(%i1) batch("temp/diffeq.sub_full_lin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sub_full_lin.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,40,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[40],convfloat)
(%i173) completearray(array_norms,[40],convfloat)
(%i174) completearray(array_fact_1,[40],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[40],convfloat)
(%i184) completearray(array_x,[40],convfloat)
(%i185) completearray(array_tmp0,[40],convfloat)
(%i186) completearray(array_tmp1,[40],convfloat)
(%i187) completearray(array_tmp2,[40],convfloat)
(%i188) completearray(array_tmp3_g,[40],convfloat)
(%i189) completearray(array_tmp3,[40],convfloat)
(%i190) completearray(array_tmp4,[40],convfloat)
(%i191) completearray(array_tmp5,[40],convfloat)
(%i192) completearray(array_tmp6,[40],convfloat)
(%i193) completearray(array_tmp7,[40],convfloat)
(%i194) completearray(array_m1,[40],convfloat)
(%i195) completearray(array_y_higher,[2,40],convfloat)
(%i196) completearray(array_y_higher_work,[2,40],convfloat)
(%i197) completearray(array_y_higher_work2,[2,40],convfloat)
(%i198) completearray(array_y_set_initial,[2,40],convfloat)
(%i199) completearray(array_given_rad_poles,[2,3],convfloat)
(%i200) completearray(array_given_ord_poles,[2,3],convfloat)
(%i201) completearray(array_rad_test_poles,[2,4],convfloat)
(%i202) completearray(array_ord_test_poles,[2,4],convfloat)
(%i203) completearray(array_fact_2,[40,40],convfloat)
(%i204) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i205) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i206) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i207) 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))
(%i208) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i209) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i210) 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)
(%i211) 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)
(%i212) 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)
(%i213) 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)
(%i214) 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)
(%i215) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i216) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i217) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i218) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i219) log_revs(file,revs):=printf(file,revs)
(%i220) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i221) 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)
(%i222) logstart(file):=(printf(file,""),0)
(%i223) logend(file):=(printf(file,"
~%"),0)
(%i224) 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)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) 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)
(%i229) c(in_val):=(ret:in_val,ret)
(%i230) 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)
(%i231) 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)
(%i232) 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)
(%i233) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i234) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i235) 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)
(%i236) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i237) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i238) 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)
(%i239) log10(x):=log(x)/glob_log_10
(%i240) c(x):=x
(%i241) 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
(%i242) 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)
(%i243) exact_soln_y(x):=block(
(-cos(c(0.1)+c(0.3)*c(x)))/c(0.3)
-c(0.2)*c(x)+c(-0.05)*c(x)*c(x))
- cos(c(0.1) + c(0.3) c(x))
(%o243) exact_soln_y(x) := block(--------------------------- - c(0.2) c(x)
c(0.3)
+ c(- 0.05) c(x) c(x))
(%i244) 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)
(%i245) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i246) 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)
(%i247) 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)
(%i248) 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))
(%i249) 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))
(%i250) 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(29)
*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)
(%i251) 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)
(%i252) 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)
(%i253) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D3[1]*array_x[1],
array_tmp2[1]:array_const_0D1[1]+array_tmp1[1],
array_tmp3[1]:sin(array_tmp2[1]),
array_tmp3_g[1]:cos(array_tmp2[1]),
array_tmp4[1]:array_tmp3[1]+array_const_0D0[1],
array_tmp5[1]:array_const_0D1[1]*array_x[1],
array_tmp6[1]:array_const_0D2[1]+array_tmp5[1],
array_tmp7[1]:array_tmp4[1]-array_tmp6[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp7[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_0D3[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:array_tmp3_g[1]*array_tmp2[2]/c(1),
array_tmp3_g[2]:neg(array_tmp3[1])*array_tmp2[2]/c(1),
array_tmp4[2]:array_tmp3[2],
array_tmp5[2]:array_const_0D1[1]*array_x[2],
array_tmp6[2]:array_tmp5[2],
array_tmp7[2]:array_tmp4[2]-array_tmp6[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp7[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_tmp2[2]/c(2),
array_tmp3_g[3]:neg(array_tmp3[2])*array_tmp2[2]/c(2),
array_tmp4[3]:array_tmp3[3],array_tmp7[3]:array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp7[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_tmp2[2]/c(3),
array_tmp3_g[4]:neg(array_tmp3[3])*array_tmp2[2]/c(3),
array_tmp4[4]:array_tmp3[4],array_tmp7[4]:array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp7[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_tmp2[2]/c(4),
array_tmp3_g[5]:neg(array_tmp3[4])*array_tmp2[2]/c(4),
array_tmp4[5]:array_tmp3[5],array_tmp7[5]:array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp7[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_tmp2[2]/c(kkk-1),
array_tmp3_g[kkk]
:neg(array_tmp3[kkk-1])*array_tmp2[2]/c(kkk-1),
array_tmp4[kkk]:array_tmp3[kkk],
array_tmp7[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_tmp7[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)
(%i254) exact_soln_y(x):=block(
(-cos(c(0.1)+c(0.3)*c(x)))/c(0.3)
-c(0.2)*c(x)+c(-0.05)*c(x)*c(x))
- cos(c(0.1) + c(0.3) c(x))
(%o254) exact_soln_y(x) := block(--------------------------- - c(0.2) c(x)
c(0.3)
+ c(- 0.05) c(x) c(x))
(%i255) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp6[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp7[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
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_tmp6),
zero_ats_ar(array_tmp7),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_0D3),array_const_0D3[1]:c(0.3),
zero_ats_ar(array_const_0D1),array_const_0D1[1]:c(0.1),
zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/sub_full_linpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.1),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,""),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always,""),
omniout_str(always,
" (c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)) "),
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 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "),
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,
"2015-04-24T22:38:22-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sub_full_lin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"sub_full_lin diffeq.max"),
logitem_str(html_log_file,
"sub_full_lin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i256) main():=(glob_iolevel:2,compile(all),main_prog())
(%i257) 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_0D3 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D1 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_const_0D0 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp6 in translation.
