 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 1.226959340724270600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = 0.927092457590009 " "
y[1] (numeric) = 0.9270924575901226 " "
absolute error = 1.13575815419153510000000000000E-13 " "
relative error = 1.225075390154673200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = 0.9275204707380664 " "
y[1] (numeric) = 0.9275204707381801 " "
absolute error = 1.13686837721616030000000000000E-13 " "
relative error = 1.225707046995423300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = 0.9278573958107583 " "
y[1] (numeric) = 0.9278573958108718 " "
absolute error = 1.134647931166910000000000000E-13 " "
relative error = 1.222868876499560300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = 0.9281027993919605 " "
y[1] (numeric) = 0.9281027993920737 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 1.22015307556400100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = 0.9282562570912749 " "
y[1] (numeric) = 0.9282562570913884 " "
absolute error = 1.134647931166910000000000000E-13 " "
relative error = 1.222343423487788900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = 0.9283173536264537 " "
y[1] (numeric) = 0.9283173536265672 " "
absolute error = 1.134647931166910000000000000E-13 " "
relative error = 1.222262975839490400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = 0.9282856829049202 " "
y[1] (numeric) = 0.9282856829050335 " "
absolute error = 1.13353770814228480000000000000E-13 " "
relative error = 1.221108683476687400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = 0.928160848104375 " "
y[1] (numeric) = 0.9281608481044883 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 1.220076765175419200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = 0.9279424617524779 " "
y[1] (numeric) = 0.9279424617525911 " "
absolute error = 1.13242748511765970000000000000E-13 " "
relative error = 1.220363903790973200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = 0.9276301458055884 " "
y[1] (numeric) = 0.9276301458057015 " "
absolute error = 1.13020703906840940000000000000E-13 " "
relative error = 1.218381101755695400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 0.9272235317265591 " "
y[1] (numeric) = 0.9272235317266723 " "
absolute error = 1.13131726209303450000000000000E-13 " "
relative error = 1.220112759634602700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 0.9267222605615653 " "
y[1] (numeric) = 0.9267222605616783 " "
absolute error = 1.13020703906840940000000000000E-13 " "
relative error = 1.21957471743857610000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 0.9261259830159598 " "
y[1] (numeric) = 0.9261259830160727 " "
absolute error = 1.12909681604378420000000000000E-13 " "
relative error = 1.21916114734935200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 0.9254343595291462 " "
y[1] (numeric) = 0.9254343595292592 " "
absolute error = 1.13020703906840940000000000000E-13 " "
relative error = 1.22127196535413900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 0.9246470603484516 " "
y[1] (numeric) = 0.9246470603485646 " "
absolute error = 1.13020703906840940000000000000E-13 " "
relative error = 1.222311828518108100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 0.9237637656019924 " "
y[1] (numeric) = 0.9237637656021055 " "
absolute error = 1.13131726209303450000000000000E-13 " "
relative error = 1.224682439623278700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 0.9227841653705225 " "
y[1] (numeric) = 0.9227841653706356 " "
absolute error = 1.13020703906840940000000000000E-13 " "
relative error = 1.22477940290035300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 0.9217079597582487 " "
y[1] (numeric) = 0.9217079597583614 " "
absolute error = 1.12687636999453390000000000000E-13 " "
relative error = 1.222595897175606500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 0.9205348589626041 " "
y[1] (numeric) = 0.9205348589627167 " "
absolute error = 1.12576614696990870000000000000E-13 " "
relative error = 1.222947872108384900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 0.9192645833429718 " "
y[1] (numeric) = 0.9192645833430845 " "
absolute error = 1.12687636999453390000000000000E-13 " "
relative error = 1.225845518704274400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 0.9178968634883427 " "
y[1] (numeric) = 0.9178968634884549 " "
absolute error = 1.12243547789603330000000000000E-13 " "
relative error = 1.222833983363195600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 0.916431440283899 " "
y[1] (numeric) = 0.916431440284011 " "
absolute error = 1.1202150318467830000000000000E-13 " "
relative error = 1.222366434198017500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 0.9148680649765146 " "
y[1] (numeric) = 0.9148680649766266 " "
absolute error = 1.1202150318467830000000000000E-13 " "
relative error = 1.224455279106872900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 0.9132064992391594 " "
y[1] (numeric) = 0.9132064992392714 " "
absolute error = 1.1202150318467830000000000000E-13 " "
relative error = 1.226683157402069800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 0.9114465152341975 " "
