(%i1) batch("temp/diffeq.sub_lin_c.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.sub_lin_c.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,30,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[30],convfloat)
(%i173) completearray(array_norms,[30],convfloat)
(%i174) completearray(array_fact_1,[30],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[30],convfloat)
(%i184) completearray(array_x,[30],convfloat)
(%i185) completearray(array_tmp0,[30],convfloat)
(%i186) completearray(array_tmp1,[30],convfloat)
(%i187) completearray(array_tmp2,[30],convfloat)
(%i188) completearray(array_tmp3,[30],convfloat)
(%i189) completearray(array_tmp4,[30],convfloat)
(%i190) completearray(array_m1,[30],convfloat)
(%i191) completearray(array_y_higher,[2,30],convfloat)
(%i192) completearray(array_y_higher_work,[2,30],convfloat)
(%i193) completearray(array_y_higher_work2,[2,30],convfloat)
(%i194) completearray(array_y_set_initial,[2,30],convfloat)
(%i195) completearray(array_given_rad_poles,[2,3],convfloat)
(%i196) completearray(array_given_ord_poles,[2,3],convfloat)
(%i197) completearray(array_rad_test_poles,[2,4],convfloat)
(%i198) completearray(array_ord_test_poles,[2,4],convfloat)
(%i199) completearray(array_fact_2,[30,30],convfloat)
(%i200) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i201) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i202) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i203) 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))
(%i204) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i205) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i206) 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)
(%i207) 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)
(%i208) 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)
(%i209) 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)
(%i210) 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)
(%i211) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i212) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i213) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i214) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i215) log_revs(file,revs):=printf(file,revs)
(%i216) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i217) 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)
(%i218) logstart(file):=(printf(file,""),0)
(%i219) logend(file):=(printf(file,"
~%"),0)
(%i220) 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)
(%i221) 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)
(%i222) 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)
(%i223) 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)
(%i224) 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)
(%i225) c(in_val):=(ret:in_val,ret)
(%i226) 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)
(%i227) 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)
(%i228) 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)
(%i229) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i230) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i231) 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)
(%i232) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i233) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i234) 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)
(%i235) log10(x):=log(x)/glob_log_10
(%i236) c(x):=x
(%i237) 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
(%i238) 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)
(%i239) exact_soln_y(x):=block(c(0.05)*c(x)*c(x)-c(0.1)*c(x))
(%o239) exact_soln_y(x) := block(c(0.05) c(x) c(x) - c(0.1) c(x))
(%i240) 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)
(%i241) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i242) 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)
(%i243) 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)
(%i244) 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))
(%i245) 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))
(%i246) 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(22)
*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)
(%i247) 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)
(%i248) 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)
(%i249) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D1[1]*array_x[1],
array_tmp2[1]:array_const_0D2[1]+array_tmp1[1],
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
array_tmp4[1]:array_tmp3[1]-array_const_0D3[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp4[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_0D1[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],array_tmp3[2]:array_tmp2[2],
array_tmp4[2]:array_tmp3[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp4[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,
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp4[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,
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp4[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,
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp4[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 false do
(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_tmp4[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)
(%i250) exact_soln_y(x):=block(c(0.05)*c(x)*c(x)-c(0.1)*c(x))
(%o250) exact_soln_y(x) := block(c(0.05) c(x) c(x) - c(0.1) c(x))
(%i251) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:30,
glob_html_log:true,term:1,
while term <= 30 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 30 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 30 do
(term:1,
while term <= 30 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3),
zero_ats_ar(array_tmp4),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_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_const_0D3),array_const_0D3[1]:c(0.3),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/sub_lin_cpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.1),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,""),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always,""),
omniout_str(always,
" (c(0.05) * c(x) * c(x) - c(0.1) * c(x)) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:3,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ; "),
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,
"2015-04-24T22:40:33-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"sub_lin_c"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ; "),
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_lin_c diffeq.max"),
logitem_str(html_log_file,
"sub_lin_c maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i252) main():=(glob_iolevel:2,compile(all),main_prog())
(%i253) 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_0D1 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_const_0D3 in translation.
warning: encountered undefined variable array_tmp4 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_lin_cpostode.ode#################"
"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
""
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
""
" (c(0.05) * c(x) * c(x) - c(0.1) * c(x)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = -9.500000000000002000E-3 " "
y[1] (numeric) = -9.500000000000002000E-3 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = -1.039500000000000300E-2 " "
y[1] (numeric) = -1.039500000000000300E-2 " "
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) = -1.128000000000000400E-2 " "
y[1] (numeric) = -1.12800E-2 " "
absolute error = 3.469446951953614000000000000000000E-18 " "
relative error = 3.075750843930508000000000000000E-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) = -1.215500000000000500E-2 " "
y[1] (numeric) = -1.215500E-2 " "
absolute error = 5.204170427930421000000000000000000E-18 " "
relative error = 4.28150590533148400000000000000E-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) = -1.302000000000000700E-2 " "
y[1] (numeric) = -1.30200E-2 " "
absolute error = 5.204170427930421000000000000000000E-18 " "
relative error = 3.99705870040738800000000000000E-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) = -1.387500000000000400E-2 " "
y[1] (numeric) = -1.387500E-2 " "
absolute error = 5.204170427930421000000000000000000E-18 " "
relative error = 3.75075346157147300000000000000E-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) = -1.472000000000000500E-2 " "
y[1] (numeric) = -1.472000000000000000E-2 " "
absolute error = 6.938893903907228000000000000000000E-18 " "
relative error = 4.713922489067408600000000000000E-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) = -1.555500000000000800E-2 " "
y[1] (numeric) = -1.555499999999999700E-2 " "
absolute error = 8.673617379884035000000000000000000E-18 " "
relative error = 5.57609603335521100000000000000E-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) = -1.63800000000000080E-2 " "
y[1] (numeric) = -1.637999999999999500E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 8.47239792906865100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = -1.71950000000000100E-2 " "
y[1] (numeric) = -1.719499999999999400E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 8.07082745438467600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = -1.80000000000000100E-2 " "
y[1] (numeric) = -1.800E-2 " "
absolute error = 1.040834085586084300000000000000000E-17 " "
relative error = 5.78241158658935300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = -1.87950000000000100E-2 " "
y[1] (numeric) = -1.879499999999999500E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 7.38376579293133700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = -1.95800000000000100E-2 " "
y[1] (numeric) = -1.957999999999999200E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 8.85967045953424900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = -2.035500000000001200E-2 " "
y[1] (numeric) = -2.035499999999999500E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 8.52234574294672500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = -2.11200000000000100E-2 " "
y[1] (numeric) = -2.111999999999999700E-2 " "
absolute error = 1.387778780781445700000000000000000E-17 " "
relative error = 6.57092225748790200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = -2.18750000000000080E-2 " "
y[1] (numeric) = -2.18749999999999920E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 7.93016446160825800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = -2.262000000000000700E-2 " "
y[1] (numeric) = -2.26199999999999900E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 7.66898088407076200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = -2.33550000000000120E-2 " "
y[1] (numeric) = -2.335499999999999200E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 7.42763209581163000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (closed_form) = -2.40800000000000130E-2 " "
y[1] (numeric) = -2.407999999999999300E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 7.20400114608308200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (closed_form) = -2.47950000000000110E-2 " "
y[1] (numeric) = -2.47949999999999900E-2 " "
absolute error = 2.081668171172168500000000000000000E-17 " "
relative error = 8.39551591519325500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (closed_form) = -2.550000000000001000E-2 " "
y[1] (numeric) = -2.54999999999999900E-2 " "
absolute error = 2.081668171172168500000000000000000E-17 " "
relative error = 8.16340459283202900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (closed_form) = -2.61950000000000100E-2 " "
y[1] (numeric) = -2.619499999999999000E-2 " "
absolute error = 1.73472347597680700000000000000000E-17 " "
relative error = 6.6223457758228900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (closed_form) = -2.688000000000001500E-2 " "
y[1] (numeric) = -2.68799999999999930E-2 " "
absolute error = 2.4286128663675300000000000000000E-17 " "
relative error = 9.03501810404586500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (closed_form) = -2.755500000000002000E-2 " "
y[1] (numeric) = -2.75549999999999900E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 1.00727910054904360000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (closed_form) = -2.822000000000002000E-2 " "
y[1] (numeric) = -2.82199999999999900E-2 " "
absolute error = 2.4286128663675300000000000000000E-17 " "
relative error = 8.60599881774460900000000000000E-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) = -2.887500000000002000E-2 " "
y[1] (numeric) = -2.88749999999999900E-2 " "
absolute error = 2.4286128663675300000000000000000E-17 " "
relative error = 8.41078048958451400000000000000E-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) = -2.95200000000000200E-2 " "
y[1] (numeric) = -2.951999999999998500E-2 " "
absolute error = 3.12250225675825300000000000000000E-17 " "
relative error = 1.0577582170590280000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (closed_form) = -3.015500000000001500E-2 " "
y[1] (numeric) = -3.015499999999999000E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 9.20430297318152700000000000000E-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) = -3.078000000000002000E-2 " "
y[1] (numeric) = -3.077999999999998500E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 9.01740598298534800000000000000E-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) = -3.13950000000000200E-2 " "
y[1] (numeric) = -3.13949999999999950E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 8.8407630564194610000000000000E-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) = -3.200000000000002000E-2 " "