warning: encountered undefined variable array_tmp7 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/sub_full_linpostode.ode#################"
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
""
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
""
" (c(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = -3.325706312382627 " "
y[1] (numeric) = -3.325706312382627 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = -3.326500099483691 " "
y[1] (numeric) = -3.326500099483691 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = -3.3272741515511597 " "
y[1] (numeric) = -3.3272741515511615 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.33877510084980900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (closed_form) = -3.328028480653558 " "
y[1] (numeric) = -3.3280284806535585 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.334391254256491200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (closed_form) = -3.3287630991269133 " "
y[1] (numeric) = -3.3287630991269137 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.334096769958008600000000000000E-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) = -3.329478019574649 " "
y[1] (numeric) = -3.3294780195746503 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.00143092015483300000000000000E-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) = -3.3301732548674736 " "
y[1] (numeric) = -3.330173254867475 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.00059554740255230000000000000E-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) = -3.330848818143258 " "
y[1] (numeric) = -3.330848818143259 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.66652276399392260000000000000E-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) = -3.3315047228069226 " "
y[1] (numeric) = -3.3315047228069243 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.33199556116372700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = -3.332140982530316 " "
y[1] (numeric) = -3.3321409825303183 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.66372179596128800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = -3.33275761125209 " "
y[1] (numeric) = -3.332757611252092 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.66248887033854800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = -3.3333546231775752 " "
y[1] (numeric) = -3.333354623177577 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.329036481893754000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = -3.3339320327786535 " "
y[1] (numeric) = -3.3339320327786557 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.66014192076882400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = -3.3344898547936275 " "
y[1] (numeric) = -3.33448985479363 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.99083330623983700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = -3.3350281042270877 " "
y[1] (numeric) = -3.33502810422709 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.65795303624559600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = -3.3355467963497785 " "
y[1] (numeric) = -3.3355467963497802 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.32553415633139500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = -3.3360459466984578 " "
y[1] (numeric) = -3.33604594669846 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.65592166513112300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = -3.3365255710757613 " "
y[1] (numeric) = -3.336525571075763 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.3239719029862500000000000000E-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) = -3.336985685550058 " "
y[1] (numeric) = -3.3369856855500597 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.323237816369121000000000000000E-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) = -3.337426306455305 " "
y[1] (numeric) = -3.3374263064553062 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.99190126527526300000000000000E-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) = -3.3378474503909015 " "
y[1] (numeric) = -3.3378474503909024 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.660931731904372000000000000000E-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) = -3.338249134221539 " "
y[1] (numeric) = -3.3382491342215412 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.65152887029238700000000000000E-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) = -3.338631375077051 " "
y[1] (numeric) = -3.338631375077053 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.320613867888468000000000000000E-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) = -3.338994190352257 " "
y[1] (numeric) = -3.3389941903522584 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 3.99002679729022300000000000000E-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) = -3.3393375977068054 " "
y[1] (numeric) = -3.3393375977068076 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.64936079171851600000000000000E-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) = -3.339661615065017 " "
y[1] (numeric) = -3.3396616150650194 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.64871566398826600000000000000E-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) = -3.339966260615722 " "
y[1] (numeric) = -3.3399662606157245 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.97773106429275500000000000000E-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) = -3.340251552812096 " "
y[1] (numeric) = -3.340251552812099 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 9.30655796367595400000000000000E-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) = -3.3405175103714964 " "
y[1] (numeric) = -3.340517510371499 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.9764145849487100000000000000E-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) = -3.3407641522752898 " "
y[1] (numeric) = -3.340764152275292 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.64652141857436000000000000000E-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) = -3.340991497768685 " "
y[1] (numeric) = -3.340991497768688 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.97528296878310600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (closed_form) = -3.341199566360558 " "
y[1] (numeric) = -3.341199566360561 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 9.30391737221654500000000000000E-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) = -3.341388377823277 " "
y[1] (numeric) = -3.3413883778232796 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.97433568867611700000000000000E-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) = -3.341557952192523 " "
y[1] (numeric) = -3.3415579521925265 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.0631908019040730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (closed_form) = -3.341708309767112 " "
y[1] (numeric) = -3.3417083097671156 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.06314296445822770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (closed_form) = -3.3418394711088104 " "
y[1] (numeric) = -3.3418394711088144 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.19598889270538150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = -3.3419514570421502 " "
y[1] (numeric) = -3.3419514570421542 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.19594881614109370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = -3.3420442886542423 " "
y[1] (numeric) = -3.3420442886542467 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.3287951071075910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (closed_form) = -3.342117987294586 " "
y[1] (numeric) = -3.342117987294591 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.46164238573307700000000000000E-13 "%"
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) = -3.342172574574878 " "
y[1] (numeric) = -3.342172574574883 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.46161851291358140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = -3.342208072368816 " "
y[1] (numeric) = -3.342208072368821 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.4616029889750160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = -3.342224502811903 " "
y[1] (numeric) = -3.3422245028119084 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.59446814949661870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (closed_form) = -3.342221888301249 " "
y[1] (numeric) = -3.3422218883012538 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.46159694706373270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (closed_form) = -3.3422002514953664 " "
y[1] (numeric) = -3.342200251495371 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.3287330992551039000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = -3.3421596153139697 " "
y[1] (numeric) = -3.342159615313975 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.59449910584241400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (closed_form) = -3.3421000029377677 " "
y[1] (numeric) = -3.3421000029377734 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.72740484215795460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = -3.342021437808254 " "
y[1] (numeric) = -3.3420214378082593 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.59456503118532740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (closed_form) = -3.341923943627496 " "
y[1] (numeric) = -3.3419239436275023 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86038014113282160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = -3.341807544357925 " "
y[1] (numeric) = -3.3418075443579314 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86044494046272850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = -3.3416722642221153 " "
y[1] (numeric) = -3.3416722642221224 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.12630886447957050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = -3.34151812770257 " "
y[1] (numeric) = -3.3415181277025767 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99350651206279120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = -3.341345159541499 " "
y[1] (numeric) = -3.341345159541506 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99360970797312380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = -3.341153384740597 " "
y[1] (numeric) = -3.3411533847406036 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99372413675288880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = -3.3409428285608183 " "
y[1] (numeric) = -3.340942828560825 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99384978719329110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = -3.3407135165221495 " "
y[1] (numeric) = -3.340713516522157 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.2598515347435388000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = -3.3404654744033797 " "
y[1] (numeric) = -3.3404654744033877 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.39296165116893360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = -3.3401987282418686 " "
y[1] (numeric) = -3.3401987282418757 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.12724689028936350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = -3.339913304333311 " "
y[1] (numeric) = -3.339913304333318 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99446438897330190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = -3.3396092292315034 " "
y[1] (numeric) = -3.3396092292315105 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.12762238629819330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = -3.3392865297481005 " "
y[1] (numeric) = -3.339286529748107 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99483874426715860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = -3.3389452329523786 " "
y[1] (numeric) = -3.338945232952385 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99504265059802070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = -3.3385853661709866 " "
y[1] (numeric) = -3.338585366170993 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99525769664257780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = -3.338206956987707 " "
y[1] (numeric) = -3.3382069569877126 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.72941935668971560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = -3.3378100332431995 " "
y[1] (numeric) = -3.337810033243205 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.5965769367116242000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = -3.3373946230347578 " "
y[1] (numeric) = -3.337394623034763 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.5967756648912330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = -3.3369607547160522 " "
y[1] (numeric) = -3.3369607547160585 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86314715542104520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = -3.336508456896877 " "
y[1] (numeric) = -3.3365084568968837 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99649970434851640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = -3.33603775844289 " "
y[1] (numeric) = -3.3360377584428966 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99678140059785990000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = -3.335548688475355 " "
y[1] (numeric) = -3.3355486884753622 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.13021245414613290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = -3.335041276370881 " "