y[1] (numeric) = 0.9114465152343092 " "
absolute error = 1.11688436277290750000000000000E-13 " "
relative error = 1.225397589551288600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 0.9095878956755692 " "
y[1] (numeric) = 0.9095878956756807 " "
absolute error = 1.11466391672365720000000000000E-13 " "
relative error = 1.225460367297185700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 0.9076304338898479 " "
y[1] (numeric) = 0.9076304338899595 " "
absolute error = 1.11577413974828230000000000000E-13 " "
relative error = 1.229326494668528500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 0.905573933876161 " "
y[1] (numeric) = 0.9055739338762722 " "
absolute error = 1.11133324764978170000000000000E-13 " "
relative error = 1.227214262774660200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 0.9034182103649628 " "
y[1] (numeric) = 0.9034182103650736 " "
absolute error = 1.10800257857590620000000000000E-13 " "
relative error = 1.226455882628595100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 0.9011630888756534 " "
y[1] (numeric) = 0.9011630888757639 " "
absolute error = 1.10467190950203080000000000000E-13 " "
relative error = 1.225829068165993800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 0.8988084057730314 " "
y[1] (numeric) = 0.8988084057731418 " "
absolute error = 1.10356168647740560000000000000E-13 " "
relative error = 1.22780525792732600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 0.8963540083225714 " "
y[1] (numeric) = 0.8963540083226816 " "
absolute error = 1.10245146345278040000000000000E-13 " "
relative error = 1.229928636695559500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 0.8937997547445174 " "
y[1] (numeric) = 0.8937997547446271 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 1.227232769428529400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 0.8911455142667811 " "
y[1] (numeric) = 0.8911455142668906 " "
absolute error = 1.09467990228040430000000000000E-13 " "
relative error = 1.228396355875827800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 0.8883911671766397 " "
y[1] (numeric) = 0.8883911671767488 " "
absolute error = 1.09134923320652890000000000000E-13 " "
relative error = 1.228455745091322800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 0.8855366048712188 " "
y[1] (numeric) = 0.8855366048713276 " "
absolute error = 1.08801856413265340000000000000E-13 " "
relative error = 1.228654533474515100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 0.8825817299067567 " "
y[1] (numeric) = 0.8825817299068655 " "
absolute error = 1.08801856413265340000000000000E-13 " "
relative error = 1.232768056786764500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 0.879526456046638 " "
y[1] (numeric) = 0.8795264560467465 " "
absolute error = 1.0846878950587780000000000000E-13 " "
relative error = 1.233263522207523900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 0.8763707083081886 " "
y[1] (numeric) = 0.876370708308297 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 1.236437573462458400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 0.8731144230082252 " "
y[1] (numeric) = 0.873114423008333 " "
absolute error = 1.0780265569110270000000000000E-13 " "
relative error = 1.234691042208188900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 0.869757547807347 " "
y[1] (numeric) = 0.8697575478074545 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 1.235626975065008300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 0.8663000417529685 " "
y[1] (numeric) = 0.8663000417530757 " "
absolute error = 1.07247544178790120000000000000E-13 " "
relative error = 1.23799537123158210000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 0.862741875321076 " "
y[1] (numeric) = 0.8627418753211825 " "
absolute error = 1.06470388061552510000000000000E-13 " "
relative error = 1.234093198755754800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 0.859083030456707 " "
y[1] (numeric) = 0.8590830304568131 " "
absolute error = 1.06137321154164970000000000000E-13 " "
relative error = 1.235472211547934800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 0.8553235006131434 " "
y[1] (numeric) = 0.8553235006132491 " "
absolute error = 1.0569323194431490000000000000E-13 " "
relative error = 1.235710603865649800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 0.8514632907898081 " "
y[1] (numeric) = 0.8514632907899132 " "
absolute error = 1.05138120432002320000000000000E-13 " "
relative error = 1.234793344226001200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 0.847502417568859 " "
y[1] (numeric) = 0.8475024175689638 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 1.236634272091612500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 0.8434409091504755 " "
y[1] (numeric) = 0.8434409091505797 " "
absolute error = 1.04138919709839680000000000000E-13 " "
relative error = 1.234691352767436100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 0.8392788053868254 " "
y[1] (numeric) = 0.8392788053869289 " "
absolute error = 1.03472785895064590000000000000E-13 " "