y[1] (numeric) = -3.19999999999999840E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 8.67361737988403200000000000000E-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) = -3.25950000000000200E-2 " "
y[1] (numeric) = -3.259499999999998500E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 1.06441078446191510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (closed_form) = -3.318000000000001500E-2 " "
y[1] (numeric) = -3.31799999999999900E-2 " "
absolute error = 2.775557561562891400000000000000000E-17 " "
relative error = 8.36515238566271900000000000000E-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) = -3.37550000000000240E-2 " "
y[1] (numeric) = -3.375499999999998500E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 1.0278320106513440000000000000E-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) = -3.43200000000000170E-2 " "
y[1] (numeric) = -3.43199999999999840E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 1.01091111653660030000000000000E-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) = -3.48750000000000170E-2 " "
y[1] (numeric) = -3.48749999999999840E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 9.9482349876806100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = -3.54200000000000200E-2 " "
y[1] (numeric) = -3.541999999999998500E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 9.79516361364656100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = -3.59550000000000200E-2 " "
y[1] (numeric) = -3.59549999999999800E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.15792972947972030000000000000E-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) = -3.64800000000000200E-2 " "
y[1] (numeric) = -3.64799999999999800E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.1412654447215830000000000000E-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) = -3.69950000000000200E-2 " "
y[1] (numeric) = -3.69949999999999800E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.12537811659530610000000000000E-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) = -3.75000000000000200E-2 " "
y[1] (numeric) = -3.749999999999998300E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 9.25185853854296600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = -3.79950000000000230E-2 " "
y[1] (numeric) = -3.79949999999999800E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.09575900574926570000000000000E-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) = -3.84800000000000200E-2 " "
y[1] (numeric) = -3.84799999999999800E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.0819481139148480000000000000E-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) = -3.89550000000000200E-2 " "
y[1] (numeric) = -3.89549999999999840E-2 " "
absolute error = 3.46944695195361400000000000000000E-17 " "
relative error = 8.90629431896704500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = -3.94200000000000160E-2 " "
y[1] (numeric) = -3.941999999999998000E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.05614823499348930000000000000E-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) = -3.98750000000000200E-2 " "
y[1] (numeric) = -3.98749999999999700E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.21811303642258480000000000000E-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) = -4.03200000000000200E-2 " "
y[1] (numeric) = -4.031999999999997000E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.20466908053944870000000000000E-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) = -4.07550000000000200E-2 " "
y[1] (numeric) = -4.07549999999999800E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 1.0215522861843540000000000000E-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) = -4.11800000000000200E-2 " "
y[1] (numeric) = -4.117999999999997000E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.17951086273313690000000000000E-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) = -4.15950000000000200E-2 " "
y[1] (numeric) = -4.15949999999999700E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.16774269328887070000000000000E-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) = -4.20000000000000260E-2 " "
y[1] (numeric) = -4.199999999999997600E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.15648231731787070000000000000E-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) = -4.239500000000001600E-2 " "
y[1] (numeric) = -4.239499999999997000E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.8203475465133500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = -4.27800000000000200E-2 " "
y[1] (numeric) = -4.27799999999999740E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.13539638446354780000000000000E-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) = -4.31550000000000100E-2 " "
y[1] (numeric) = -4.31549999999999700E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.6474020214212400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = -4.35200000000000140E-2 " "
y[1] (numeric) = -4.351999999999997500E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.56648975722503500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = -4.38750000000000100E-2 " "
y[1] (numeric) = -4.38749999999999700E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.4890856805568900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = -4.42200000000000100E-2 " "
y[1] (numeric) = -4.42199999999999700E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.41505278684834100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = -4.45550000000000100E-2 " "
y[1] (numeric) = -4.45549999999999670E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.34426291627053300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = -4.48800000000000200E-2 " "
y[1] (numeric) = -4.48799999999999700E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.08226954829212530000000000000E-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) = -4.51950000000000130E-2 " "
y[1] (numeric) = -4.519499999999996300E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.07472634865251870000000000000E-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) = -4.55000000000000100E-2 " "
y[1] (numeric) = -4.549999999999996000E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.06752213906265020000000000000E-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) = -4.579500000000002000E-2 " "
y[1] (numeric) = -4.57949999999999700E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.06064542695382850000000000000E-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) = -4.60800000000000100E-2 " "
y[1] (numeric) = -4.60799999999999650E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 9.0350181040458700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = -4.635500000000001300E-2 " "
y[1] (numeric) = -4.635499999999997000E-2 " "
absolute error = 4.8572257327350600000000000000000E-17 " "
relative error = 1.04783210715889520000000000000E-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) = -4.66200000000000060E-2 " "
y[1] (numeric) = -4.66199999999999670E-2 " "
absolute error = 4.16333634234433700000000000000000E-17 " "
relative error = 8.93036538469398700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = -4.68750000000000200E-2 " "
y[1] (numeric) = -4.687499999999996700E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.18423789293349980000000000E-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) = -4.71200000000000230E-2 " "
y[1] (numeric) = -4.71199999999999600E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.32534051645087050000000000000E-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) = -4.73550000000000250E-2 " "
y[1] (numeric) = -4.73549999999999600E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.3187634913982690000000000000E-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) = -4.75800000000000170E-2 " "
y[1] (numeric) = -4.75799999999999600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.1666908623635519000000000000E-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) = -4.77950000000000200E-2 " "
y[1] (numeric) = -4.77949999999999650E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.16144264528209670000000000000E-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) = -4.80000000000000200E-2 " "
y[1] (numeric) = -4.79999999999999600E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.30104260698260480000000000000E-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) = -4.819500000000001600E-2 " "
y[1] (numeric) = -4.81949999999999600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.15180311715443110000000000000E-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) = -4.83800000000000230E-2 " "
y[1] (numeric) = -4.83799999999999560E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.2908235869194920000000000000E-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) = -4.855500000000001500E-2 " "
y[1] (numeric) = -4.85549999999999600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.14326333500685450000000000000E-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) = -4.87200000000000130E-2 " "
y[1] (numeric) = -4.87199999999999600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.13939144563337050000000000000E-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) = -4.887500000000001300E-2 " "
y[1] (numeric) = -4.88749999999999600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.13577803030706510000000000000E-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) = -4.902000000000001400E-2 " "
y[1] (numeric) = -4.90199999999999600E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.13241842577025310000000000000E-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) = -4.91550000000000150E-2 " "
y[1] (numeric) = -4.915499999999995400E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.27047187743190000000000000000E-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) = -4.92800000000000100E-2 " "
y[1] (numeric) = -4.927999999999995700E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.1264438155693550000000000000E-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) = -4.939500000000001700E-2 " "
y[1] (numeric) = -4.93949999999999560E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.26429891963083380000000000000E-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) = -4.950000000000001600E-2 " "
y[1] (numeric) = -4.949999999999995500E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.26161707343767750000000000000E-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) = -4.959500000000001000E-2 " "
y[1] (numeric) = -4.95949999999999500E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.25920042615515730000000000000E-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) = -4.96800000000000100E-2 " "
y[1] (numeric) = -4.96799999999999500E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11737421963079360000000000000E-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) = -4.97550000000000050E-2 " "
y[1] (numeric) = -4.97549999999999500E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11568990516044240000000000000E-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) = -4.98200000000000100E-2 " "
y[1] (numeric) = -4.981999999999995300E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11423426798992000000000000000E-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) = -4.98750000000000100E-2 " "
y[1] (numeric) = -4.987499999999995000E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11300553847133470000000000000E-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) = -4.992000000000001000E-2 " "
y[1] (numeric) = -4.99199999999999530E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.1120022281902610000000000000E-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) = -4.995500000000000500E-2 " "
y[1] (numeric) = -4.99549999999999500E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11122312543805060000000000000E-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) = -4.99800000000000130E-2 " "
y[1] (numeric) = -4.99799999999999470E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.24950070298449470000000000000E-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) = -4.999500000000000600E-2 " "
y[1] (numeric) = -4.99949999999999500E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11033405803095950000000000000E-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) = -5.00E-2 " "
y[1] (numeric) = -4.99999999999999440E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11022302462515650000000000000E-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) = -4.999500000000000600E-2 " "
y[1] (numeric) = -4.99949999999999500E-2 " "
absolute error = 5.55111512312578300000000000000000E-17 " "
relative error = 1.11033405803095950000000000000E-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) = -4.99800000000000130E-2 " "
y[1] (numeric) = -4.99799999999999470E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.24950070298449470000000000000E-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) = -4.99550000000000160E-2 " "
y[1] (numeric) = -4.99549999999999500E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.25012601611780680000000000000E-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) = -4.99200000000000200E-2 " "
y[1] (numeric) = -4.99199999999999600E-2 " "
absolute error = 6.24500451351650600000000000000000E-17 " "
relative error = 1.2510025067140430000000000000E-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) = -4.98750000000000300E-2 " "
y[1] (numeric) = -4.98749999999999600E-2 " "
absolute error = 6.93889390390722800000000000000000E-17 " "
relative error = 1.39125692308916780000000000000E-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) = -4.98200000000000360E-2 " "