y[1] (numeric) = -3.335041276370888 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 1.99737802195949470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = -3.334515551761154 " "
y[1] (numeric) = -3.3345155517611604 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86451340273917200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = -3.333971544532673 " "
y[1] (numeric) = -3.3339715445326794 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8648176371200420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = -3.3334092848264807 " "
y[1] (numeric) = -3.333409284826487 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8651321834979870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = -3.332828803037892 " "
y[1] (numeric) = -3.3328288030378976 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73221010415792940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = -3.3322301298162187 " "
y[1] (numeric) = -3.332230129816225 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86579218592077680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = -3.3316132960644977 " "
y[1] (numeric) = -3.331613296064504 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86613762925158970000000000000E-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) = -3.330978332939209 " "
y[1] (numeric) = -3.330978332939215 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73317240492424860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = -3.330325271849998 " "
y[1] (numeric) = -3.3303252718500036 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73351227186400920000000000000E-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) = -3.3296541444593895 " "
y[1] (numeric) = -3.3296541444593952 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73386167979562240000000000000E-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) = -3.3289649826825065 " "
y[1] (numeric) = -3.3289649826825127 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86762220997920140000000000000E-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) = -3.3282578186867817 " "
y[1] (numeric) = -3.3282578186867875 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73458909812723240000000000000E-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) = -3.3275326848916653 " "
y[1] (numeric) = -3.327532684891671 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73496709867442560000000000000E-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) = -3.3267896139683386 " "
y[1] (numeric) = -3.326789613968344 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.60186580354385740000000000000E-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) = -3.3260286388394134 " "
y[1] (numeric) = -3.326028638839419 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73575165909133720000000000000E-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) = -3.325249792678642 " "
y[1] (numeric) = -3.3252497926786484 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.86970884160031660000000000000E-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) = -3.3244531089106157 " "
y[1] (numeric) = -3.324453108910622 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8701569052776310000000000000E-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) = -3.3236386212104616 " "
y[1] (numeric) = -3.323638621210468 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.87061520413930230000000000000E-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) = -3.322806363503544 " "
y[1] (numeric) = -3.3228063635035503 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8710837339752330000000000000E-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) = -3.3219563699651573 " "
y[1] (numeric) = -3.321956369965163 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.7378794556869410000000000000E-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) = -3.3210886750202158 " "
y[1] (numeric) = -3.3210886750202215 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73833350836850900000000000000E-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) = -3.32020331334295 " "
y[1] (numeric) = -3.3202033133429563 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8725506696880662000000000000E-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) = -3.3193003198565885 " "
y[1] (numeric) = -3.3193003198565942 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.73927007855084530000000000000E-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) = -3.3183797297330453 " "
y[1] (numeric) = -3.3183797297330506 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.6059254673151768000000000000E-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) = -3.317441578392605 " "
y[1] (numeric) = -3.3174415783926112 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.87410954827222950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = -3.3164859015036035 " "
y[1] (numeric) = -3.3164859015036097 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8746495907255770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = -3.3155127349821063 " "
y[1] (numeric) = -3.3155127349821116 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.60731414540306730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = -3.3145221149915844 " "
y[1] (numeric) = -3.3145221149915893 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.47381165032989730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = -3.3135140779425893 " "
y[1] (numeric) = -3.313514077942595 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.7423072883503352000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = -3.3124886604924293 " "
y[1] (numeric) = -3.3124886604924346 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.60878151275196800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = -3.311445899544832 " "
y[1] (numeric) = -3.3114458995448373 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.60928811155672150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = -3.3103858322496182 " "
y[1] (numeric) = -3.3103858322496245 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.87810401957763940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = -3.309308496002366 " "
y[1] (numeric) = -3.309308496002373 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.14710334989449750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = -3.308213928444074 " "
y[1] (numeric) = -3.308213928444081 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.14781374823085960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = -3.3071021674608203 " "
y[1] (numeric) = -3.3071021674608274 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.14853578686276860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = -3.305973251183426 " "
y[1] (numeric) = -3.3059732511834334 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.28359880551017580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = -3.304827217987109 " "
y[1] (numeric) = -3.3048272179871168 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.2843907016867568000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = -3.303664106491139 " "
y[1] (numeric) = -3.3036641064911465 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.28519496053413730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = -3.3024839555584897 " "
y[1] (numeric) = -3.302483955558497 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.15154031123805660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = -3.3012868042954913 " "
y[1] (numeric) = -3.3012868042954975 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8832804619735740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = -3.300072692051474 " "
y[1] (numeric) = -3.3000726920514816 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.28768190035169960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = -3.29884165841842 " "
y[1] (numeric) = -3.2988416584184272 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.15391585693979340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = -3.297593743230601 " "
y[1] (numeric) = -3.2975937432306095 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 2.5587430242043440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = -3.296328986564225 " "
y[1] (numeric) = -3.296328986564232 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.15555770876104600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = -3.29504742873707 " "
y[1] (numeric) = -3.2950474287370763 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.8868465696968229000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = -3.293749110308127 " "
y[1] (numeric) = -3.293749110308133 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.75276244021838670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = -3.292434072077231 " "
y[1] (numeric) = -3.2924340720772367 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.75346251486471430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = -3.2911023550846954 " "
y[1] (numeric) = -3.2911023550847007 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.61923572810412030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = -3.289754000610942 " "
y[1] (numeric) = -3.289754000610947 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.6198993958852510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = -3.288389050176131 " "
y[1] (numeric) = -3.2883890501761357 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.48552413775038030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = -3.2870075455397827 " "
y[1] (numeric) = -3.287007545539788 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.62125290081304830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = -3.2856095287004097 " "
y[1] (numeric) = -3.285609528700414 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.35161894915041130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = -3.2841950418951305 " "
y[1] (numeric) = -3.284195041895135 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.35220108484727150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = -3.2827641275992945 " "
y[1] (numeric) = -3.2827641275993 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.623348590109620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = -3.2813168285260996 " "
y[1] (numeric) = -3.2813168285261036 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.21804845356729720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = -3.2798531876262036 " "
y[1] (numeric) = -3.279853187626208 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.35399112230225330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = -3.278373248087343 " "
y[1] (numeric) = -3.2783732480873478 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.49006258247155580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = -3.2768770533339415 " "
y[1] (numeric) = -3.2768770533339455 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.21969876305983450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = -3.275364647026719 " "
y[1] (numeric) = -3.2753646470267226 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.08467729906822780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = -3.2738360730622977 " "
y[1] (numeric) = -3.273836073062302 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.35647967686625240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = -3.272291375572813 " "
y[1] (numeric) = -3.2722913755728174 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.3571200082154208000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = -3.270730598925506 " "
y[1] (numeric) = -3.2707305989255118 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.7650979050207930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = -3.269153787722336 " "
y[1] (numeric) = -3.269153787722341 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.49426476255010380000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = -3.267560986799568 " "
y[1] (numeric) = -3.2675609867995723 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.3590846862357370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = -3.2659522412273776 " "
y[1] (numeric) = -3.265952241227382 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.3597541453428280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = -3.2643275963094407 " "
y[1] (numeric) = -3.264327596309445 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.3604308904294340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = -3.262687097582527 " "
y[1] (numeric) = -3.2626870975825315 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.36111492327630340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = -3.261030790816091 " "
y[1] (numeric) = -3.261030790816096 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.49798687031967440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = -3.25935872201186 " "
y[1] (numeric) = -3.2593587220118647 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.4987553457556838000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = -3.257670937403417 " "
y[1] (numeric) = -3.257670937403422 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.49953184413535250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = -3.25596748345579 " "