relative error = 1.232877385094620200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 0.8350161578147094 " "
y[1] (numeric) = 0.8350161578148125 " "
absolute error = 1.03139718987677040000000000000E-13 " "
relative error = 1.235182313808157500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 0.8306530296868746 " "
y[1] (numeric) = 0.8306530296869771 " "
absolute error = 1.02473585172901950000000000000E-13 " "
relative error = 1.233650892858726800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 0.8261894960019884 " "
y[1] (numeric) = 0.8261894960020906 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 1.236284396736854500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 0.8216256435332714 " "
y[1] (numeric) = 0.8216256435333732 " "
absolute error = 1.01807451358126850000000000000E-13 " "
relative error = 1.239097783271709600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 0.8169615708557761 " "
y[1] (numeric) = 0.8169615708558774 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 1.239377021611326700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 0.8121973883723104 " "
y[1] (numeric) = 0.8121973883724111 " "
absolute error = 1.0069722833350170000000000000E-13 " "
relative error = 1.239812264544517300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 0.8073332183379964 " "
y[1] (numeric) = 0.8073332183380967 " "
absolute error = 1.00253139123651640000000000000E-13 " "
relative error = 1.241781421183636600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 0.802369194883462 " "
y[1] (numeric) = 0.8023691948835618 " "
absolute error = 9.98090499138015700000000000000E-14 " "
relative error = 1.24392923544750600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 0.7973054640366545 " "
y[1] (numeric) = 0.797305464036754 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 1.247652091869281700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 0.7921421837432758 " "
y[1] (numeric) = 0.7921421837433746 " "
absolute error = 9.88098491916389300000000000000E-14 " "
relative error = 1.247375171016799000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 0.786879523885829 " "
y[1] (numeric) = 0.7868795238859272 " "
absolute error = 9.81437153768638400000000000000E-14 " "
relative error = 1.247252119259667500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 0.7815176663012745 " "
y[1] (numeric) = 0.7815176663013723 " "
absolute error = 9.78106484694762900000000000000E-14 " "
relative error = 1.251547504132432000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 0.7760568047972891 " "
y[1] (numeric) = 0.7760568047973864 " "
absolute error = 9.72555369571637100000000000000E-14 " "
relative error = 1.253201265113157200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 0.770497145167122 " "
y[1] (numeric) = 0.7704971451672185 " "
absolute error = 9.6478380839926100000000000000E-14 " "
relative error = 1.252157538091848400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 0.764838905203044 " "
y[1] (numeric) = 0.7648389052031397 " "
absolute error = 9.5701224722688490000000000000E-14 " "
relative error = 1.251259893706406200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 0.7590823147083854 " "
y[1] (numeric) = 0.7590823147084804 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 1.251973456191280000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 0.7532276155081571 " "
y[1] (numeric) = 0.7532276155082516 " "
absolute error = 9.44799793956008200000000000000E-14 " "
relative error = 1.254335043622383500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 0.7472750614582513 " "
y[1] (numeric) = 0.7472750614583452 " "
absolute error = 9.39248678832882400000000000000E-14 " "
relative error = 1.256898198904174700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 0.741224918453216 " "
y[1] (numeric) = 0.7412249184533094 " "
absolute error = 9.33697563709756700000000000000E-14 " "
relative error = 1.259668341504480700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 0.7350774644326021 " "
y[1] (numeric) = 0.7350774644326946 " "
absolute error = 9.24815779512755400000000000000E-14 " "
relative error = 1.258120163194786600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 0.7288329893858749 " "
y[1] (numeric) = 0.7288329893859669 " "
absolute error = 9.19264664389629600000000000000E-14 " "
relative error = 1.261283006912482200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 0.722491795355892 " "
y[1] (numeric) = 0.7224917953559834 " "
absolute error = 9.13713549266503800000000000000E-14 " "
relative error = 1.264669792985563300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 0.7160541964409373 " "
y[1] (numeric) = 0.7160541964410279 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 1.265186340080129700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 0.7095205187953141 " "
y[1] (numeric) = 0.7095205187954038 " "
absolute error = 8.97060203897126500000000000000E-14 " "
relative error = 1.264318902884209500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 0.7028911006284881 " "
y[1] (numeric) = 0.7028911006285772 " "
absolute error = 8.90398865749375500000000000000E-14 " "