y[1] (numeric) = -4.98199999999999640E-2 " "
absolute error = 7.63278329429795100000000000000000E-17 " "
relative error = 1.53207211848613940000000000000E-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) = -4.975500000000005500E-2 " "
y[1] (numeric) = -4.975499999999996600E-2 " "
absolute error = 9.02056207507939700000000000000000E-17 " "
relative error = 1.81299609588571750000000000000E-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) = -4.96800000000000700E-2 " "
y[1] (numeric) = -4.967999999999997400E-2 " "
absolute error = 9.7144514654701200000000000000000E-17 " "
relative error = 1.95540488435388630000000000000E-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) = -4.95950000000000900E-2 " "
y[1] (numeric) = -4.95949999999999800E-2 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.23857853538694360000000000000E-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) = -4.950000000000010500E-2 " "
y[1] (numeric) = -4.94999999999999900E-2 " "
absolute error = 1.17961196366422880000000000000000E-16 " "
relative error = 2.3830544720489420000000000000E-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) = -4.939500000000013000E-2 " "
y[1] (numeric) = -4.939500E-2 " "
absolute error = 1.2490009027033011000000000000000E-16 " "
relative error = 2.5285978392616620000000000000E-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) = -4.92800000000001570E-2 " "
y[1] (numeric) = -4.92800000000000100E-2 " "
absolute error = 1.4571677198205180000000000000000E-16 " "
relative error = 2.95691501586954800000000000000E-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) = -4.915500000000018000E-2 " "
y[1] (numeric) = -4.915500000000002600E-2 " "
absolute error = 1.59594559789866250000000000000000E-16 " "
relative error = 3.24676146454817740000000000000E-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) = -4.902000000000022000E-2 " "
y[1] (numeric) = -4.90200000000000400E-2 " "
absolute error = 1.7347234759768070000000000000000E-16 " "
relative error = 3.5388075805320270000000000000E-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) = -4.88750000000002350E-2 " "
y[1] (numeric) = -4.88750000000000600E-2 " "
absolute error = 1.80411241501587940000000000000000E-16 " "
relative error = 3.6912785984979450000000000000E-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) = -4.87200000000002740E-2 " "
y[1] (numeric) = -4.872000000000007400E-2 " "
absolute error = 2.01227923213309620000000000000000E-16 " "
relative error = 4.13029399042094570000000000000E-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) = -4.855500000000030300E-2 " "
y[1] (numeric) = -4.85550000000000900E-2 " "
absolute error = 2.15105711021124080000000000000000E-16 " "
relative error = 4.4301454231515340000000000000E-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) = -4.83800000000003560E-2 " "
y[1] (numeric) = -4.83800000000001100E-2 " "
absolute error = 2.428612866367530000000000000000E-16 " "
relative error = 5.0198695046868790000000000000E-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) = -4.81950000000003900E-2 " "
y[1] (numeric) = -4.81950000000001270E-2 " "
absolute error = 2.6367796834847470000000000000000E-16 " "
relative error = 5.4710648064835050000000000000E-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) = -4.80000000000004300E-2 " "
y[1] (numeric) = -4.80000000000001500E-2 " "
absolute error = 2.84494650060196360000000000000000E-16 " "
relative error = 5.9269718762540380000000000000E-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) = -4.779500000000047600E-2 " "
y[1] (numeric) = -4.779500000000016500E-2 " "
absolute error = 3.1225022567582530000000000000000E-16 " "
relative error = 6.5331148797117310000000000000E-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) = -4.758000000000052000E-2 " "
y[1] (numeric) = -4.758000000000018300E-2 " "
absolute error = 3.4000580129145420000000000000000E-16 " "
relative error = 7.1459815319766800000000000000E-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) = -4.73550000000005800E-2 " "
y[1] (numeric) = -4.73550000000002100E-2 " "
absolute error = 3.6776137690708310000000000000000E-16 " "
relative error = 7.7660516715674920000000000000E-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) = -4.71200000000006170E-2 " "
y[1] (numeric) = -4.71200000000002400E-2 " "
absolute error = 3.81639164714897560000000000000000E-16 " "
relative error = 8.0993031560885520000000000000E-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) = -4.68750000000006800E-2 " "
y[1] (numeric) = -4.687500000000026600E-2 " "
absolute error = 4.1633363423443370000000000000000E-16 " "
relative error = 8.8817841970011240000000000000E-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) = -4.66200000000007300E-2 " "
y[1] (numeric) = -4.66200000000002950E-2 " "
absolute error = 4.3715031594615540000000000000000E-16 " "
relative error = 9.376883653928540000000000000E-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) = -4.635500000000078400E-2 " "
y[1] (numeric) = -4.63550000000003200E-2 " "
absolute error = 4.6490589156178430000000000000000E-16 " "
relative error = 1.0029250168520686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = -4.60800000000008400E-2 " "
y[1] (numeric) = -4.60800000000003500E-2 " "
absolute error = 4.9266146717741320000000000000000E-16 " "
relative error = 1.0691438089787418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = -4.579500000000090700E-2 " "
y[1] (numeric) = -4.579500000000038500E-2 " "
absolute error = 5.2041704279304210000000000000000E-16 " "
relative error = 1.1364058145933657000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = -4.55000000000009730E-2 " "
y[1] (numeric) = -4.55000000000004230E-2 " "
absolute error = 5.481726184086710000000000000000E-16 " "
relative error = 1.204774985513537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = -4.51950000000010400E-2 " "
y[1] (numeric) = -4.51950000000004500E-2 " "
absolute error = 5.8980598183211440000000000000000E-16 " "
relative error = 1.3050248519351718000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = -4.4880000000001097E-2 " "
y[1] (numeric) = -4.48800000000004800E-2 " "
absolute error = 6.1756155744774330000000000000000E-16 " "
relative error = 1.3760284256856686000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = -4.45550000000011770E-2 " "
y[1] (numeric) = -4.45550000000005160E-2 " "
absolute error = 6.5919492087118670000000000000000E-16 " "
relative error = 1.4795082950761290000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = -4.422000000000124700E-2 " "
y[1] (numeric) = -4.42200000000005500E-2 " "
absolute error = 6.9388939039072280000000000000000E-16 " "
relative error = 1.5691754644746794000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = -4.38750000000013300E-2 " "
y[1] (numeric) = -4.38750000000005860E-2 " "
absolute error = 7.4246164771807340000000000000000E-16 " "
relative error = 1.6922202796992616000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = -4.352000000000140000E-2 " "
y[1] (numeric) = -4.35200000000006250E-2 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.7857447546819500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = -4.315500000000148700E-2 " "
y[1] (numeric) = -4.315500000000066500E-2 " "
absolute error = 8.1878948066105300000000000000000E-16 " "
relative error = 1.897322397546112000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = -4.27800000000015670E-2 " "
y[1] (numeric) = -4.278000000000070600E-2 " "
absolute error = 8.6042284408449630000000000000000E-16 " "
relative error = 2.0112735953353547000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = -4.239500000000165400E-2 " "
y[1] (numeric) = -4.23950000000007500E-2 " "
absolute error = 9.0205620750793970000000000000000E-16 " "
relative error = 2.127741968411144000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = -4.20000000000017300E-2 " "
y[1] (numeric) = -4.200000000000079000E-2 " "
absolute error = 9.3675067702747580000000000000000E-16 " "
relative error = 2.2303587548272316000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = -4.159500000000182500E-2 " "
y[1] (numeric) = -4.15950000000008370E-2 " "
absolute error = 9.8532293435482640000000000000000E-16 " "
relative error = 2.368849463528749000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = -4.11800000000019100E-2 " "
y[1] (numeric) = -4.11800000000008900E-2 " "
absolute error = 1.0200174038743626000000000000000E-15 " "
relative error = 2.4769728117394738000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = -4.07550000000020100E-2 " "
y[1] (numeric) = -4.075500000000093500E-2 " "
absolute error = 1.0755285551056204000000000000000E-15 " "
relative error = 2.6390100726427856000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = -4.032000000000210400E-2 " "
y[1] (numeric) = -4.03200000000009800E-2 " "
absolute error = 1.124100812432971000000000000000E-15 " "
relative error = 2.7879484435340085000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = -3.9875000000002203E-2 " "
y[1] (numeric) = -3.98750000000010260E-2 " "
absolute error = 1.1726730697603216000000000000000E-15 " "
relative error = 2.9408729022200800000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = -3.9420000000002300E-2 " "
y[1] (numeric) = -3.94200000000010700E-2 " "
absolute error = 1.2281842209915794000000000000000E-15 " "
relative error = 3.1156372932306137000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = -3.895500000000240400E-2 " "
y[1] (numeric) = -3.89550000000011200E-2 " "
absolute error = 1.2836953722228372000000000000000E-15 " "
relative error = 3.295328898017605000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = -3.8480000000002500E-2 " "
y[1] (numeric) = -3.84800000000011740E-2 " "
absolute error = 1.3253287356462806000000000000000E-15 " "
relative error = 3.444201495962044300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = -3.79950000000026100E-2 " "
y[1] (numeric) = -3.79950000000012300E-2 " "
absolute error = 1.3808398868775384000000000000000E-15 " "
relative error = 3.63426736906815000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = -3.75000000000027100E-2 " "
y[1] (numeric) = -3.75000000000012800E-2 " "
absolute error = 1.429412144204889000000000000000E-15 " "
relative error = 3.811765717879429000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = -3.69950000000028300E-2 " "
y[1] (numeric) = -3.69950000000013400E-2 " "
absolute error = 1.4918621893400540000000000000000E-15 " "
relative error = 4.032604917799540400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = -3.648000000000295500E-2 " "
y[1] (numeric) = -3.64800000000013950E-2 " "
absolute error = 1.5612511283791264000000000000000E-15 " "
relative error = 4.279745417705592000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = -3.59550000000030700E-2 " "
y[1] (numeric) = -3.59550000000014500E-2 " "
absolute error = 1.6167622796103842000000000000000E-15 " "
relative error = 4.496627116145866500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = -3.542000000000318000E-2 " "
y[1] (numeric) = -3.54200000000015100E-2 " "
absolute error = 1.672273430841642000000000000000E-15 " "
relative error = 4.721268861777221400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = -3.487500000000331000E-2 " "
y[1] (numeric) = -3.48750000000015700E-2 " "
absolute error = 1.734723475976807000000000000000E-15 " "
relative error = 4.974117493839836400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = -3.43200000000034140E-2 " "
y[1] (numeric) = -3.43200000000016270E-2 " "
absolute error = 1.790234627208065000000000000000E-15 " "
relative error = 5.216301361328340000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = -3.375500000000354300E-2 " "
y[1] (numeric) = -3.375500000000169000E-2 " "
absolute error = 1.8596235662471372000000000000000E-15 " "
relative error = 5.509179577090629000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = -3.318000000000366000E-2 " "
y[1] (numeric) = -3.31800000000017500E-2 " "
absolute error = 1.915134717478395000000000000000E-15 " "
relative error = 5.771955146106641000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = -3.25950000000037900E-2 " "
y[1] (numeric) = -3.25950000000018100E-2 " "
absolute error = 1.97758476261356000000000000000E-15 " "
relative error = 6.067141471432214000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = -3.20000000000039400E-2 " "
y[1] (numeric) = -3.200000000000187000E-2 " "
absolute error = 2.067790383364354000000000000000E-15 " "
relative error = 6.46184494801281000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = -3.13950000000040600E-2 " "
y[1] (numeric) = -3.13950000000019440E-2 " "
absolute error = 2.1163626406917047000000000000000E-15 " "
relative error = 6.741081830518971000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = -3.078000000000419300E-2 " "
y[1] (numeric) = -3.078000000000200600E-2 " "
absolute error = 2.185751579730777000000000000000E-15 " "
relative error = 7.101207211599998000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = -3.015500000000434500E-2 " "
y[1] (numeric) = -3.015500000000207500E-2 " "
absolute error = 2.2690183065776637000000000000000E-15 " "
relative error = 7.524517680574819000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = -2.95200000000044600E-2 " "
y[1] (numeric) = -2.952000000000214500E-2 " "
absolute error = 2.3141211169530607000000000000000E-15 " "
relative error = 7.839163675314063000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = -2.88750000000046200E-2 " "
y[1] (numeric) = -2.88750000000022160E-2 " "
absolute error = 2.400857290751901000000000000000E-15 " "