y[1] (numeric) = -3.255967483455795 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.50031636776848580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = -3.2542484068650284 " "
y[1] (numeric) = -3.2542484068650332 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.5011089190504120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = -3.2525137545577874 " "
y[1] (numeric) = -3.2525137545577913 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.22883504583179550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = -3.250763573690901 " "
y[1] (numeric) = -3.250763573690905 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.229496639188870100000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = -3.2489979116509633 " "
y[1] (numeric) = -3.2489979116509664 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 9.56794849822111800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = -3.247216816053895 " "
y[1] (numeric) = -3.2472168160538986 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.09407960110216920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = -3.245420334744522 " "
y[1] (numeric) = -3.2454203347445247 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 8.21013916309896600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = -3.243608515796139 " "
y[1] (numeric) = -3.2436085157961427 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.09529669240262560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = -3.2417814075100813 " "
y[1] (numeric) = -3.241781407510085 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.09591401522943460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = -3.2399390584152865 " "
y[1] (numeric) = -3.2399390584152896 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 9.5947004338745900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = -3.2380815172678603 " "
y[1] (numeric) = -3.2380815172678625 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.85728891446754100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = -3.2362088330506356 " "
y[1] (numeric) = -3.236208833050638 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.86125699483118300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = -3.2343210549727344 " "
y[1] (numeric) = -3.2343210549727353 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.746104683499371000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = -3.2324182324691213 " "
y[1] (numeric) = -3.2324182324691217 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.37386061428950600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = -3.2305004152001615 " "
y[1] (numeric) = -3.2305004152001624 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.749352439396277600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = -3.228567653051175 " "
y[1] (numeric) = -3.2285676530511758 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.750998322307874300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = -3.226619996131981 " "
y[1] (numeric) = -3.2266199961319817 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.75265888380056800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = -3.224657494776455 " "
y[1] (numeric) = -3.2246574947764564 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.13150119573410800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = -3.222680199542072 " "
y[1] (numeric) = -3.222680199542072 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = -3.2206881612094507 " "
y[1] (numeric) = -3.2206881612094502 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.378864353273170600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = -3.218681430781897 " "
y[1] (numeric) = -3.218681430781897 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = -3.2166600594849473 " "
y[1] (numeric) = -3.2166600594849464 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 2.761182105896327000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = -3.2146240987659045 " "
y[1] (numeric) = -3.214624098765903 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.14439632323308300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = -3.212573600293376 " "
y[1] (numeric) = -3.2125736002933745 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 4.14704157884047800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = -3.210508615956809 " "
y[1] (numeric) = -3.2105086159568073 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.53294524914661600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = -3.2084291978660238 " "
y[1] (numeric) = -3.208429197866022 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 5.53653121154031600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = -3.2063353983507437 " "
y[1] (numeric) = -3.2063353983507414 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.92518334292929300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = -3.2042272699601257 " "
y[1] (numeric) = -3.2042272699601235 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.92973956643825900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = -3.2021048654622843 " "
y[1] (numeric) = -3.202104865462282 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.93433270471530800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = -3.1999682378438217 " "
y[1] (numeric) = -3.1999682378438195 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 6.93896277778831100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = -3.197817440309346 " "
y[1] (numeric) = -3.197817440309343 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 9.7210817283231800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = -3.1956525262809947 " "
y[1] (numeric) = -3.195652526280991 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.11173340955659020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = -3.193473549397954 " "
y[1] (numeric) = -3.19347354939795 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.25155346578776470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = -3.1912805635159756 " "
y[1] (numeric) = -3.191280563515971 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 1.39157056551865750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = -3.189073622706892 " "
y[1] (numeric) = -3.1890736227068865 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.67104029215776630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = -3.186852781258129 " "
y[1] (numeric) = -3.1868527812581235 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.67220480015299070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = -3.1846180936722197 " "
y[1] (numeric) = -3.184618093672213 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.09172275978300240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = -3.1823696146663103 " "
y[1] (numeric) = -3.1823696146663036 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.09320065056284140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = -3.1801073991716717 " "
y[1] (numeric) = -3.1801073991716646 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 2.23433565779940800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = -3.1778315023332016 " "
y[1] (numeric) = -3.1778315023331936 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.5154278228509370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = -3.17554197950893 " "
y[1] (numeric) = -3.1755419795089215 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 2.6570881574225030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = -3.1732388862695204 " "
y[1] (numeric) = -3.1732388862695124 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.5190683915696177000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = -3.170922278397771 " "
y[1] (numeric) = -3.170922278397763 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.52090876895923130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = -3.168592211888109 " "
y[1] (numeric) = -3.1685922118881016 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.38260907766116050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = -3.166248742946093 " "
y[1] (numeric) = -3.1662487429460855 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.3843725431459570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = -3.1638919279878994 " "
y[1] (numeric) = -3.163891927987892 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.3861486862644632000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = -3.161521823639821 " "
y[1] (numeric) = -3.161521823639813 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.52840442774429000000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = -3.159138486737754 " "
y[1] (numeric) = -3.1591384867377466 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.3897390377612032000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = -3.1567419743266885 " "
y[1] (numeric) = -3.1567419743266805 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 2.53223286613601330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = -3.154332343660193 " "
y[1] (numeric) = -3.1543323436601844 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 2.6749543383118407000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = -3.1519096521998993 " "
y[1] (numeric) = -3.15190965219989 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 2.95880099238956640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = -3.1494739576149886 " "
y[1] (numeric) = -3.149473957614979 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 3.1020934759847660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = -3.147025317781668 " "
y[1] (numeric) = -3.147025317781659 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 2.82227923201520500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = -3.1445637907826525 " "
y[1] (numeric) = -3.144563790782643 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 2.96571290243413800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = -3.1420894349066426 " "
y[1] (numeric) = -3.1420894349066324 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.2507196367740937000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = -3.1396023086477958 " "
y[1] (numeric) = -3.1396023086477856 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.2532947878199770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = -3.137102470705205 " "
y[1] (numeric) = -3.1371024707051944 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 3.3974475287081090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = -3.1345899799823678 " "
y[1] (numeric) = -3.1345899799823567 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.5418444891200780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = -3.1320648955866552 " "
y[1] (numeric) = -3.132064895586645 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.26112394444441500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = -3.1295272768287834 " "
y[1] (numeric) = -3.1295272768287736 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 3.12186530184248400000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = -3.1269771832222766 " "
y[1] (numeric) = -3.126977183222267 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 3.1244112266382640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = -3.1244146744829324 " "
y[1] (numeric) = -3.1244146744829226 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 3.12697373254983650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = -3.121839810528284 " "
y[1] (numeric) = -3.1218398105282734 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 3.4140576337252590000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = -3.119252651477062 " "
y[1] (numeric) = -3.1192526514770518 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.27451892097126940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = -3.116653257648653 " "
y[1] (numeric) = -3.1166532576486428 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.27724998008196540000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = -3.1140416895625553 " "
y[1] (numeric) = -3.1140416895625447 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 3.42260704862262230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = -3.1114180079378375 " "
y[1] (numeric) = -3.1114180079378264 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.5682220190047110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = -3.1087822736925874 " "
y[1] (numeric) = -3.1087822736925763 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 3.5712472823207470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = -3.106134547943368 " "
y[1] (numeric) = -3.1061345479433564 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 3.7172631377950680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = -3.103474892004664 " "
y[1] (numeric) = -3.1034748920046527 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 3.72044880590072350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = -3.1008033673883344 " "
y[1] (numeric) = -3.100803367388323 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 3.7236541915350690000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = -3.0981200358030527 " "
y[1] (numeric) = -3.098120035803041 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 3.7268793083121280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = -3.095424959153758 " "
y[1] (numeric) = -3.095424959153746 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.873590484076760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = -3.092718199541093 " "