relative error = 1.266766452090840000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 0.6961662922027843 " "
y[1] (numeric) = 0.6961662922028723 " "
absolute error = 8.80406858527749100000000000000E-14 " "
relative error = 1.264650225655134200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 0.689346455829625 " "
y[1] (numeric) = 0.6893464558297123 " "
absolute error = 8.73745520379998200000000000000E-14 " "
relative error = 1.267498386320779500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 0.682431965864318 " "
y[1] (numeric) = 0.6824319658644046 " "
absolute error = 8.65973959207622100000000000000E-14 " "
relative error = 1.268952807787723500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 0.6754232086993812 " "
y[1] (numeric) = 0.6754232086994671 " "
absolute error = 8.59312621059871200000000000000E-14 " "
relative error = 1.272258059823845600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 0.6683205827564098 " "
y[1] (numeric) = 0.668320582756495 " "
absolute error = 8.51541059887495100000000000000E-14 " "
relative error = 1.274150582607248000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 0.6611244984764788 " "
y[1] (numeric) = 0.6611244984765632 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 1.276264153967270000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 0.6538353783090801 " "
y[1] (numeric) = 0.6538353783091635 " "
absolute error = 8.33777491493492600000000000000E-14 " "
relative error = 1.275210120397233200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 0.6464536566995932 " "
y[1] (numeric) = 0.6464536566996759 " "
absolute error = 8.27116153345741600000000000000E-14 " "
relative error = 1.279467050381466500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 0.638979780075287 " "
y[1] (numeric) = 0.6389797800753692 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 1.285744970092505800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 0.631414206829851 " "
y[1] (numeric) = 0.6314142068299323 " "
absolute error = 8.12683254025614600000000000000E-14 " "
relative error = 1.28708420753765300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 0.6237574073064549 " "
y[1] (numeric) = 0.6237574073065354 " "
absolute error = 8.04911692853238500000000000000E-14 " "
relative error = 1.290424263383187000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 0.616009863779335 " "
y[1] (numeric) = 0.6160098637794145 " "
absolute error = 7.94919685631612100000000000000E-14 " "
relative error = 1.290433371885690600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 0.6081720704339063 " "
y[1] (numeric) = 0.608172070433985 " "
absolute error = 7.8714812445923600000000000000E-14 " "
relative error = 1.294285224077517000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 0.6002445333454024 " "
y[1] (numeric) = 0.6002445333454803 " "
absolute error = 7.79376563286859900000000000000E-14 " "
relative error = 1.298431755709765800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 0.5922277704560356 " "
y[1] (numeric) = 0.5922277704561124 " "
absolute error = 7.68274333040608300000000000000E-14 " "
relative error = 1.297261579694263300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 0.5841223115506847 " "
y[1] (numeric) = 0.5841223115507607 " "
absolute error = 7.59392548843607100000000000000E-14 " "
relative error = 1.300057426033989200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 0.575928698231105 " "
y[1] (numeric) = 0.5759286982311799 " "
absolute error = 7.48290318597355500000000000000E-14 " "
relative error = 1.299275970958971600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 0.5676474838886618 " "
y[1] (numeric) = 0.5676474838887358 " "
absolute error = 7.39408534400354300000000000000E-14 " "
relative error = 1.302584007481272800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 0.559279233675584 " "
y[1] (numeric) = 0.5592792336756609 " "
absolute error = 7.69384556065233500000000000000E-14 " "
relative error = 1.375671596116374900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 0.5508245244747572 " "
y[1] (numeric) = 0.5508245244748369 " "
absolute error = 7.97140131680862400000000000000E-14 " "
relative error = 1.447176180909848500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 0.5422839448680176 " "
y[1] (numeric) = 0.5422839448680998 " "
absolute error = 8.2267526124724100000000000000E-14 " "
relative error = 1.51705627472977420000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 0.5336580951029856 " "
y[1] (numeric) = 0.5336580951030708 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 1.597748241310900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 0.5249475870584223 " "
y[1] (numeric) = 0.5249475870585106 " "
absolute error = 8.83737527601624600000000000000E-14 " "
relative error = 1.683477644984911800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 0.5161530442081118 " "
y[1] (numeric) = 0.5161530442082033 " "
absolute error = 9.1482377229112900000000000000E-14 " "
relative error = 1.772388601707585700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 0.5072751015832709 " "