relative error = 8.314657283987937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = -2.82200000000047700E-2 " "
y[1] (numeric) = -2.822000000000229300E-2 " "
absolute error = 2.4771851236948805000000000000000E-15 " "
relative error = 8.778118794098022000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = -2.75550000000049100E-2 " "
y[1] (numeric) = -2.755500000000236000E-2 " "
absolute error = 2.546574062733953000000000000000E-15 " "
relative error = 9.241785747535834000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = -2.68800000000050400E-2 " "
y[1] (numeric) = -2.688000000000243500E-2 " "
absolute error = 2.6055546609171640000000000000000E-15 " "
relative error = 9.693283708767395000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = -2.619500000000521400E-2 " "
y[1] (numeric) = -2.619500000000251000E-2 " "
absolute error = 2.706168622523819000000000000000E-15 " "
relative error = 1.033085941028165800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = -2.55000000000053500E-2 " "
y[1] (numeric) = -2.55000000000025800E-2 " "
absolute error = 2.7720881146109380000000000000000E-15 " "
relative error = 1.087093378278570900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = -2.479500000000550700E-2 " "
y[1] (numeric) = -2.479500000000265400E-2 " "
absolute error = 2.851885394505871000000000000000E-15 " "
relative error = 1.150185680381220900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = -2.408000000000565200E-2 " "
y[1] (numeric) = -2.408000000000273500E-2 " "
absolute error = 2.9178048865929895000000000000000E-15 " "
relative error = 1.211712992770890600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = -2.335500000000581600E-2 " "
y[1] (numeric) = -2.33550000000028120E-2 " "
absolute error = 3.00454106039183000000000000000E-15 " "
relative error = 1.286465878994254600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = -2.262000000000599600E-2 " "
y[1] (numeric) = -2.26200000000028900E-2 " "
absolute error = 3.1051550219984847000000000000000E-15 " "
relative error = 1.37274757824830280000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = -2.18750000000061400E-2 " "
y[1] (numeric) = -2.187500000000297500E-2 " "
absolute error = 3.164135620181696000000000000000E-15 " "
relative error = 1.446461997796941000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = -2.1120000000006300E-2 " "
y[1] (numeric) = -2.112000000000305600E-2 " "
absolute error = 3.2439329000766290000000000000000E-15 " "
relative error = 1.535953077687339800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = -2.03550000000064800E-2 " "
y[1] (numeric) = -2.03550000000031430E-2 " "
absolute error = 3.337607967779377000000000000000E-15 " "
relative error = 1.63969932094242900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = -1.958000000000664800E-2 " "
y[1] (numeric) = -1.95800000000032300E-2 " "
absolute error = 3.41740524767431000000000000000E-15 " "
relative error = 1.745355080527655500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = -1.879500000000683400E-2 " "
y[1] (numeric) = -1.879500000000331500E-2 " "
absolute error = 3.5180192092809650000000000000000E-15 " "
relative error = 1.871784628507414400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = -1.80000000000070100E-2 " "
y[1] (numeric) = -1.8000000000003400E-2 " "
absolute error = 3.611694276983712400000000000000E-15 " "
relative error = 2.006496820545725400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = -1.719500000000717700E-2 " "
y[1] (numeric) = -1.719500000000348500E-2 " "
absolute error = 3.6914915568786455000000000000000E-15 " "
relative error = 2.146840102865428500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = -1.63800000000073600E-2 " "
y[1] (numeric) = -1.638000000000357200E-2 " "
absolute error = 3.788636071533346700000000000000E-15 " "
relative error = 2.312964634634703500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = -1.555500000000753500E-2 " "
y[1] (numeric) = -1.55550000000036600E-2 " "
absolute error = 3.875372245332187000000000000000E-15 " "
relative error = 2.49139970770190320000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = -1.472000000000772700E-2 " "
y[1] (numeric) = -1.472000000000375200E-2 " "
absolute error = 3.974251483462865000000000000000E-15 " "
relative error = 2.69989910561194200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = -1.387500000000791000E-2 " "
y[1] (numeric) = -1.387500000000384500E-2 " "
absolute error = 4.062722380737682000000000000000E-15 " "
relative error = 2.928088202331795600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = -1.30200000000080800E-2 " "
y[1] (numeric) = -1.302000000000393700E-2 " "
absolute error = 4.144254384108592000000000000000E-15 " "
relative error = 3.182991078422442400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = -1.21550000000082700E-2 " "
y[1] (numeric) = -1.215500000000402900E-2 " "
absolute error = 4.241398898763293300000000000000E-15 " "
relative error = 3.48942731284278660000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = -1.128000000000847800E-2 " "
y[1] (numeric) = -1.128000000000412100E-2 " "
absolute error = 4.355890648177762600000000000000E-15 " "
relative error = 3.861605184551852000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = -1.039500000000867500E-2 " "
y[1] (numeric) = -1.039500000000421800E-2 " "
absolute error = 4.458239333260394000000000000000E-15 " "
relative error = 4.288830527423447300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = -9.500000000008862000E-3 " "
y[1] (numeric) = -9.500000000004314000E-3 " "
absolute error = 4.548444954011188000000000000000E-15 " "
relative error = 4.78783679369152060000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = -8.595000000009068000E-3 " "
y[1] (numeric) = -8.595000000004411000E-3 " "
absolute error = 4.65599780952175000000000000000E-15 " "
relative error = 5.417100418286025000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = -7.680000000009263000E-3 " "
y[1] (numeric) = -7.680000000004512000E-3 " "
absolute error = 4.750540238962486000000000000000E-15 " "
relative error = 6.18559926947494300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = -6.755000000009476000E-3 " "
y[1] (numeric) = -6.755000000004613000E-3 " "
absolute error = 4.86242990316299030000000000000E-15 " "
relative error = 7.19826780630076900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = -5.8200000000096790000E-3 " "
y[1] (numeric) = -5.820000000004716000E-3 " "
absolute error = 4.962176503031656700000000000000E-15 " "
relative error = 8.52607646567595200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = -4.8750000000098714000E-3 " "
y[1] (numeric) = -4.875000000004818000E-3 " "
absolute error = 5.053249485520439000000000000000E-15 " "
relative error = 1.03656399702773460000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = -3.920000000010082000E-3 " "
y[1] (numeric) = -3.920000000004921000E-3 " "
absolute error = 5.160802341031001000000000000000E-15 " "
relative error = 1.31653120944329800000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = -2.9550000000103105000E-3 " "
y[1] (numeric) = -2.955000000005026000E-3 " "
absolute error = 5.284401388694349000000000000000E-15 " "
relative error = 1.78829150208998670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = -1.980000000010501000E-3 " "
y[1] (numeric) = -1.980000000005132000E-3 " "
absolute error = 5.368969158148218000000000000000E-15 " "
relative error = 2.7116005849089614000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = -9.9500000001073730000E-4 " "
y[1] (numeric) = -9.9500000000523950000E-4 " "
absolute error = 5.497772376239496000000000000000E-15 " "
relative error = 5.5253993730453950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = -1.093569679255779200000000000000E-14 " "
y[1] (numeric) = -5.347949188529155000000000000000E-15 " "
absolute error = 5.587747604028637000000000000000E-15 " "
relative error = 51.096402085977154 "%"
Desired digits = 8
Estimated correct digits = 0
Correct digits = 2
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 1.0049999999888481000E-3 " "
y[1] (numeric) = 1.0049999999945426000E-3 " "
absolute error = 5.694446650328366000000000000000E-15 " "
relative error = 5.6661160700413470000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 2.019999999988642000E-3 " "
y[1] (numeric) = 2.019999999994432000E-3 " "
absolute error = 5.790073281941588000000000000000E-15 " "
relative error = 2.8663729118683884000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 3.044999999988418000E-3 " "
y[1] (numeric) = 3.044999999994321000E-3 " "
absolute error = 5.90283030788008000000000000000E-15 " "
relative error = 1.93853212082184980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 4.079999999988176400E-3 " "
y[1] (numeric) = 4.079999999994209000E-3 " "
absolute error = 6.032500887709347000000000000000E-15 " "
relative error = 1.47855413914873250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 5.124999999987945000E-3 " "
y[1] (numeric) = 5.124999999994094000E-3 " "
absolute error = 6.149594722337781000000000000000E-15 " "
relative error = 1.19992092143458490000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 6.179999999987723000E-3 " "
y[1] (numeric) = 6.1799999999939780000E-3 " "
absolute error = 6.255412854372366000000000000000E-15 " "
relative error = 1.01220272724673030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 7.244999999987484000E-3 " "
y[1] (numeric) = 7.244999999993862000E-3 " "
absolute error = 6.377710859428731000000000000000E-15 " "
relative error = 8.80291353959937900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 8.319999999987254000E-3 " "
y[1] (numeric) = 8.319999999993744000E-3 " "
absolute error = 6.489600523629235000000000000000E-15 " "
relative error = 7.80000062937401100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 9.404999999987007000E-3 " "
y[1] (numeric) = 9.404999999993623000E-3 " "
absolute error = 6.616235337375542000000000000000E-15 " "
relative error = 7.034806313008700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 1.04999999999867700E-2 " "
y[1] (numeric) = 1.0499999999993500E-2 " "
absolute error = 6.7307270867900120000000000000000E-15 " "
relative error = 6.41021627314142100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 1.160499999998654300E-2 " "
y[1] (numeric) = 1.160499999999338300E-2 " "
absolute error = 6.84001466577655000000000000000E-15 " "
relative error = 5.89402383953854600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 1.271999999998629800E-2 " "
y[1] (numeric) = 1.271999999999326200E-2 " "
absolute error = 6.9649147560468800000000000000000E-15 " "
relative error = 5.47556191513709400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 1.384499999998603500E-2 " "
y[1] (numeric) = 1.384499999999314300E-2 " "
absolute error = 7.107162081076979000000000000000E-15 " "
relative error = 5.13337817340855700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = 1.497999999998578200E-2 " "
y[1] (numeric) = 1.49799999999930200E-2 " "
absolute error = 7.237266341775239000000000000000E-15 " "
relative error = 4.83128594244466500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 1.61249999999855400E-2 " "
y[1] (numeric) = 1.61249999999928920E-2 " "
absolute error = 7.351758091189708000000000000000E-15 " "
relative error = 4.55922982399770600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 1.72799999999852800E-2 " "
y[1] (numeric) = 1.727999999999276200E-2 " "
absolute error = 7.483597075363946000000000000000E-15 " "
relative error = 4.3307853445430100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 1.84449999999850300E-2 " "
y[1] (numeric) = 1.84449999999926400E-2 " "
absolute error = 7.61196661258623000000000000000E-15 " "
relative error = 4.126845547623968000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 1.96199999999847600E-2 " "
y[1] (numeric) = 1.961999999999251600E-2 " "
absolute error = 7.754213937616328000000000000000E-15 " "
relative error = 3.9521987449655200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 2.080499999998450300E-2 " "
y[1] (numeric) = 2.080499999999238500E-2 " "
absolute error = 7.882583474838611000000000000000E-15 " "
relative error = 3.788792826168941300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 2.199999999998425400E-2 " "
y[1] (numeric) = 2.19999999999922600E-2 " "
absolute error = 8.004014118156988000000000000000E-15 " "
relative error = 3.638188235528507000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 2.32049999999839880E-2 " "
y[1] (numeric) = 2.320499999999212600E-2 " "
absolute error = 8.139322549283179000000000000000E-15 " "
relative error = 3.50757274263684300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 2.441999999998370500E-2 " "
y[1] (numeric) = 2.441999999999199300E-2 " "
absolute error = 8.288508768217184000000000000000E-15 " "
relative error = 3.39414773473493700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 2.56449999999834600E-2 " "
y[1] (numeric) = 2.564499999999186300E-2 " "
absolute error = 8.403000517631654000000000000000E-15 " "
relative error = 3.2766623192189803000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 2.687999999998319500E-2 " "
y[1] (numeric) = 2.687999999999172700E-2 " "
absolute error = 8.531370054853937000000000000000E-15 " "
relative error = 3.17387278826609800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 2.812499999998291400E-2 " "
y[1] (numeric) = 2.812499999999158500E-2 " "
absolute error = 8.673617379884035000000000000000E-15 " "
relative error = 3.08395284618286400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 2.937999999998264000E-2 " "
y[1] (numeric) = 2.93799999999914500E-2 " "
absolute error = 8.808925811010226000000000000000E-15 " "