y[1] (numeric) = -3.092718199541081 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.8769806663054085000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = -3.0899998192608478 " "
y[1] (numeric) = -3.089999819260836 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 3.88039138100010950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = -3.0872698808033983 " "
y[1] (numeric) = -3.0872698808033854 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 4.1715132083951240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = -3.084528446853142 " "
y[1] (numeric) = -3.0845284468531298 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 4.03124759263851660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = -3.08177558028794 " "
y[1] (numeric) = -3.0817755802879265 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 4.32305206800850160000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = -3.079011344178541 " "
y[1] (numeric) = -3.0790113441785274 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 4.47116426881006450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = -3.0762358017880254 " "
y[1] (numeric) = -3.076235801788011 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 4.6195596276924260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = -3.0734490165712254 " "
y[1] (numeric) = -3.07344901657121 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0572247208096780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = -3.070651052174161 " "
y[1] (numeric) = -3.0706510521741452 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0618328428256130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = -3.0678419724334627 " "
y[1] (numeric) = -3.067841972433447 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0664677269615450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = -3.0650218413758017 " "
y[1] (numeric) = -3.065021841375786 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0711293912918170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = -3.0621907232173085 " "
y[1] (numeric) = -3.062190723217293 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0758178538343020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = -3.059348682362998 " "
y[1] (numeric) = -3.059348682362982 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 5.225691222045981000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = -3.05649578340619 " "
y[1] (numeric) = -3.056495783406174 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 5.2305688237482020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = -3.0536320911279264 " "
y[1] (numeric) = -3.053632091127911 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0900442099463900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = -3.050757670496389 " "
y[1] (numeric) = -3.0507576704963735 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.0948400441858650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = -3.0478725866663146 " "
y[1] (numeric) = -3.0478725866662986 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 5.2453674161257040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = -3.044976904978408 " "
y[1] (numeric) = -3.0449769049783924 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 5.1045123919790150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = -3.0420706909587567 " "
y[1] (numeric) = -3.0420706909587403 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 5.401354022865830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = -3.039154010318237 " "
y[1] (numeric) = -3.0391540103182195 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 5.6987829920270740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = -3.0362269289519235 " "
y[1] (numeric) = -3.0362269289519066 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 5.5580134058449980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = -3.0332895129385014 " "
y[1] (numeric) = -3.0332895129384836 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 5.8562060489880630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = -3.0303418285396644 " "
y[1] (numeric) = -3.030341828539646 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 6.0084500805728970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = -3.0273839421995214 " "
y[1] (numeric) = -3.0273839421995032 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 6.0143205987357980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = -3.0244159205440004 " "
y[1] (numeric) = -3.024415920543981 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 6.4607268797500960000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = -3.021437830380246 " "
y[1] (numeric) = -3.0214378303802265 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 6.4670949165098880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = -3.018449738696019 " "
y[1] (numeric) = -3.0184497386959994 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 6.473496968627370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = -3.015451712659095 " "
y[1] (numeric) = -3.0154517126590754 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 6.4799330565873980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = -3.0124438196166574 " "
y[1] (numeric) = -3.0124438196166374 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 6.6338214552316020000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = -3.009426127094692 " "
y[1] (numeric) = -3.009426127094672 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 6.6404734986950610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = -3.006398702797382 " "
y[1] (numeric) = -3.0063987027973624 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 6.4994457372607710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = -3.003361614606495 " "
y[1] (numeric) = -3.0033616146064746 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 6.8017462678330860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = -3.0003149305807733 " "
y[1] (numeric) = -3.0003149305807524 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 6.9566673318899550000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = -2.997258718955322 " "
y[1] (numeric) = -2.9972587189553006 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 7.1119259535368630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = -2.9941930481409944 " "
y[1] (numeric) = -2.994193048140973 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 7.1192076563124920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = -2.9911179867237765 " "
y[1] (numeric) = -2.9911179867237556 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 6.9780573536701630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = -2.98803360346417 " "
y[1] (numeric) = -2.9880336034641486 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 7.1338829818011480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = -2.9849399672965715 " "
y[1] (numeric) = -2.98493996729655 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 7.1412766442029770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = -2.981837147328655 " "
y[1] (numeric) = -2.9818371473286343 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 6.9997762559406570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = -2.978725212840749 " "
y[1] (numeric) = -2.978725212840728 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 7.0070890637970470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = -2.9756042332852113 " "
y[1] (numeric) = -2.9756042332851895 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 7.3129252335511570000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = -2.972474278285805 " "
y[1] (numeric) = -2.9724742782857834 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 7.3206255951866640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = -2.9693354176370743 " "
y[1] (numeric) = -2.9693354176370517 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 7.6274810746629520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = -2.9661877213037107 " "
y[1] (numeric) = -2.966187721303688 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 7.6355753008102310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = -2.9630312594199295 " "
y[1] (numeric) = -2.9630312594199064 " "
absolute error = 2.309263891220325600000000000000E-14 " "
relative error = 7.7935859902889060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = -2.9598661022888355 " "
y[1] (numeric) = -2.959866102288812 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 7.9519570509803130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = -2.9566923203817894 " "
y[1] (numeric) = -2.9566923203817654 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 8.1106908441547980000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = -2.9535099843377757 " "
y[1] (numeric) = -2.9535099843377512 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 8.2697897319720410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = -2.9503191649627647 " "
y[1] (numeric) = -2.95031916496274 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 8.429256077424211000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = -2.947119933229079 " "
y[1] (numeric) = -2.947119933229053 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 8.890463901971469000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = -2.9439123602747497 " "
y[1] (numeric) = -2.9439123602747235 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 8.9001506073055730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = -2.9406965174028805 " "
y[1] (numeric) = -2.940696517402854 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 9.0608984753503210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = -2.937472476081004 " "
y[1] (numeric) = -2.9374724760809774 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 9.0708433212461460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = -2.9342403079404376 " "
y[1] (numeric) = -2.9342403079404105 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 9.2321824247135630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = -2.931000084775641 " "
y[1] (numeric) = -2.9310000847756132 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 9.3939031778675270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = -2.9277518785435683 " "
y[1] (numeric) = -2.9277518785435404 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 9.5560079478017850000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = -2.9244957613630227 " "
y[1] (numeric) = -2.9244957613629947 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 9.5666475534621350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = -2.921231805514003 " "
y[1] (numeric) = -2.921231805513975 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 9.5773365769003620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = -2.917960083437059 " "
y[1] (numeric) = -2.917960083437031 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 9.5880750320611530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = -2.9146806677326342 " "
y[1] (numeric) = -2.914680667732606 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 9.7512258358352520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = -2.911393631160415 " "
y[1] (numeric) = -2.9113936311603865 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 9.7622352148499280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = -2.908099046638677 " "
y[1] (numeric) = -2.908099046638648 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 9.9260025801454620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = -2.904796987243625 " "
y[1] (numeric) = -2.904796987243596 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 9.9372860709432760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = -2.901487526208739 " "
y[1] (numeric) = -2.9014875262087094 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.02547320266555000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = -2.898170736924113 " "
y[1] (numeric) = -2.8981707369240826 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 1.0572929706748559000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = -2.8948466929357966 " "
y[1] (numeric) = -2.8948466929357655 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 1.0738477020342103000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = -2.891515467945129 " "
y[1] (numeric) = -2.891515467945098 " "
absolute error = 3.10862446895043830000000000000E-14 " "
relative error = 1.0750848485550725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = -2.88817713580808 " "
y[1] (numeric) = -2.8881771358080486 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 1.0917036046174712000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = -2.8848317705345843 " "
y[1] (numeric) = -2.8848317705345523 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.1083635252422144000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = -2.881479446287872 " "
y[1] (numeric) = -2.88147944628784 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.1096529996212968000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = -2.878120237383808 " "
y[1] (numeric) = -2.878120237383775 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.157237640948254900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = -2.8747542182902146 " "