y[1] (numeric) = 0.5072751015833652 " "
absolute error = 9.42579347906757900000000000000E-14 " "
relative error = 1.85812263398074580000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 0.4983144057334876 " "
y[1] (numeric) = 0.4983144057335848 " "
absolute error = 9.72000258059324600000000000000E-14 " "
relative error = 1.950576276494758500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 0.4892716146861906 " "
y[1] (numeric) = 0.48927161468629093 " "
absolute error = 1.00308650274882900000000000000E-13 " "
relative error = 2.050162880166651600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 0.48014739790465044 " "
y[1] (numeric) = 0.48014739790475386 " "
absolute error = 1.03417274743833330000000000000E-13 " "
relative error = 2.153865150475528500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 0.47094243624451404 " "
y[1] (numeric) = 0.47094243624462057 " "
absolute error = 1.06525899212783770000000000000E-13 " "
relative error = 2.261972823308608400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 0.4616574219088755 " "
y[1] (numeric) = 0.4616574219089852 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 2.376005012102170600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 0.45229305840188494 " "
y[1] (numeric) = 0.45229305840199774 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 2.493928597986323200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 0.4428500604808968 " "
y[1] (numeric) = 0.4428500604810129 " "
absolute error = 1.16073817224560120000000000000E-13 " "
relative error = 2.62106359652551470000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 0.4333291541071626 " "
y[1] (numeric) = 0.4333291541072819 " "
absolute error = 1.19293463995973070000000000000E-13 " "
relative error = 2.75295264270337300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 0.42373107639506735 " "
y[1] (numeric) = 0.4237310763951898 " "
absolute error = 1.22457599616154770000000000000E-13 " "
relative error = 2.889983917582220000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 0.4140565755599158 " "
y[1] (numeric) = 0.4140565755600416 " "
absolute error = 1.25788268690030240000000000000E-13 " "
relative error = 3.03794882426225600000000000E-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) = 0.4043064108642702 " "
y[1] (numeric) = 0.40430641086439917 " "
absolute error = 1.28952404310211930000000000000E-13 " "
relative error = 3.18947216381148540000000000E-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) = 0.39448135256284167 " "
y[1] (numeric) = 0.39448135256297384 " "
absolute error = 1.32172051081624900000000000000E-13 " "
relative error = 3.35052722322456600000000000E-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) = 0.38458218184594095 " "
y[1] (numeric) = 0.38458218184607657 " "
absolute error = 1.35613742457962870000000000000E-13 " "
relative error = 3.52626171620941400000000000E-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) = 0.37460969078149076 " "
y[1] (numeric) = 0.37460969078162965 " "
absolute error = 1.38888900380607080000000000000E-13 " "
relative error = 3.70756293279184700000000000E-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) = 0.36456468225560323 " "
y[1] (numeric) = 0.3645646822557455 " "
absolute error = 1.4227508060571380000000000000E-13 " "
relative error = 3.90260185724633700000000000E-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) = 0.3544479699117277 " "
y[1] (numeric) = 0.3544479699118733 " "
absolute error = 1.45550238528358020000000000000E-13 " "
relative error = 4.10639221786503900000000000E-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) = 0.34426037808837123 " "
y[1] (numeric) = 0.34426037808852017 " "
absolute error = 1.48936418753464750000000000000E-13 " "
relative error = 4.326272444725920400000000000E-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) = 0.3340027417553982 " "
y[1] (numeric) = 0.33400274175555056 " "
absolute error = 1.52378110129802740000000000000E-13 " "
relative error = 4.56218141590569700000000000E-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) = 0.32367590644891175 " "
y[1] (numeric) = 0.3236759064490676 " "
absolute error = 1.55819801506140720000000000000E-13 " "
relative error = 4.814068591501264000000000000E-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) = 0.3132807282047225 " "
y[1] (numeric) = 0.3132807282048818 " "
absolute error = 1.5926149288247870000000000000E-13 " "
relative error = 5.08366709293412300000000000E-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) = 0.30281807349041 " "
y[1] (numeric) = 0.3028180734905727 " "
absolute error = 1.6270318425881670000000000000E-13 " "
relative error = 5.37296807893368200000000000E-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) = 0.29228881913597965 " "
y[1] (numeric) = 0.29228881913614585 " "
absolute error = 1.66200386786385930000000000000E-13 " "
relative error = 5.68616983973874100000000000E-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) = 0.28169385226312404 " "
y[1] (numeric) = 0.28169385226329385 " "
absolute error = 1.6980861161641770000000000000E-13 " "