relative error = 2.99827291048857400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 3.064499999998232500E-2 " "
y[1] (numeric) = 3.06449999999913100E-2 " "
absolute error = 8.98586760555986100000000000000E-15 " "
relative error = 2.93224591468919660000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 3.191999999998207400E-2 " "
y[1] (numeric) = 3.19199999999911700E-2 " "
absolute error = 9.096889908022376000000000000000E-15 " "
relative error = 2.849902853392069500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = 3.32049999999817770E-2 " "
y[1] (numeric) = 3.320499999999102500E-2 " "
absolute error = 9.249545573908335000000000000000E-15 " "
relative error = 2.78558818669279100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = 3.44999999999814900E-2 " "
y[1] (numeric) = 3.449999999999088000E-2 " "
absolute error = 9.395262345890387000000000000000E-15 " "
relative error = 2.723264448085631600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = 3.58049999999812130E-2 " "
y[1] (numeric) = 3.58049999999907500E-2 " "
absolute error = 9.534040223968532000000000000000E-15 " "
relative error = 2.66276783241824700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = 3.711999999998094600E-2 " "
y[1] (numeric) = 3.711999999999060500E-2 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 2.60208521396654600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = 3.844499999998063400E-2 " "
y[1] (numeric) = 3.84449999999904600E-2 " "
absolute error = 9.825473767932635000000000000000E-15 " "
relative error = 2.555722140184051300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = 3.97799999999803300E-2 " "
y[1] (numeric) = 3.977999999999032000E-2 " "
absolute error = 9.985068327722502000000000000000E-15 " "
relative error = 2.510072480575022400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = 4.11249999999800400E-2 " "
y[1] (numeric) = 4.11249999999901700E-2 " "
absolute error = 1.013078509970455300000000000000E-14 " "
relative error = 2.463412790202910700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = 4.247999999997975600E-2 " "
y[1] (numeric) = 4.24799999999900200E-2 " "
absolute error = 1.02626240838787910000000000000E-14 " "
relative error = 2.41587195948297600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = 4.38449999999794300E-2 " "
y[1] (numeric) = 4.38449999999898700E-2 " "
absolute error = 1.044303532538037900000000000000E-14 " "
relative error = 2.381807577918868500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = 4.521999999997916600E-2 " "
y[1] (numeric) = 4.52199999999897200E-2 " "
absolute error = 1.055405762784289400000000000000E-14 " "
relative error = 2.33393578678632400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = 4.66049999999788600E-2 " "
y[1] (numeric) = 4.660499999998956600E-2 " "
absolute error = 1.070671329372885300000000000000E-14 " "
relative error = 2.29733146523628580000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = 4.79999999999785600E-2 " "
y[1] (numeric) = 4.79999999999894100E-2 " "
absolute error = 1.085243006571090500000000000000E-14 " "
relative error = 2.260922930357448800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = 4.940499999997821600E-2 " "
y[1] (numeric) = 4.940499999998926000E-2 " "
absolute error = 1.1039780201116400000000000000E-14 " "
relative error = 2.234547151325021500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = 5.08199999999779400E-2 " "
y[1] (numeric) = 5.0819999999989110E-2 " "
absolute error = 1.11646802913867300000000000000E-14 " "
relative error = 2.19690678697197500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = 5.224499999997761000E-2 " "
y[1] (numeric) = 5.224499999998895000E-2 " "
absolute error = 1.133121374508050400000000000000E-14 " "
relative error = 2.16886089483880900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = 5.3679999999977300E-2 " "
y[1] (numeric) = 5.36799999999887900E-2 " "
absolute error = 1.14908083048703700000000000000E-14 " "
relative error = 2.140612575423850300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = 5.512499999997700E-2 " "
y[1] (numeric) = 5.512499999998863000E-2 " "
absolute error = 1.163652507685242200000000000000E-14 " "
relative error = 2.110934254305175400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = 5.65799999999766500E-2 " "
y[1] (numeric) = 5.65799999999884800E-2 " "
absolute error = 1.183081410616182400000000000000E-14 " "
relative error = 2.09098870734653700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = 5.80449999999763100E-2 " "
y[1] (numeric) = 5.80449999999883200E-2 " "
absolute error = 1.201122534766341200000000000000E-14 " "
relative error = 2.069295434174918400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = 5.95199999999759800E-2 " "
y[1] (numeric) = 5.95199999999881600E-2 " "
absolute error = 1.217775880135718600000000000000E-14 " "
relative error = 2.04599442227185800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = 6.10049999999756600E-2 " "
y[1] (numeric) = 6.10049999999880000E-2 " "
absolute error = 1.233041446724314500000000000000E-14 " "
relative error = 2.021213747602338000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = 6.24999999999753500E-2 " "
y[1] (numeric) = 6.24999999999878300E-2 " "
absolute error = 1.247613123922519700000000000000E-14 " "
relative error = 1.996180998276818600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = 6.400499999997500E-2 " "
y[1] (numeric) = 6.40049999999876600E-2 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.977430275874029800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = 6.55199999999747100E-2 " "
y[1] (numeric) = 6.55199999999874900E-2 " "
absolute error = 1.278144257099711500000000000000E-14 " "
relative error = 1.950769623168810700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = 6.70449999999743800E-2 " "
y[1] (numeric) = 6.70449999999873200E-2 " "
absolute error = 1.294797602469088800000000000000E-14 " "
relative error = 1.93123663579623200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = 6.857999999997400E-2 " "
y[1] (numeric) = 6.85799999999871500E-2 " "
absolute error = 1.315614284180810500000000000000E-14 " "
relative error = 1.918364368884965500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = 7.01249999999736800E-2 " "
y[1] (numeric) = 7.01249999999869900E-2 " "
absolute error = 1.330879850769406400000000000000E-14 " "
relative error = 1.897867879885783700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = 7.16799999999733200E-2 " "
y[1] (numeric) = 7.16799999999868200E-2 " "
absolute error = 1.350308753700346600000000000000E-14 " "
relative error = 1.88380127469426500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = 7.32449999999729700E-2 " "
y[1] (numeric) = 7.32449999999866600E-2 " "
absolute error = 1.368349877850505400000000000000E-14 " "
relative error = 1.8681819617052500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = 7.48199999999726300E-2 " "
y[1] (numeric) = 7.48199999999864800E-2 " "
absolute error = 1.385003223219882800000000000000E-14 " "
relative error = 1.85111363702270710000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = 7.6404999999972300E-2 " "
y[1] (numeric) = 7.6404999999986300E-2 " "
absolute error = 1.400268789808478700000000000000E-14 " "
relative error = 1.83269261149006800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = 7.79999999999719300E-2 " "
y[1] (numeric) = 7.79999999999861400E-2 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.82190445066757900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = 7.96049999999716200E-2 " "
y[1] (numeric) = 7.96049999999859500E-2 " "
absolute error = 1.433575480547233400000000000000E-14 " "
relative error = 1.800861102377670500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = 8.12199999999712600E-2 " "
y[1] (numeric) = 8.12199999999857700E-2 " "
absolute error = 1.451616604697392200000000000000E-14 " "
relative error = 1.78726496515378700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = 8.28449999999708600E-2 " "
y[1] (numeric) = 8.2844999999985600E-2 " "
absolute error = 1.473821065189895300000000000000E-14 " "
relative error = 1.779010278460273500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = 8.44799999999705200E-2 " "
y[1] (numeric) = 8.44799999999854100E-2 " "
absolute error = 1.489086631778491200000000000000E-14 " "
relative error = 1.762649895571745700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = 8.61249999999701400E-2 " "
y[1] (numeric) = 8.61249999999852400E-2 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.753153339321609800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = 8.77799999999698300E-2 " "
y[1] (numeric) = 8.77799999999850500E-2 " "
absolute error = 1.52239332251724600000000000000E-14 " "
relative error = 1.734328232533343700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = 8.94449999999694100E-2 " "
y[1] (numeric) = 8.94449999999848800E-2 " "
absolute error = 1.545985561790530500000000000000E-14 " "
relative error = 1.72842032734200800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = 9.11199999999690600E-2 " "
y[1] (numeric) = 9.1119999999984700E-2 " "
absolute error = 1.564026685940689300000000000000E-14 " "
relative error = 1.716447197038213600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = 9.28049999999687200E-2 " "
y[1] (numeric) = 9.28049999999845000E-2 " "
absolute error = 1.579292252529285200000000000000E-14 " "
relative error = 1.70173185984571680000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = 9.44999999999683300E-2 " "
y[1] (numeric) = 9.44999999999843300E-2 " "
absolute error = 1.60010893424100700000000000000E-14 " "
relative error = 1.693236967451368400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = 9.62049999999679600E-2 " "
y[1] (numeric) = 9.62049999999841300E-2 " "
absolute error = 1.618150058391165700000000000000E-14 " "
relative error = 1.681981246704126500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = 9.79199999999675900E-2 " "
y[1] (numeric) = 9.79199999999839500E-2 " "
absolute error = 1.636191182541324500000000000000E-14 " "
relative error = 1.670946877595859700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = 9.96449999999671800E-2 " "
y[1] (numeric) = 9.96449999999837600E-2 " "
absolute error = 1.658395643033827600000000000000E-14 " "
relative error = 1.664303921957322200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = 0.10137999999996683 " "
y[1] (numeric) = 0.10137999999998357 " "
absolute error = 1.673661209622423500000000000000E-14 " "
relative error = 1.650879078341853400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = 0.10312499999996644 " "
y[1] (numeric) = 0.10312499999998338 " "
absolute error = 1.694477891334145200000000000000E-14 " "
relative error = 1.643130076445766500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = 0.10487999999996606 " "
y[1] (numeric) = 0.10487999999998318 " "
absolute error = 1.71251901548430400000000000000E-14 " "
relative error = 1.632836589897843600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = 0.10664499999996563 " "
y[1] (numeric) = 0.10664499999998299 " "
absolute error = 1.736111254757588500000000000000E-14 " "
relative error = 1.62793497562768800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = 0.10841999999996527 " "
y[1] (numeric) = 0.1084199999999828 " "
absolute error = 1.75276460012696600000000000000E-14 " "
relative error = 1.616643239372373400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = 0.11020499999996486 " "
y[1] (numeric) = 0.1102049999999826 " "
absolute error = 1.773581281838687600000000000000E-14 " "
relative error = 1.609347381551883300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = 0.11199999999996446 " "
y[1] (numeric) = 0.1119999999999824 " "
absolute error = 1.794397963550409300000000000000E-14 " "
relative error = 1.602141038884802600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = 0.11380499999996407 " "
y[1] (numeric) = 0.11380499999998221 " "
absolute error = 1.813826866481349500000000000000E-14 " "
relative error = 1.59380243968360100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = 0.1156199999999637 " "
y[1] (numeric) = 0.11561999999998201 " "
absolute error = 1.831867990631508300000000000000E-14 " "
relative error = 1.584386776191042400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = 0.11744499999996327 " "
y[1] (numeric) = 0.11744499999998181 " "
absolute error = 1.854072451124011400000000000000E-14 " "
relative error = 1.578672954254835300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = 0.11927999999996286 " "
y[1] (numeric) = 0.11927999999998161 " "
absolute error = 1.87488913283573300000000000000E-14 " "
relative error = 1.571838642552244300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = 0.12112499999996246 " "
y[1] (numeric) = 0.12112499999998141 " "
absolute error = 1.895705814547454800000000000000E-14 " "
relative error = 1.56508219983326500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = 0.12297999999996206 " "
y[1] (numeric) = 0.1229799999999812 " "
absolute error = 1.913746938697613600000000000000E-14 " "
relative error = 1.556144851763054000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = 0.12484499999996163 " "
y[1] (numeric) = 0.124844999999981 " "
absolute error = 1.937339177970898200000000000000E-14 " "
relative error = 1.551795568882609300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = 0.12671999999996125 " "
y[1] (numeric) = 0.1267199999999808 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.541976423090967000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = 0.12860499999996083 " "
y[1] (numeric) = 0.12860499999998057 " "
absolute error = 1.973421426271215800000000000000E-14 " "