y[1] (numeric) = -2.8747542182901813 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.1585926381756609000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = -2.871381463626208 " "
y[1] (numeric) = -2.871381463626175 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 1.1444874860828537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = -2.8680020481615243 " "
y[1] (numeric) = -2.8680020481614923 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.114867513072422000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = -2.8646160468158466 " "
y[1] (numeric) = -2.864616046815814 " "
absolute error = 3.24185123190545700000000000000E-14 " "
relative error = 1.1316878698312553000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = -2.8612235346581314 " "
y[1] (numeric) = -2.861223534658098 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.1640716055669623000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = -2.85782458690593 " "
y[1] (numeric) = -2.8578245869058967 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.1654560917195664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = -2.854419278924717 " "
y[1] (numeric) = -2.8544192789246834 " "
absolute error = 3.37507799486047600000000000000E-14 " "
relative error = 1.1824044280319938000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = -2.8510076862272076 " "
y[1] (numeric) = -2.851007686227173 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.2149724651967975000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = -2.8475898844726784 " "
y[1] (numeric) = -2.8475898844726437 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.2164307282163066000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = -2.844165949466289 " "
y[1] (numeric) = -2.844165949466254 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.2335091623165774000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = -2.8407359571583974 " "
y[1] (numeric) = -2.840735957158363 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.2193656464627713000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = -2.8372999836438773 " "
y[1] (numeric) = -2.837299983643842 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.236494124005126000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = -2.833858105161433 " "
y[1] (numeric) = -2.8338581051613976 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.2536667493442186000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = -2.8304103980929147 " "
y[1] (numeric) = -2.830410398092878 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.3022636025641537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = -2.826956938962627 " "
y[1] (numeric) = -2.8269569389625904 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 1.288145380136848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = -2.823497804436644 " "
y[1] (numeric) = -2.8234978044366077 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 1.289723517775884000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = -2.820033071322121 " "
y[1] (numeric) = -2.8200330713220843 " "
absolute error = 3.6859404417555197000000000000E-14 " "
relative error = 1.3070557502460190000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = -2.8165628165665977 " "
y[1] (numeric) = -2.81656281656656 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.3402002829558687000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = -2.813087117257308 " "
y[1] (numeric) = -2.81308711725727 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 1.357642705510711000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = -2.809606050620489 " "
y[1] (numeric) = -2.8096060506204505 " "
absolute error = 3.86357612569554500000000000000E-14 " "
relative error = 1.3751309102008416000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = -2.8061196940206816 " "
y[1] (numeric) = -2.8061196940206434 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 1.3610136491499178000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = -2.802628124960038 " "
y[1] (numeric) = -2.8026281249599987 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.4102455950062630000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = -2.7991314210776204 " "
y[1] (numeric) = -2.79913142107758 " "
absolute error = 4.0412118096355700000000000000E-14 " "
relative error = 1.4437377892316924000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = -2.795629660148706 " "
y[1] (numeric) = -2.795629660148665 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.4614313150488080000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = -2.7921229200840845 " "
y[1] (numeric) = -2.7921229200840427 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.4950769332407743000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = -2.7886112789293582 " "
y[1] (numeric) = -2.788611278929316 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 1.5128847557395497000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = -2.7850948148642383 " "
y[1] (numeric) = -2.785094814864196 " "
absolute error = 4.21884749357559500000000000000E-14 " "
relative error = 1.514794925852909000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = -2.7815736062018432 " "
y[1] (numeric) = -2.7815736062018006 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.5326779075898525000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = -2.7780477313879923 " "
y[1] (numeric) = -2.7780477313879492 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 1.5506088275140523000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = -2.7745172690004996 " "
y[1] (numeric) = -2.7745172690004556 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.5845939135565093000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = -2.770982297748467 " "
y[1] (numeric) = -2.7709822977484238 " "
absolute error = 4.307665335545607400000000000000E-14 " "
relative error = 1.5545625603764257000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = -2.767442896471578 " "
y[1] (numeric) = -2.7674428964715343 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.5725976720529275000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = -2.7638991441393834 " "
y[1] (numeric) = -2.7638991441393395 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.590681478677684000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = -2.7603511198505952 " "
y[1] (numeric) = -2.7603511198505513 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.592726065136808000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = -2.7567989028323736 " "
y[1] (numeric) = -2.756798902832329 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 1.6108872119536870000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = -2.7532425724396115 " "
y[1] (numeric) = -2.7532425724395666 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.6290976553915723000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = -2.7496822081542227 " "
y[1] (numeric) = -2.749682208154177 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.6635081857427117000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = -2.746117889584426 " "
y[1] (numeric) = -2.7461178895843794 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.69801038808691020000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = -2.742549696464029 " "
y[1] (numeric) = -2.7425496964639824 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.7002195837827785000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = -2.73897770865171 " "
y[1] (numeric) = -2.7389777086516633 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.7024368941363294000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = -2.7354020061302995 " "
y[1] (numeric) = -2.7354020061302515 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 1.7533669477583227000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = -2.7318226690060596 " "
y[1] (numeric) = -2.7318226690060112 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.771920425979504000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = -2.728239777507964 " "
y[1] (numeric) = -2.7282397775079157 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.7742474203595004000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = -2.724653411986977 " "
y[1] (numeric) = -2.7246534119869286 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.7765827998782618000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = -2.7210636529153267 " "
y[1] (numeric) = -2.721063652915278 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 1.7952469811270153000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = -2.7174705808857853 " "
y[1] (numeric) = -2.717470580885735 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 1.8466466966019462000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = -2.71387427661094 " "
y[1] (numeric) = -2.7138742766108894 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.8654574517036437000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = -2.7102748209224687 " "
y[1] (numeric) = -2.7102748209224177 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.884320318312773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = -2.706672294770412 " "
y[1] (numeric) = -2.7066722947703608 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 1.886828310594916000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = -2.703066779222444 " "
y[1] (numeric) = -2.7030667792223926 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.905774165055061000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = -2.699458355463145 " "
y[1] (numeric) = -2.699458355463093 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 1.9247727029129458000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = -2.695847104793266 " "
y[1] (numeric) = -2.6958471047932138 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.943824138584667000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = -2.6922331086290034 " "
y[1] (numeric) = -2.692233108628951 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 1.946433486548753100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = -2.6886164485012616 " "
y[1] (numeric) = -2.688616448501208 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 1.998603944486444800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = -2.68499720605492 " "
y[1] (numeric) = -2.6849972060548657 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 2.0178376156045597000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = -2.6813754630480986 " "
y[1] (numeric) = -2.6813754630480444 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 2.0205631157718912000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = -2.6777513013514245 " "
y[1] (numeric) = -2.6777513013513703 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 2.0232978161326742000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = -2.6741248029472904 " "
y[1] (numeric) = -2.6741248029472358 " "
absolute error = 5.4622972811557700000000000000E-14 " "
relative error = 2.042648598575313700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = -2.670496049929121 " "
y[1] (numeric) = -2.6704960499290658 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 2.062053678112324200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = -2.666865124500631 " "
y[1] (numeric) = -2.6668651245005757 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 2.0815132614422055000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = -2.6632321089750883 " "
y[1] (numeric) = -2.6632321089750333 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 2.0676779104544377000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = -2.659597085774571 " "
y[1] (numeric) = -2.6595970857745153 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 2.1038991484987168000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = -2.655960137429225 " "
y[1] (numeric) = -2.6559601374291693 " "
absolute error = 5.59552404411078900000000000000E-14 " "
relative error = 2.106780130189321000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = -2.6523213465765245 " "
y[1] (numeric) = -2.652321346576468 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 2.126413894898339000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = -2.6486807959605247 " "
y[1] (numeric) = -2.6486807959604675 " "
absolute error = 5.72875080706580800000000000000E-14 " "
relative error = 2.162869461583542300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = -2.6450385684311186 " "
y[1] (numeric) = -2.645038568431061 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 2.1826372579039985000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = -2.641394746943292 " "
y[1] (numeric) = -2.641394746943234 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 2.2024608990262057000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = -2.6377494145563762 " "
y[1] (numeric) = -2.637749414556317 " "
absolute error = 5.90638649100583300000000000000E-14 " "
relative error = 2.239176495845866800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = -2.6341026544333004 " "
y[1] (numeric) = -2.6341026544332413 " "
absolute error = 5.90638649100583300000000000000E-14 " "
relative error = 2.2422765039415407000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = -2.6304545498398433 " "
y[1] (numeric) = -2.6304545498397833 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 2.2791514619938466000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = -2.6268051841438824 " "