relative error = 6.02812628859941100000000000E-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) = 0.2710340702130905 " "
y[1] (numeric) = 0.2710340702132639 " "
absolute error = 1.73416836446449450000000000000E-13 " "
relative error = 6.39834085471641600000000000E-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) = 0.2603103804731621 " "
y[1] (numeric) = 0.260310380473339 " "
absolute error = 1.7691403897401870000000000000E-13 " "
relative error = 6.79627292052068200000000000E-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) = 0.2495237006017575 " "
y[1] (numeric) = 0.24952370060193801 " "
absolute error = 1.80522263804050450000000000000E-13 " "
relative error = 7.23467403572079600000000000E-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) = 0.2386749581521569 " "
y[1] (numeric) = 0.238674958152341 " "
absolute error = 1.84102733058466580000000000000E-13 " "
relative error = 7.71353368965921700000000000E-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) = 0.22776509059485678 " "
y[1] (numeric) = 0.2277650905950445 " "
absolute error = 1.87710957888498340000000000000E-13 " "
relative error = 8.24142792902333700000000000E-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) = 0.2167950452385637 " "
y[1] (numeric) = 0.2167950452387551 " "
absolute error = 1.914024494453770000000000000E-13 " "
relative error = 8.82872803826100300000000000E-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) = 0.20576577914983063 " "
y[1] (numeric) = 0.20576577915002578 " "
absolute error = 1.9514945215348690000000000000E-13 " "
relative error = 9.48405769704721700000000000E-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) = 0.19467825907134426 " "
y[1] (numeric) = 0.19467825907154307 " "
absolute error = 1.9881318813474990000000000000E-13 " "
relative error = 1.02123980912470730000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 0.18353346133886833 " "
y[1] (numeric) = 0.18353346133907086 " "
absolute error = 2.02532435267244180000000000000E-13 " "
relative error = 1.1035177661325579000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 0.172332371796852 " "
y[1] (numeric) = 0.17233237179705832 " "
absolute error = 2.06307193550969710000000000000E-13 " "
relative error = 1.19714706761053420000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 0.16107598571270848 " "
y[1] (numeric) = 0.16107598571291848 " "
absolute error = 2.09998685107848360000000000000E-13 " "
relative error = 1.3037243520731720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 0.1497653076897721 " "
y[1] (numeric) = 0.14976530768998586 " "
absolute error = 2.1377344339157390000000000000E-13 " "
relative error = 1.42738960503716930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 0.13840135157894154 " "
y[1] (numeric) = 0.13840135157915912 " "
absolute error = 2.17575957250915050000000000000E-13 " "
relative error = 1.5720652635882232000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 0.1269851403890161 " "
y[1] (numeric) = 0.12698514038923753 " "
absolute error = 2.21433982261487470000000000000E-13 " "
relative error = 1.74377869397261380000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 0.11551770619573355 " "
y[1] (numeric) = 0.11551770619595876 " "
absolute error = 2.252087405452130000000000000E-13 " "
relative error = 1.94956035712498170000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 0.10400009004951645 " "
y[1] (numeric) = 0.10400009004974552 " "
absolute error = 2.2906676555578542000000000000E-13 " "
relative error = 2.20256314630806860000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 9.24333418819366500E-2 " "
y[1] (numeric) = 9.24333418821696200E-2 " "
absolute error = 2.3296642392978129000000000000E-13 " "
relative error = 2.520372185908250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 8.08185204109048800E-2 " "
y[1] (numeric) = 8.08185204111416700E-2 " "
absolute error = 2.36782815576930260000000000000E-13 " "
relative error = 2.9298088405115250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 6.91566930445942200E-2 " "
y[1] (numeric) = 6.91566930448349200E-2 " "
absolute error = 2.40696351738733940000000000000E-13 " "
relative error = 3.48044912418709830000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 5.7448935784106900E-2 " "
y[1] (numeric) = 5.74489357843515100E-2 " "
absolute error = 2.4460988790053761000000000000E-13 " "
relative error = 4.25786630443045270000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 4.56963331248919700E-2 " "
y[1] (numeric) = 4.56963331251405200E-2 " "
absolute error = 2.4855117963795692000000000000E-13 " "
relative error = 5.4391930958364950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 3.389997795692374400E-2 " "
y[1] (numeric) = 3.38999779571762200E-2 " "
absolute error = 2.5247165469366450000000000000E-13 " "
relative error = 7.447546279070650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 2.20609714636495700E-2 " "
y[1] (numeric) = 2.20609714639060100E-2 " "
absolute error = 2.56440702006699440000000000000E-13 " "
relative error = 1.162417994281183000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 1.01804230197167290E-2 " "