relative error = 1.53448266107213300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = 0.13049999999996043 " "
y[1] (numeric) = 0.13049999999998035 " "
absolute error = 1.99285032920215600000000000000E-14 " "
relative error = 1.527088374868015600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = 0.13240499999995997 " "
y[1] (numeric) = 0.13240499999998015 " "
absolute error = 2.01783034725622200000000000000E-14 " "
relative error = 1.523983495530253600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = 0.13431999999995958 " "
y[1] (numeric) = 0.13431999999997993 " "
absolute error = 2.034483692625599400000000000000E-14 " "
relative error = 1.51465432744655400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = 0.13624499999995915 " "
y[1] (numeric) = 0.13624499999997972 " "
absolute error = 2.056688153118102500000000000000E-14 " "
relative error = 1.509551288574787500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = 0.13817999999995872 " "
y[1] (numeric) = 0.1381799999999795 " "
absolute error = 2.078892613610605600000000000000E-14 " "
relative error = 1.504481555660172600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = 0.1401249999999583 " "
y[1] (numeric) = 0.1401249999999793 " "
absolute error = 2.09832151654154600000000000000E-14 " "
relative error = 1.497464061760692400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = 0.14207999999995785 " "
y[1] (numeric) = 0.14207999999997908 " "
absolute error = 2.12330153459561200000000000000E-14 " "
relative error = 1.49444083234532800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = 0.14404499999995746 " "
y[1] (numeric) = 0.14404499999997886 " "
absolute error = 2.139954879964989200000000000000E-14 " "
relative error = 1.485615522902996300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = 0.14601999999995702 " "
y[1] (numeric) = 0.14601999999997864 " "
absolute error = 2.162159340457492400000000000000E-14 " "
relative error = 1.480728215626714900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = 0.1480049999999566 " "
y[1] (numeric) = 0.14800499999997843 " "
absolute error = 2.184363800949995500000000000000E-14 " "
relative error = 1.475871626600882600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = 0.1499999999999561 " "
y[1] (numeric) = 0.1499999999999782 " "
absolute error = 2.209343819004061500000000000000E-14 " "
relative error = 1.47289587933647200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = 0.1520049999999557 " "
y[1] (numeric) = 0.152004999999978 " "
absolute error = 2.228772721935001800000000000000E-14 " "
relative error = 1.466249611483603500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = 0.15401999999995525 " "
y[1] (numeric) = 0.15401999999997776 " "
absolute error = 2.25097718242750500000000000000E-14 " "
relative error = 1.461483692006336200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = 0.1560449999999548 " "
y[1] (numeric) = 0.15604499999997754 " "
absolute error = 2.27318164292000800000000000000E-14 " "
relative error = 1.456747504194730300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = 0.15807999999995437 " "
y[1] (numeric) = 0.15807999999997732 " "
absolute error = 2.29538610341251110000000000000E-14 " "
relative error = 1.452040804284649400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = 0.1601249999999539 " "
y[1] (numeric) = 0.1601249999999771 " "
absolute error = 2.320366121466577200000000000000E-14 " "
relative error = 1.449096719105227300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = 0.16217999999995347 " "
y[1] (numeric) = 0.16217999999997687 " "
absolute error = 2.339795024397517400000000000000E-14 " "
relative error = 1.442714899739911700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = 0.164244999999953 " "
y[1] (numeric) = 0.16424499999997666 " "
absolute error = 2.364775042451583400000000000000E-14 " "
relative error = 1.439785103018210700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = 0.16631999999995256 " "
y[1] (numeric) = 0.16631999999997643 " "
absolute error = 2.386979502944086600000000000000E-14 " "
relative error = 1.435172861318402500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = 0.16840499999995207 " "
y[1] (numeric) = 0.1684049999999762 " "
absolute error = 2.414735078559715500000000000000E-14 " "
relative error = 1.433885620118407000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = 0.17049999999995163 " "
y[1] (numeric) = 0.17049999999997598 " "
absolute error = 2.434163981490655700000000000000E-14 " "
relative error = 1.427662159232461200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = 0.17260499999995116 " "
y[1] (numeric) = 0.17260499999997575 " "
absolute error = 2.459143999544721700000000000000E-14 " "
relative error = 1.424723501373319200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = 0.1747199999999507 " "
y[1] (numeric) = 0.17471999999997553 " "
absolute error = 2.484124017598787800000000000000E-14 " "
relative error = 1.421774277472234700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = 0.17684499999995024 " "
y[1] (numeric) = 0.1768449999999753 " "
absolute error = 2.50632847809129100000000000000E-14 " "
relative error = 1.417245880908137900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = 0.17897999999994973 " "
y[1] (numeric) = 0.17897999999997505 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 1.414296846656647500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = 0.1811249999999493 " "
y[1] (numeric) = 0.1811249999999748 " "
absolute error = 2.55073739907629700000000000000E-14 " "
relative error = 1.408274616467639000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = 0.18327999999994882 " "
y[1] (numeric) = 0.18327999999997457 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 1.4053456007917300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = 0.18544499999994835 " "
y[1] (numeric) = 0.18544499999997432 " "
absolute error = 2.597921877622866300000000000000E-14 " "
relative error = 1.400912333912259500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = 0.18761999999994783 " "
y[1] (numeric) = 0.18761999999997409 " "
absolute error = 2.625677453238495000000000000000E-14 " "
relative error = 1.399465650378011500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 0.18980499999994738 " "
y[1] (numeric) = 0.18980499999997386 " "
absolute error = 2.647881913730998300000000000000E-14 " "
relative error = 1.395053825627213500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 0.19199999999994688 " "
y[1] (numeric) = 0.1919999999999736 " "
absolute error = 2.672861931785064400000000000000E-14 " "
relative error = 1.392115589471773000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 0.19420499999994645 " "
y[1] (numeric) = 0.19420499999997337 " "
absolute error = 2.692290834716004600000000000000E-14 " "
relative error = 1.386313861495196700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 0.19641999999994597 " "
y[1] (numeric) = 0.19641999999997312 " "
absolute error = 2.714495295208508000000000000000E-14 " "
relative error = 1.38198518236903300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 0.19864499999994545 " "
y[1] (numeric) = 0.19864499999997287 " "
absolute error = 2.742250870824136700000000000000E-14 " "
relative error = 1.380478175048397700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 0.200879999999945 " "
y[1] (numeric) = 0.20087999999997264 " "
absolute error = 2.764455331316640000000000000000E-14 " "
relative error = 1.376172506629528300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 0.2031249999999445 " "
y[1] (numeric) = 0.20312499999997238 " "
absolute error = 2.789435349370706000000000000000E-14 " "
relative error = 1.373260479690569000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 0.20537999999994394 " "
y[1] (numeric) = 0.20537999999997214 " "
absolute error = 2.819966482547897600000000000000E-14 " "
relative error = 1.373048243523550000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 0.20764499999994346 " "
y[1] (numeric) = 0.20764499999997188 " "
absolute error = 2.84217094304040100000000000000E-14 " "
relative error = 1.368764450403898400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 0.20991999999994293 " "
y[1] (numeric) = 0.20991999999997163 " "
absolute error = 2.869926518656029700000000000000E-14 " "
relative error = 1.367152495549166200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 0.21220499999994247 " "
y[1] (numeric) = 0.2122049999999714 " "
absolute error = 2.89213097914853300000000000000E-14 " "
relative error = 1.362894832425869700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 0.21449999999994196 " "
y[1] (numeric) = 0.21449999999997113 " "
absolute error = 2.91711099720259900000000000000E-14 " "
relative error = 1.359958506854726200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 0.2168049999999414 " "
y[1] (numeric) = 0.21680499999997088 " "
absolute error = 2.947642130379790600000000000000E-14 " "
relative error = 1.359582173095909800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 0.21911999999994092 " "
y[1] (numeric) = 0.21911999999997064 " "
absolute error = 2.972622148433856600000000000000E-14 " "
relative error = 1.356618359088471200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 0.22144499999994038 " "
y[1] (numeric) = 0.2214449999999704 " "
absolute error = 3.000377724049485600000000000000E-14 " "
relative error = 1.354908769243059800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 0.22377999999993992 " "
y[1] (numeric) = 0.22377999999997014 " "
absolute error = 3.022582184541988700000000000000E-14 " "
relative error = 1.350693620762713500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 0.2261249999999394 " "
y[1] (numeric) = 0.22612499999996988 " "
absolute error = 3.04756220259605470000000000000E-14 " "
relative error = 1.347733422928412000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 0.22847999999993884 " "
y[1] (numeric) = 0.22847999999996962 " "
absolute error = 3.078093335773246500000000000000E-14 " "
relative error = 1.34720471628767100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 0.23084499999993835 " "
y[1] (numeric) = 0.23084499999996938 " "
absolute error = 3.103073353827312500000000000000E-14 " "
relative error = 1.344223766522186500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 0.2332199999999378 " "
y[1] (numeric) = 0.23321999999996912 " "
absolute error = 3.130828929442941400000000000000E-14 " "
relative error = 1.342435867182821500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 0.23560499999993734 " "
y[1] (numeric) = 0.23560499999996884 " "
absolute error = 3.150257832373881700000000000000E-14 " "
relative error = 1.337092944706062800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 0.23799999999993682 " "
y[1] (numeric) = 0.23799999999996857 " "
absolute error = 3.17523785042794770000000000000E-14 " "
relative error = 1.334133550600332400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 0.24040499999993625 " "
y[1] (numeric) = 0.2404049999999683 " "
absolute error = 3.205768983605139500000000000000E-14 " "
relative error = 1.333486817497967800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 0.24281999999993575 " "
y[1] (numeric) = 0.24281999999996803 " "
absolute error = 3.227973444097642600000000000000E-14 " "
relative error = 1.32936885104130510000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 0.2452449999999352 " "
y[1] (numeric) = 0.24524499999996777 " "
absolute error = 3.255729019713271600000000000000E-14 " "
relative error = 1.327541446192228900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 0.24767999999993462 " "
y[1] (numeric) = 0.2476799999999675 " "
absolute error = 3.28903571045202600000000000000E-14 " "
relative error = 1.327937544594999500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 0.2501249999999341 " "
y[1] (numeric) = 0.25012499999996723 " "
absolute error = 3.31401572850609200000000000000E-14 " "
relative error = 1.324943819493039600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 0.2525799999999335 " "
y[1] (numeric) = 0.25257999999996705 " "
absolute error = 3.35287353436797300000000000000E-14 " "
relative error = 1.327450128422224800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 0.255044999999933 " "
y[1] (numeric) = 0.2550449999999667 " "
absolute error = 3.3695268797373500000000000000E-14 " "
relative error = 1.321149945985310400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 0.25751999999993247 " "
y[1] (numeric) = 0.25751999999996655 " "
absolute error = 3.408384685599230600000000000000E-14 " "
relative error = 1.323541738738787000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 0.260004999999932 " "
y[1] (numeric) = 0.2600049999999662 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 1.315161983748918700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 0.26249999999993134 " "
y[1] (numeric) = 0.26249999999996604 " "
absolute error = 3.46944695195361400000000000000E-14 " "
relative error = 1.321694076935055800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 0.2650049999999309 " "
y[1] (numeric) = 0.26500499999996563 " "
absolute error = 3.4749980670767400000000000000E-14 " "
relative error = 1.311295283891868400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 0.26751999999993026 " "
y[1] (numeric) = 0.26751999999996545 " "
absolute error = 3.51940698806174600000000000000E-14 " "
relative error = 1.31556780355213200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 0.2700449999999297 " "
y[1] (numeric) = 0.27004499999996506 " "
absolute error = 3.536060333431123600000000000000E-14 " "
relative error = 1.309433736389136700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 0.2725799999999292 " "