y[1] (numeric) = -2.6268051841438225 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 2.2823178396192245000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = -2.623154640814649 " "
y[1] (numeric) = -2.6231546408145885 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 2.302423639074967200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = -2.6195030034219675 " "
y[1] (numeric) = -2.619503003421908 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 2.2717268902601234000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = -2.615850355635514 " "
y[1] (numeric) = -2.615850355635454 " "
absolute error = 5.99520433297584500000000000000E-14 " "
relative error = 2.2918758789316626000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = -2.612196781224054 " "
y[1] (numeric) = -2.6121967812239935 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 2.312082036610863300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = -2.6085423640546948 " "
y[1] (numeric) = -2.6085423640546344 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 2.3153211299865303000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = -2.604887188092129 " "
y[1] (numeric) = -2.6048871880920683 " "
absolute error = 6.08402217494585800000000000000E-14 " "
relative error = 2.335618295778066000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = -2.601231337397876 " "
y[1] (numeric) = -2.601231337397815 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 2.3559731146639953000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = -2.5975748961295295 " "
y[1] (numeric) = -2.597574896129468 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 2.376385768939175000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = -2.593917948539997 " "
y[1] (numeric) = -2.593917948539935 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 2.3968564392718333000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = -2.590260578976745 " "
y[1] (numeric) = -2.5902605789766824 " "
absolute error = 6.26165785888588300000000000000E-14 " "
relative error = 2.4173853046705765000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = -2.586602871881035 " "
y[1] (numeric) = -2.5866028718809715 " "
absolute error = 6.35047570085589500000000000000E-14 " "
relative error = 2.4551413631724953000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = -2.582944911787168 " "
y[1] (numeric) = -2.582944911787103 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 2.5101977336887027000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = -2.579286783321721 " "
y[1] (numeric) = -2.579286783321655 " "
absolute error = 6.61692922676593300000000000000E-14 " "
relative error = 2.565410434214824000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = -2.575628571202787 " "
y[1] (numeric) = -2.5756285712027203 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 2.5862961073770730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = -2.571970360239211 " "
y[1] (numeric) = -2.5719703602391437 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 2.6245076903192380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = -2.568312235329828 " "
y[1] (numeric) = -2.5683122353297603 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 2.6455369472759555000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = -2.5646542814626994 " "
y[1] (numeric) = -2.5646542814626314 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 2.6493102636940270000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = -2.5609965837143456 " "
y[1] (numeric) = -2.5609965837142767 " "
absolute error = 6.8833827526759700000000000000E-14 " "
relative error = 2.68777506243005000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = -2.557339227248982 " "
y[1] (numeric) = -2.5573392272489133 " "
absolute error = 6.8833827526759700000000000000E-14 " "
relative error = 2.6916189605712426000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = -2.5536822973177538 " "
y[1] (numeric) = -2.553682297317684 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 2.730253721055746000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = -2.5500258792579653 " "
y[1] (numeric) = -2.550025879257896 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 2.716753476900753000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = -2.5463700584923155 " "
y[1] (numeric) = -2.5463700584922457 " "
absolute error = 6.97220059464598300000000000000E-14 " "
relative error = 2.7380940061689880000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = -2.5427149205281276 " "
y[1] (numeric) = -2.5427149205280575 " "
absolute error = 7.01660951563098900000000000000E-14 " "
relative error = 2.7594951596750860000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = -2.5390605509565787 " "
y[1] (numeric) = -2.539060550956508 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 2.7809570882253243000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = -2.53540703545193 " "
y[1] (numeric) = -2.5354070354518594 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 2.784964440771691000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = -2.5317544597707577 " "
y[1] (numeric) = -2.5317544597706867 " "
absolute error = 7.10542735760100200000000000000E-14 " "
relative error = 2.8065230931772017000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = -2.5281029097511785 " "
y[1] (numeric) = -2.5281029097511065 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 2.8457089985625184000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = -2.5244524713120775 " "
y[1] (numeric) = -2.5244524713120056 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 2.849823984141727000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = -2.5208032304523367 " "
y[1] (numeric) = -2.5208032304522647 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 2.853949531903793000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = -2.517155273250059 " "
y[1] (numeric) = -2.517155273249986 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 2.893370591372936300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = -2.5135086858617948 " "
y[1] (numeric) = -2.513508685861721 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 2.932904479295037000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = -2.5098635545217656 " "
y[1] (numeric) = -2.5098635545216914 " "
absolute error = 7.41628980449604600000000000000E-14 " "
relative error = 2.954857761544396000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = -2.5062199655410886 " "
y[1] (numeric) = -2.506219965541015 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 2.9414341058924026000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = -2.5025780053070013 " "
y[1] (numeric) = -2.5025780053069258 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 3.0166958038636390000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = -2.498937760282079 " "
y[1] (numeric) = -2.498937760282003 " "
absolute error = 7.59392548843607100000000000000E-14 " "
relative error = 3.038861395082874000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = -2.4952993170034627 " "
y[1] (numeric) = -2.4952993170033864 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 3.0610894482164750000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = -2.4916627620820773 " "
y[1] (numeric) = -2.491662762082001 " "
absolute error = 7.63833440942107700000000000000E-14 " "
relative error = 3.065557075243341000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = -2.488028182201851 " "
y[1] (numeric) = -2.488028182201775 " "
absolute error = 7.59392548843607100000000000000E-14 " "
relative error = 3.0521862825989426000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = -2.4843956641189378 " "
y[1] (numeric) = -2.4843956641188636 " "
absolute error = 7.41628980449604600000000000000E-14 " "
relative error = 2.9851484252715220000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = -2.4807652946609355 " "
y[1] (numeric) = -2.4807652946608627 " "
absolute error = 7.28306304154102700000000000000E-14 " "
relative error = 2.9358130159332374000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = -2.4771371607261057 " "
y[1] (numeric) = -2.477137160726034 " "
absolute error = 7.14983627858600800000000000000E-14 " "
relative error = 2.886330394595601000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = -2.473511349282587 " "
y[1] (numeric) = -2.4735113492825165 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 2.8546537450349524000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = -2.4698879473676176 " "
y[1] (numeric) = -2.469887947367549 " "
absolute error = 6.8833827526759700000000000000E-14 " "
relative error = 2.7869210666063665000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = -2.46626704208675 " "
y[1] (numeric) = -2.4662670420866815 " "
absolute error = 6.83897383169096400000000000000E-14 " "
relative error = 2.773006213432749300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = -2.462648720613065 " "
y[1] (numeric) = -2.4626487206129974 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 2.741014556083554000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = -2.459033070186391 " "
y[1] (numeric) = -2.459033070186326 " "
absolute error = 6.5281113847959200000000000000E-14 " "
relative error = 2.65474729231726000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = -2.4554201781125173 " "
y[1] (numeric) = -2.455420178112453 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 2.622481317138884000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = -2.4518101317624064 " "
y[1] (numeric) = -2.4518101317623424 " "
absolute error = 6.39488462184090200000000000000E-14 " "
relative error = 2.6082299518210006000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = -2.4482030185714088 " "
y[1] (numeric) = -2.4482030185713466 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 2.539515265171434000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = -2.4445989260384793 " "
y[1] (numeric) = -2.444598926038418 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 2.5069270180291325000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = -2.440997941725384 " "
y[1] (numeric) = -2.4409979417253247 " "
absolute error = 5.95079541199083900000000000000E-14 " "
relative error = 2.437853514855733700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = -2.4374001532559166 " "
y[1] (numeric) = -2.437400153255858 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 2.4050123908420643000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = -2.4338056483151074 " "
y[1] (numeric) = -2.43380564831505 " "
absolute error = 5.72875080706580800000000000000E-14 " "
relative error = 2.3538242714785995000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = -2.4302145146484344 " "
y[1] (numeric) = -2.430214514648378 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 2.320755197164845000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = -2.4266268400610356 " "
y[1] (numeric) = -2.4266268400609805 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 2.269284304958181800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = -2.423042712416916 " "
y[1] (numeric) = -2.423042712416862 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 2.2176577456308497000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = -2.419462219638158 " "
y[1] (numeric) = -2.4194622196381057 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 2.165874975726814000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = -2.4158854497041315 " "
y[1] (numeric) = -2.4158854497040805 " "
absolute error = 5.1070259132757200000000000000E-14 " "
relative error = 2.1139354574535674000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = -2.4123124906506996 " "
y[1] (numeric) = -2.4123124906506503 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 2.043429385057006800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = -2.408743430569428 " "
y[1] (numeric) = -2.4087434305693805 " "
absolute error = 4.7517545453956700000000000000E-14 " "
relative error = 1.972710951731523000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = -2.4051783576067907 " "
y[1] (numeric) = -2.4051783576067436 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.95717112185168000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = -2.4016173599633777 " "
y[1] (numeric) = -2.4016173599633324 " "
absolute error = 4.52970994047063870000000000000E-14 " "
relative error = 1.886108093647238000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = -2.3980605258931034 " "
y[1] (numeric) = -2.3980605258930585 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.870386911028937800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = -2.3945079437024064 " "
y[1] (numeric) = -2.3945079437023624 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.836069572906800800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = -2.3909597017494613 " "
y[1] (numeric) = -2.3909597017494195 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 1.7459259432671154000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = -2.3874158884433787 " "
y[1] (numeric) = -2.387415888443338 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.7113150458609228000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = -2.3838765922434124 " "