y[1] (numeric) = 1.018042301997712200E-2 " "
absolute error = 2.6039240208497460000000000000E-13 " "
relative error = 2.557775856471434000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = -1.740549912512726000E-3 " "
y[1] (numeric) = -1.7405499122483434000E-3 " "
absolute error = 2.64382699760590260000000000000E-13 " "
relative error = 1.518960748324172400000000E-8 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = -1.370082188764890600E-2 " "
y[1] (numeric) = -1.370082188738053800E-2 " "
absolute error = 2.68368660627515960000000000000E-13 " "
relative error = 1.9587778224417796000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = -2.569925958315369000E-2 " "
y[1] (numeric) = -2.569925958288132000E-2 " "
absolute error = 2.7236893296311850000000000000E-13 " "
relative error = 1.0598318293250016000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = -3.77347219064025630E-2 " "
y[1] (numeric) = -3.77347219061261400E-2 " "
absolute error = 2.76424716449952260000000000000E-13 " "
relative error = 7.3254737940191480000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = -4.980606010291873700E-2 " "
y[1] (numeric) = -4.980606010263831700E-2 " "
absolute error = 2.8042151933860280000000000000E-13 " "
relative error = 5.6302690628237330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = -6.19121178657698300E-2 " "
y[1] (numeric) = -6.19121178654853400E-2 " "
absolute error = 2.84494650060196360000000000000E-13 " "
relative error = 4.59513678205940750000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = -7.40517314461155900E-2 " "
y[1] (numeric) = -7.40517314458270500E-2 " "
absolute error = 2.88533086312270370000000000000E-13 " "
relative error = 3.8963719102533630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = -8.62237297648974300E-2 " "
y[1] (numeric) = -8.62237297646048200E-2 " "
absolute error = 2.92599278139960000000000000E-13 " "
relative error = 3.39348899586897960000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = -9.84269345256580000E-2 " "
y[1] (numeric) = -9.84269345253613400E-2 " "
absolute error = 2.96665469967649640000000000000E-13 " "
relative error = 3.0140679621624780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = -0.11066016032848074 " "
y[1] (numeric) = -0.11066016032817998 " "
absolute error = 3.0075941737095490000000000000E-13 " "
relative error = 2.7178653679715310000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = -0.12292221478503766 " "
y[1] (numeric) = -0.12292221478473281 " "
absolute error = 3.04853364774260170000000000000E-13 " "
relative error = 2.48005102501104250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = -0.13521189863473498 " "
y[1] (numeric) = -0.1352118986344261 " "
absolute error = 3.0889180102633420000000000000E-13 " "
relative error = 2.28450161668672880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = -0.1475280058619447 " "
y[1] (numeric) = -0.1475280058616317 " "
absolute error = 3.12999626217447260000000000000E-13 " "
relative error = 2.12162853004567360000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = -0.15986932381431088 " "
y[1] (numeric) = -0.1598693238139937 " "
absolute error = 3.1716296255979160000000000000E-13 " "
relative error = 1.98388880988937060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = -0.17223463332211897 " "
y[1] (numeric) = -0.17223463332179767 " "
absolute error = 3.2129854332652030000000000000E-13 " "
relative error = 1.86547001104950260000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = -0.18462270881871698 " "
y[1] (numeric) = -0.18462270881839152 " "
absolute error = 3.25461879668864640000000000000E-13 " "
relative error = 1.76284857779028220000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = -0.1970323184619752 " "
y[1] (numeric) = -0.19703231846164562 " "
absolute error = 3.2956970485997770000000000000E-13 " "
relative error = 1.67266825784004870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = -0.2094622242567744 " "
y[1] (numeric) = -0.20946222425644062 " "
absolute error = 3.3378855235355330000000000000E-13 " "
relative error = 1.59355011882414880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = -0.22191118217850841 " "
y[1] (numeric) = -0.22191118217817046 " "
absolute error = 3.37951888695897650000000000000E-13 " "
relative error = 1.52291509322880570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = -0.23437794229759001 " "
y[1] (numeric) = -0.23437794229724795 " "
absolute error = 3.42059713887010730000000000000E-13 " "
relative error = 1.459436457773389800000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = -0.24686124890494754 " "
y[1] (numeric) = -0.2468612489046013 " "
absolute error = 3.4625080580497070000000000000E-13 " "
relative error = 1.40261303603099100000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = -0.25935984063849876 " "
y[1] (numeric) = -0.2593598406381483 " "
absolute error = 3.50441897722930660000000000000E-13 " "
relative error = 1.35118026314406950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = -0.2718724506105904 " "
y[1] (numeric) = -0.2718724506102356 " "
absolute error = 3.54771767518968800000000000000E-13 " "