y[1] (numeric) = 0.27257999999996485 " "
absolute error = 3.563815909046752500000000000000E-14 " "
relative error = 1.307438516783211400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 0.27512499999992857 " "
y[1] (numeric) = 0.2751249999999645 " "
absolute error = 3.591571484662381400000000000000E-14 " "
relative error = 1.305432615961222800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 0.2776799999999281 " "
y[1] (numeric) = 0.2776799999999643 " "
absolute error = 3.619327060278010300000000000000E-14 " "
relative error = 1.303416544324023400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 0.28024499999992747 " "
y[1] (numeric) = 0.28024499999996394 " "
absolute error = 3.64708263589363900000000000000E-14 " "
relative error = 1.301390795873105000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 0.2828199999999269 " "
y[1] (numeric) = 0.2828199999999637 " "
absolute error = 3.68038932663239400000000000000E-14 " "
relative error = 1.301318621962147300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 0.2854049999999263 " "
y[1] (numeric) = 0.2854049999999634 " "
absolute error = 3.70814490224802300000000000000E-14 " "
relative error = 1.29925716166464500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 0.28799999999992576 " "
y[1] (numeric) = 0.2879999999999631 " "
absolute error = 3.73590047786365200000000000000E-14 " "
relative error = 1.297187665925213500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 0.2906049999999252 " "
y[1] (numeric) = 0.2906049999999628 " "
absolute error = 3.763656053479280700000000000000E-14 " "
relative error = 1.295110563644896000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 0.29321999999992465 " "
y[1] (numeric) = 0.2932199999999625 " "
absolute error = 3.78586051397178400000000000000E-14 " "
relative error = 1.29113311301164880000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 0.2958449999999241 " "
y[1] (numeric) = 0.2958449999999622 " "
absolute error = 3.81361608958741270000000000000E-14 " "
relative error = 1.289058827963423800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 0.2984799999999235 " "
y[1] (numeric) = 0.29847999999996194 " "
absolute error = 3.846922780326167400000000000000E-14 " "
relative error = 1.288837704478408600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 0.3011249999999229 " "
y[1] (numeric) = 0.3011249999999617 " "
absolute error = 3.874678355941796300000000000000E-14 " "
relative error = 1.286734198735670600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 0.30377999999992233 " "
y[1] (numeric) = 0.30377999999996136 " "
absolute error = 3.90243393155742500000000000000E-14 " "
relative error = 1.284625035077497600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 0.3064449999999217 " "
y[1] (numeric) = 0.3064449999999611 " "
absolute error = 3.94129173741930570000000000000E-14 " "
relative error = 1.286133478249053800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 0.3091199999999211 " "
y[1] (numeric) = 0.30911999999996076 " "
absolute error = 3.96349619791180900000000000000E-14 " "
relative error = 1.28218691702666300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 0.3118049999999205 " "
y[1] (numeric) = 0.31180499999996053 " "
absolute error = 4.002354003773689300000000000000E-14 " "
relative error = 1.283608025456522400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 0.31449999999991995 " "
y[1] (numeric) = 0.31449999999996014 " "
absolute error = 4.019007349143066700000000000000E-14 " "
relative error = 1.27790376761338300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 0.31720499999991936 " "
y[1] (numeric) = 0.31720499999995994 " "
absolute error = 4.05786515500494700000000000000E-14 " "
relative error = 1.27925636575904500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 0.3199199999999187 " "
y[1] (numeric) = 0.31991999999995957 " "
absolute error = 4.08562073062057600000000000000E-14 " "
relative error = 1.277075747256068400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 0.32264499999991814 " "
y[1] (numeric) = 0.3226449999999594 " "
absolute error = 4.124478536482456500000000000000E-14 " "
relative error = 1.278333318812782700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 0.3253799999999175 " "
y[1] (numeric) = 0.325379999999959 " "
absolute error = 4.146682996974959700000000000000E-14 " "
relative error = 1.274412378442439700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 0.32812499999991696 " "
y[1] (numeric) = 0.3281249999999588 " "
absolute error = 4.1855408028368400000000000000E-14 " "
relative error = 1.275593387531550300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 0.33087999999991635 " "
y[1] (numeric) = 0.3308799999999584 " "
absolute error = 4.202194148206217500000000000000E-14 " "
relative error = 1.270005484830536700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 0.3336449999999157 " "
y[1] (numeric) = 0.33364499999995817 " "
absolute error = 4.24660306919122400000000000000E-14 " "
relative error = 1.272790861302371400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 0.3364199999999151 " "
y[1] (numeric) = 0.33641999999995775 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.267242261031352700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 0.3392049999999145 " "
y[1] (numeric) = 0.3392049999999575 " "
absolute error = 4.302114220422481600000000000000E-14 " "
relative error = 1.26829327999987200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 0.34199999999991393 " "
y[1] (numeric) = 0.3419999999999571 " "
absolute error = 4.31876756579185900000000000000E-14 " "
relative error = 1.262797533857586400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 0.3448049999999133 " "
y[1] (numeric) = 0.3448049999999569 " "
absolute error = 4.357625371653739400000000000000E-14 " "
relative error = 1.263794136295829400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 0.34761999999991267 " "
y[1] (numeric) = 0.3476199999999565 " "
absolute error = 4.385380947269368300000000000000E-14 " "
relative error = 1.261544487449073600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 0.3504449999999121 " "
y[1] (numeric) = 0.35044499999995626 " "
absolute error = 4.41868763800812300000000000000E-14 " "
relative error = 1.260879064620477300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 0.35327999999991144 " "
y[1] (numeric) = 0.3532799999999559 " "
absolute error = 4.44644321362375200000000000000E-14 " "
relative error = 1.258617304581314000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 0.35612499999991076 " "
y[1] (numeric) = 0.3561249999999556 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.25947378574566700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 0.35897999999991015 " "
y[1] (numeric) = 0.3589799999999553 " "
absolute error = 4.513056595101261300000000000000E-14 " "
relative error = 1.25718886709632600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 0.3618449999999095 " "
y[1] (numeric) = 0.36184499999995495 " "
absolute error = 4.54636328584001600000000000000E-14 " "
relative error = 1.256439438389684300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 0.3647199999999089 " "
y[1] (numeric) = 0.36471999999995464 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.254145333805875000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 0.36760499999990826 " "
y[1] (numeric) = 0.36760499999995433 " "
absolute error = 4.607425552194399600000000000000E-14 " "
relative error = 1.253363134939826700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 0.3704999999999077 " "
y[1] (numeric) = 0.37049999999995403 " "
absolute error = 4.635181127810028600000000000000E-14 " "
relative error = 1.25106103314741780000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 0.37340499999990695 " "
y[1] (numeric) = 0.3734049999999537 " "
absolute error = 4.67403893367190900000000000000E-14 " "
relative error = 1.251734426071711100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 0.3763199999999064 " "
y[1] (numeric) = 0.3763199999999534 " "
absolute error = 4.70179450928753800000000000000E-14 " "
relative error = 1.24941393210265400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 0.3792449999999057 " "
y[1] (numeric) = 0.37924499999995304 " "
absolute error = 4.735101200026292600000000000000E-14 " "
relative error = 1.248559954653975700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 0.38217999999990504 " "
y[1] (numeric) = 0.3821799999999528 " "
absolute error = 4.77395900588817300000000000000E-14 " "
relative error = 1.249138888976230700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 0.38512499999990446 " "
y[1] (numeric) = 0.38512499999995237 " "
absolute error = 4.790612351257550500000000000000E-14 " "
relative error = 1.243911029213564100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 0.3880799999999037 " "
y[1] (numeric) = 0.38807999999995213 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 1.247313024986312800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 0.39104499999990316 " "
y[1] (numeric) = 0.39104499999995174 " "
absolute error = 4.8572257327350600000000000000E-14 " "
relative error = 1.242114266321334600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 0.39401999999990245 " "
y[1] (numeric) = 0.3940199999999515 " "
absolute error = 4.90718576884319200000000000000E-14 " "
relative error = 1.245415402478150100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 0.3970049999999018 " "
y[1] (numeric) = 0.3970049999999511 " "
absolute error = 4.92939022933569500000000000000E-14 " "
relative error = 1.241644369551243700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 0.3999999999999011 " "
y[1] (numeric) = 0.3999999999999509 " "
absolute error = 4.97935026544382700000000000000E-14 " "
relative error = 1.244837566361264600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 0.4030049999999018 " "
y[1] (numeric) = 0.40300499999995043 " "
absolute error = 4.862776847858185600000000000000E-14 " "
relative error = 1.206629408533236700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 0.40601999999990246 " "
y[1] (numeric) = 0.40601999999995025 " "
absolute error = 4.77951012101129900000000000000E-14 " "
relative error = 1.177161253389598200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 0.4090449999999032 " "
y[1] (numeric) = 0.4090449999999498 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.139956900445369300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 0.41207999999990386 " "
y[1] (numeric) = 0.4120799999999496 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.110007489190621300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 0.4151249999999046 " "
y[1] (numeric) = 0.4151249999999492 " "
absolute error = 4.457545443870003500000000000000E-14 " "
relative error = 1.07378390698489090000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 0.4181799999999053 " "
y[1] (numeric) = 0.418179999999949 " "
absolute error = 4.36872760189999100000000000000E-14 " "
relative error = 1.044700273064465300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 0.42124499999990606 " "
y[1] (numeric) = 0.4212449999999486 " "
absolute error = 4.252154184314349500000000000000E-14 " "
relative error = 1.009425437528112700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 0.42431999999990677 " "
y[1] (numeric) = 0.42431999999994835 " "
absolute error = 4.15778522722121100000000000000E-14 " "
relative error = 9.798701987231628000000000000E-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) = 0.42740499999990744 " "
y[1] (numeric) = 0.42740499999994797 " "
absolute error = 4.052314039881821400000000000000E-14 " "
relative error = 9.48120410356149000000000000E-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) = 0.4304999999999082 " "
y[1] (numeric) = 0.43049999999994776 " "
absolute error = 3.95794508278868300000000000000E-14 " "
relative error = 9.193832944923409000000000000E-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) = 0.433604999999909 " "
y[1] (numeric) = 0.4336049999999474 " "
absolute error = 3.841371665203041600000000000000E-14 " "
relative error = 8.859149837303185000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 0.43671999999990974 " "
y[1] (numeric) = 0.43671999999994715 " "
absolute error = 3.741451592986777500000000000000E-14 " "
relative error = 8.567163383833007000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 0.43984499999991045 " "
y[1] (numeric) = 0.4398449999999468 " "
absolute error = 3.635980405647387700000000000000E-14 " "
relative error = 8.266503894890537000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 0.4429799999999112 " "
y[1] (numeric) = 0.4429799999999466 " "
absolute error = 3.536060333431123600000000000000E-14 " "
relative error = 7.982437883046261000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 0.44612499999991195 " "
y[1] (numeric) = 0.44612499999994626 " "
absolute error = 3.43058914609173370000000000000E-14 " "
relative error = 7.689748716374134000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 0.44927999999991275 " "
y[1] (numeric) = 0.449279999999946 " "
absolute error = 3.32511795875234400000000000000E-14 " "
relative error = 7.400992607623287000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 0.4524449999999135 " "
y[1] (numeric) = 0.4524449999999457 " "
absolute error = 3.21964677141295400000000000000E-14 " "
relative error = 7.1161064248993120000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = 0.4556199999999143 " "
y[1] (numeric) = 0.45561999999994546 " "
absolute error = 3.11417558407356400000000000000E-14 " "
relative error = 6.835028278113667000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 0.4588049999999151 " "