y[1] (numeric) = -2.3838765922433724 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 1.676598067892962000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = -2.380341901658162 " "
y[1] (numeric) = -2.380341901658123 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.6417746727721017000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = -2.3768119052447756 " "
y[1] (numeric) = -2.3768119052447374 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 1.6068445282872404000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = -2.373286691608155 " "
y[1] (numeric) = -2.3732866916081186 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 1.5343833231976653000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = -2.3697663494001566 " "
y[1] (numeric) = -2.3697663494001215 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.480443318263646200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = -2.3662509673187935 " "
y[1] (numeric) = -2.36625096731876 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.4075721974873448000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = -2.3627406341074373 " "
y[1] (numeric) = -2.3627406341074058 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 1.3344813833645996000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = -2.3592354385540215 " "
y[1] (numeric) = -2.359235438553991 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 1.2988171921677702000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = -2.355735469490239 " "
y[1] (numeric) = -2.355735469490209 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.2630440660806752000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = -2.352240815790744 " "
y[1] (numeric) = -2.3522408157907155 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.2082822999927237000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = -2.348751566372354 " "
y[1] (numeric) = -2.348751566372327 " "
absolute error = 2.70894418008538200000000000000E-14 " "
relative error = 1.1533549221935573000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = -2.3452678101932465 " "
y[1] (numeric) = -2.345267810193221 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 1.0793259879078719000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = -2.3417896362521606 " "
y[1] (numeric) = -2.341789636252137 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 1.0050743994119768000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = -2.3383171335875956 " "
y[1] (numeric) = -2.3383171335875734 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 9.4959148926200740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = -2.3348503912770076 " "
y[1] (numeric) = -2.334850391276987 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 8.7492131099372360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = -2.331389498436011 " "
y[1] (numeric) = -2.331389498435992 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 8.0002705795041830000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = -2.327934544217574 " "
y[1] (numeric) = -2.3279345442175567 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 7.4398480091172710000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = -2.324485617811219 " "
y[1] (numeric) = -2.3244856178112028 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 7.0687900318885810000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = -2.3210428084422157 " "
y[1] (numeric) = -2.3210428084422 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 6.6966116644716560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = -2.3176062053707813 " "
y[1] (numeric) = -2.317606205370767 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 6.1316951440110970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = -2.3141758978912774 " "
y[1] (numeric) = -2.3141758978912645 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 5.5650856520401240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = -2.3107519753314034 " "
y[1] (numeric) = -2.3107519753313923 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 4.8045962374041910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = -2.307334527051396 " "
y[1] (numeric) = -2.307334527051386 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 4.2343069468936840000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = -2.3039236424432223 " "
y[1] (numeric) = -2.3039236424432135 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.8550688197211530000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = -2.300519410929777 " "
y[1] (numeric) = -2.300519410929769 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.4746960792086670000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = -2.297121921964076 " "
y[1] (numeric) = -2.297121921964069 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.09318686555642150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = -2.2937312650284536 " "
y[1] (numeric) = -2.293731265028448 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 2.51692943112897640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = -2.2903475296337543 " "
y[1] (numeric) = -2.2903475296337503 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 1.74506394201655760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = -2.2869708053185307 " "
y[1] (numeric) = -2.286970805318528 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.16509369201556440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = -2.2836011816482333 " "
y[1] (numeric) = -2.2836011816482316 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 7.77875249704561100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = -2.2802387482144084 " "
y[1] (numeric) = -2.2802387482144084 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = -2.27688359463389 " "
y[1] (numeric) = -2.276883594633891 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.900851241553871500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = -2.2735358105479926 " "
y[1] (numeric) = -2.273535810547995 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 9.76648812369098700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = -2.270195485621706 " "
y[1] (numeric) = -2.2701954856217093 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.3693201702844210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = -2.2668627095428873 " "
y[1] (numeric) = -2.266862709542891 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.56723813217471170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = -2.2635375720214532 " "
y[1] (numeric) = -2.263537572021458 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 2.1581180576508630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = -2.260220162788575 " "
y[1] (numeric) = -2.260220162788581 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 2.7507271372317410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = -2.2569105715958684 " "
y[1] (numeric) = -2.2569105715958755 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.14829814128467330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = -2.2536088882145866 " "
y[1] (numeric) = -2.2536088882145946 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 3.54702442784294860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = -2.2503152024348125 " "
y[1] (numeric) = -2.2503152024348214 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.94690672106346450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = -2.2470296040646507 " "
y[1] (numeric) = -2.247029604064662 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 4.9408473418279610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = -2.24375218292942 " "
y[1] (numeric) = -2.2437521829294313 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 5.1459869516547370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = -2.240483028870842 " "
y[1] (numeric) = -2.2404830288708557 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 6.1445524594266230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = -2.237222231746237 " "
y[1] (numeric) = -2.2372222317462516 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 6.5505088037737440000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = -2.233969881427711 " "
y[1] (numeric) = -2.2339698814277265 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 6.9576239473822780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = -2.230726067801349 " "
y[1] (numeric) = -2.230726067801366 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 7.5649763625773740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = -2.2274908807664073 " "
y[1] (numeric) = -2.2274908807664255 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 8.1740660583929770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = -2.2242644102345017 " "
y[1] (numeric) = -2.2242644102345204 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 8.3855798473780360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = -2.2210467461287986 " "
y[1] (numeric) = -2.2210467461288186 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 8.9975658900850270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = -2.217837978383209 " "
y[1] (numeric) = -2.2178379783832294 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 9.2108187578223580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = -2.214638196941573 " "
y[1] (numeric) = -2.2146381969415954 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.0026224835807315000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = -2.211447491756859 " "
y[1] (numeric) = -2.2114474917568816 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 1.0241504619384073000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = -2.2082659527903434 " "
y[1] (numeric) = -2.2082659527903674 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 1.0859569383661173000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = -2.20509367001081 " "
y[1] (numeric) = -2.205093670010836 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 1.1680761920275869000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = -2.2019307333937377 " "
y[1] (numeric) = -2.2019307333937643 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.2100904077911871000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = -2.1987772329204875 " "
y[1] (numeric) = -2.198777232920515 " "
absolute error = 2.753353101070388000000000000000E-14 " "
relative error = 1.2522201248251488000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = -2.1956332585774967 " "
y[1] (numeric) = -2.195633258577525 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.2944652445653798000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = -2.1924989003554662 " "
y[1] (numeric) = -2.192498900355495 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 1.3165707237332755000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = -2.1893742482485536 " "
y[1] (numeric) = -2.189374248248583 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 1.3387335615896337000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = -2.186259392253559 " "
y[1] (numeric) = -2.186259392253589 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.3609536528638672000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = -2.1831544223691197 " "
y[1] (numeric) = -2.1831544223691512 " "
absolute error = 3.153033389935444600000000000000E-14 " "
relative error = 1.444255778532528000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = -2.1800594285948973 " "
y[1] (numeric) = -2.1800594285949297 " "
absolute error = 3.24185123190545700000000000000E-14 " "
relative error = 1.4870471829269860000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = -2.1769745009307675 " "
y[1] (numeric) = -2.176974500930801 " "
absolute error = 3.330669073875469600000000000000E-14 " "
relative error = 1.5299531861541965000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = -2.1738997293760125 " "
y[1] (numeric) = -2.173899729376047 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 1.5934018437109568000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = -2.1708352039285086 " "
y[1] (numeric) = -2.1708352039285437 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.6161082847129987000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = -2.1677810145839174 " "
y[1] (numeric) = -2.1677810145839533 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 1.6593569994319454000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = -2.1647372513348753 " "
y[1] (numeric) = -2.1647372513349126 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 1.7232342449136600000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = -2.161704004170184 " "
y[1] (numeric) = -2.1617040041702222 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 1.7667392008077476000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = -2.1586813630740003 " "
y[1] (numeric) = -2.1586813630740393 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 1.8103575235927880000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = -2.1556694180250275 " "
y[1] (numeric) = -2.155669418025067 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 1.833487980400374000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; "
Iterations = 4900
"Total Elapsed Time "= 1 Minutes 37 Seconds
"Elapsed Time(since restart) "= 1 Minutes 37 Seconds
"Time to Timeout "= 1 Minutes 22 Seconds
Percent Done = 100.0204081632654 "%"
(%o257) temp/diffeq.sub_full_lin.max