relative error = 1.30491988696242370000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = -0.2843978065363895 " "
y[1] (numeric) = -0.2843978065360305 " "
absolute error = 3.5904612616377560000000000000E-13 " "
relative error = 1.26247853503692410000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = -0.2969346308632147 " "
y[1] (numeric) = -0.2969346308628515 " "
absolute error = 3.63209462506119960000000000000E-13 " "
relative error = 1.22319670646107730000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = -0.30948164090079255 " "
y[1] (numeric) = -0.3094816409004251 " "
absolute error = 3.67428309999695560000000000000E-13 " "
relative error = 1.18723782428657330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = -0.3220375489524279 " "
y[1] (numeric) = -0.32203754895205633 " "
absolute error = 3.7159164634203990000000000000E-13 " "
relative error = 1.15387676856568120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = -0.3346010624470726 " "
y[1] (numeric) = -0.33460106244669685 " "
absolute error = 3.75754982684384230000000000000E-13 " "
relative error = 1.12299399152033880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = -0.3471708840722808 " "
y[1] (numeric) = -0.34717088407190083 " "
absolute error = 3.79973830177959800000000000000E-13 " "
relative error = 1.09448645497255890000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = -0.3597457119080363 " "
y[1] (numeric) = -0.3597457119076521 " "
absolute error = 3.8419267767153540000000000000E-13 " "
relative error = 1.06795623951661910000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = -0.37232423956143795 " "
y[1] (numeric) = -0.37232423956104954 " "
absolute error = 3.884115251651110000000000000E-13 " "
relative error = 1.04320773104276620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = -0.38490515630223027 " "
y[1] (numeric) = -0.38490515630183775 " "
absolute error = 3.9251935035622410000000000000E-13 " "
relative error = 1.01978200065476670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = -0.3974871471991637 " "
y[1] (numeric) = -0.3974871471987671 " "
absolute error = 3.96627175547337200000000000000E-13 " "
relative error = 9.97836479348109400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = -0.4100688932571722 " "
y[1] (numeric) = -0.41006889325677137 " "
absolute error = 4.00846023040912770000000000000E-13 " "
relative error = 9.7750897381412590000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = -0.42264907155535164 " "
y[1] (numeric) = -0.4226490715549465 " "
absolute error = 4.0512038168571960000000000000E-13 " "
relative error = 9.58526609782611600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = -0.4352263553857266 " "
y[1] (numeric) = -0.4352263553853173 " "
absolute error = 4.0933922917929520000000000000E-13 " "
relative error = 9.40520315725162100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = -0.4477994143927903 " "
y[1] (numeric) = -0.44779941439237675 " "
absolute error = 4.1355807667287080000000000000E-13 " "
relative error = 9.23534206121394100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = -0.4603669147138023 " "
y[1] (numeric) = -0.46036691471338465 " "
absolute error = 4.1766590186398390000000000000E-13 " "
relative error = 9.0724569580252200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = -0.472927519119831 " "
y[1] (numeric) = -0.47292751911940906 " "
absolute error = 4.21940260508790740000000000000E-13 " "
relative error = 8.92188006513274900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = -0.48547988715752344 " "
y[1] (numeric) = -0.48547988715709733 " "
absolute error = 4.2610359685113510000000000000E-13 " "
relative error = 8.77695674162660800000000000E-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) = -0.4980226752915906 " "
y[1] (numeric) = -0.49802267529116034 " "
absolute error = 4.3026693319347940000000000000E-13 " "
relative error = 8.63950487679219800000000000E-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) = -0.51055453704799 " "
y[1] (numeric) = -0.5105545370475557 " "
absolute error = 4.34319247233361240000000000000E-13 " "
relative error = 8.50681397808314900000000000E-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) = -0.5230741231577929 " "
y[1] (numeric) = -0.5230741231573546 " "
absolute error = 4.3831605012201180000000000000E-13 " "
relative error = 8.37961640074837600000000000E-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) = -0.5355800817017191 " "
y[1] (numeric) = -0.5355800817012765 " "
absolute error = 4.4264591991804990000000000000E-13 " "
relative error = 8.26479428644198400000000000E-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) = -0.5480710582553248 " "
y[1] (numeric) = -0.5480710582548778 " "
absolute error = 4.469757897140880000000000000E-13 " "
relative error = 8.15543501123643700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = ( 0.2 * x + 0.3 ) * sin ( x ) ; "
Iterations = 4900
"Total Elapsed Time "= 1 Minutes 14 Seconds
"Elapsed Time(since restart) "= 1 Minutes 14 Seconds
"Time to Timeout "= 1 Minutes 45 Seconds
Percent Done = 100.0204081632654 "%"
(%o255) temp/diffeq.mult_lin_sin.max