y[1] (numeric) = 0.4588049999999452 " "
absolute error = 3.00870439673417400000000000000E-14 " "
relative error = 6.557697489640982000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 0.4619999999999159 " "
y[1] (numeric) = 0.4619999999999449 " "
absolute error = 2.897682094271658600000000000000E-14 " "
relative error = 6.272039165091312000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 0.4652049999999167 " "
y[1] (numeric) = 0.46520499999994464 " "
absolute error = 2.792210906932268700000000000000E-14 " "
relative error = 6.002108547699979000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 0.46841999999991757 " "
y[1] (numeric) = 0.4684199999999444 " "
absolute error = 2.68118860446975300000000000000E-14 " "
relative error = 5.723898647517666000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 0.4716449999999184 " "
y[1] (numeric) = 0.47164499999994414 " "
absolute error = 2.575717417130363000000000000000E-14 " "
relative error = 5.461135848213824000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 0.47487999999991926 " "
y[1] (numeric) = 0.47487999999994385 " "
absolute error = 2.459143999544721700000000000000E-14 " "
relative error = 5.178453503085284000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 0.4781249999999201 " "
y[1] (numeric) = 0.4781249999999436 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 4.922714378469491000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 0.48137999999992087 " "
y[1] (numeric) = 0.48137999999994335 " "
absolute error = 2.24820162486594200000000000000E-14 " "
relative error = 4.670326197320852000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 0.4846449999999217 " "
y[1] (numeric) = 0.48464499999994315 " "
absolute error = 2.14273043752655200000000000000E-14 " "
relative error = 4.421237065330082500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 0.48791999999992264 " "
y[1] (numeric) = 0.48791999999994284 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 4.1412647663922475000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 0.4912049999999234 " "
y[1] (numeric) = 0.49120499999994266 " "
absolute error = 1.926236947724646600000000000000E-14 " "
relative error = 3.9214522403577873000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 0.49449999999992433 " "
y[1] (numeric) = 0.4944999999999424 " "
absolute error = 1.804112415015879400000000000000E-14 " "
relative error = 3.6483567543299406000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 0.4978049999999252 " "
y[1] (numeric) = 0.4978049999999422 " "
absolute error = 1.698641227676489500000000000000E-14 " "
relative error = 3.412262286792509000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 0.5011199999999261 " "
y[1] (numeric) = 0.5011199999999421 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 3.1902960477739090000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 0.504444999999927 " "
y[1] (numeric) = 0.5044449999999417 " "
absolute error = 1.476596622751458200000000000000E-14 " "
relative error = 2.9271706979981404000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 0.5077799999999278 " "
y[1] (numeric) = 0.5077799999999416 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 2.711167337302355000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 0.5111249999999288 " "
y[1] (numeric) = 0.5111249999999413 " "
absolute error = 1.254552017826427000000000000000E-14 " "
relative error = 2.4544915976064596000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 0.5144799999999297 " "
y[1] (numeric) = 0.5144799999999412 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 2.2442698367484074000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 0.5178449999999306 " "
y[1] (numeric) = 0.5178449999999409 " "
absolute error = 1.032507412901395600000000000000E-14 " "
relative error = 1.993854170459373000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = 0.5212199999999315 " "
y[1] (numeric) = 0.5212199999999408 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 1.7892393628127357000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 0.5246049999999325 " "
y[1] (numeric) = 0.5246049999999405 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 1.5237380080826823000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 0.5279999999999334 " "
y[1] (numeric) = 0.5279999999999404 " "
absolute error = 6.994405055138486000000000000000E-15 " "
relative error = 1.3246979271097290000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 0.5314049999999343 " "
y[1] (numeric) = 0.5314049999999401 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.0863954475497084000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 0.5348199999999352 " "
y[1] (numeric) = 0.53481999999994 " "
absolute error = 4.773959005888173000000000000000E-15 " "
relative error = 8.926291099601270000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 0.5382449999999362 " "
y[1] (numeric) = 0.5382449999999397 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 6.394283971682770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 0.5416799999999372 " "
y[1] (numeric) = 0.5416799999999397 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 4.50910252210830640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 0.5451249999999381 " "
y[1] (numeric) = 0.5451249999999394 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 2.24030328289440200000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 0.5485799999999391 " "
y[1] (numeric) = 0.5485799999999392 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.023812433237230400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 0.5520449999999402 " "
y[1] (numeric) = 0.552044999999939 " "
absolute error = 1.2212453270876722000000000000000E-15 " "
relative error = 2.21222061079767860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 0.5555199999999412 " "
y[1] (numeric) = 0.555519999999939 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 3.9970587004078130000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 0.559004999999942 " "
y[1] (numeric) = 0.5590049999999387 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 5.9582098082768760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 0.5624999999999432 " "
y[1] (numeric) = 0.5624999999999386 " "
absolute error = 4.551914400963142000000000000000E-15 " "
relative error = 8.0922922683797370000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 0.5660049999999441 " "
y[1] (numeric) = 0.5660049999999384 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 1.019983874356478000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 0.5695199999999452 " "
y[1] (numeric) = 0.5695199999999383 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 1.208628801916812900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 0.5730449999999461 " "
y[1] (numeric) = 0.5730449999999381 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 1.3949350883965272000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 0.5765799999999472 " "
y[1] (numeric) = 0.5765799999999379 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 1.6174465654119408000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = 0.5801249999999483 " "
y[1] (numeric) = 0.5801249999999377 " "
absolute error = 1.054711873393898700000000000000E-14 " "
relative error = 1.8180769203085417000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = 0.5836799999999494 " "
y[1] (numeric) = 0.5836799999999377 " "
absolute error = 1.165734175856414400000000000000E-14 " "
relative error = 1.9972145282629447000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = 0.5872449999999503 " "
y[1] (numeric) = 0.5872449999999375 " "
absolute error = 1.2767564783189300000000000000E-14 " "
relative error = 2.174146188250284000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = 0.5908199999999513 " "
y[1] (numeric) = 0.5908199999999374 " "
absolute error = 1.387778780781445700000000000000E-14 " "
relative error = 2.348902848213602000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = 0.5944049999999523 " "
y[1] (numeric) = 0.5944049999999372 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 2.5401928205353824000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = 0.5979999999999535 " "
y[1] (numeric) = 0.5979999999999371 " "
absolute error = 1.6320278461989800000000000000E-14 " "
relative error = 2.7291435555169014000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = 0.6016049999999546 " "
y[1] (numeric) = 0.601604999999937 " "
absolute error = 1.76525460915399900000000000000E-14 " "
relative error = 2.9342419181259000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = 0.6052199999999557 " "
y[1] (numeric) = 0.6052199999999368 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 3.1185009448843465000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = 0.6088449999999568 " "
y[1] (numeric) = 0.6088449999999367 " "
absolute error = 2.009503674571533300000000000000E-14 " "
relative error = 3.300517659784799000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = 0.612479999999958 " "
y[1] (numeric) = 0.6124799999999366 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 3.4803229612076264000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = 0.616124999999959 " "
y[1] (numeric) = 0.6161249999999365 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 3.639927790209723000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = 0.61977999999996 " "
y[1] (numeric) = 0.6197799999999364 " "
absolute error = 2.364775042451583400000000000000E-14 " "
relative error = 3.815507183922902000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = 0.6234449999999612 " "
y[1] (numeric) = 0.6234449999999363 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 3.988963862346327000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = 0.6271199999999624 " "
y[1] (numeric) = 0.6271199999999362 " "
absolute error = 2.620126338115369400000000000000E-14 " "
relative error = 4.178030262335002000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = 0.6308049999999634 " "
y[1] (numeric) = 0.6308049999999361 " "
absolute error = 2.73114864057788500000000000000E-14 " "
relative error = 4.329624274661811000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = 0.6344999999999645 " "
y[1] (numeric) = 0.6344999999999359 " "
absolute error = 2.86437540353290400000000000000E-14 " "
relative error = 4.514382038665191000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = 0.6382049999999657 " "
y[1] (numeric) = 0.6382049999999359 " "
absolute error = 2.98649993624167100000000000000E-14 " "
relative error = 4.679530771839505000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = 0.641919999999967 " "
y[1] (numeric) = 0.6419199999999358 " "
absolute error = 3.1197266991966900000000000000E-14 " "
relative error = 4.85999298852949000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = 0.645644999999968 " "
y[1] (numeric) = 0.6456449999999357 " "
absolute error = 3.230749001659205500000000000000E-14 " "
relative error = 5.0039092715956380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = 0.6493799999999692 " "
y[1] (numeric) = 0.6493799999999356 " "
absolute error = 3.363975764614224300000000000000E-14 " "
relative error = 5.180288528464665000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = 0.6531249999999704 " "
y[1] (numeric) = 0.6531249999999356 " "
absolute error = 3.486100297322991500000000000000E-14 " "
relative error = 5.3375698332220470000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = 0.6568799999999715 " "
y[1] (numeric) = 0.6568799999999354 " "
absolute error = 3.60822483003175900000000000000E-14 " "
relative error = 5.4929741049079220000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = 0.6606449999999726 " "
y[1] (numeric) = 0.6606449999999354 " "
absolute error = 3.719247132494274400000000000000E-14 " "
relative error = 5.629721155074856000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = 0.6644199999999738 " "
y[1] (numeric) = 0.6644199999999353 " "
absolute error = 3.85247389544929300000000000000E-14 " "
relative error = 5.798250948871865000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = 0.6682049999999751 " "
y[1] (numeric) = 0.6682049999999353 " "
absolute error = 3.974598428158060400000000000000E-14 " "
relative error = 5.948172234805499000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = 0.6719999999999764 " "
y[1] (numeric) = 0.6719999999999352 " "
absolute error = 4.11892742135933100000000000000E-14 " "
relative error = 6.1293562817849330000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = 0.6758049999999776 " "
y[1] (numeric) = 0.6758049999999353 " "
absolute error = 4.229949723821846400000000000000E-14 " "
relative error = 6.2591275942350030000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = 0.6796199999999788 " "
y[1] (numeric) = 0.679619999999935 " "
absolute error = 4.37427871702311700000000000000E-14 " "
relative error = 6.4363596083447420000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = 0.6834449999999799 " "
y[1] (numeric) = 0.6834449999999351 " "
absolute error = 4.47419878923938100000000000000E-14 " "
relative error = 6.546538184110664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = 0.6872799999999812 " "
y[1] (numeric) = 0.6872799999999349 " "
absolute error = 4.62963001268690300000000000000E-14 " "
relative error = 6.736162863297389000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = 0.6911249999999824 " "
y[1] (numeric) = 0.691124999999935 " "
absolute error = 4.740652315149418400000000000000E-14 " "
relative error = 6.8593269164760920000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = 0.6949799999999837 " "
y[1] (numeric) = 0.6949799999999349 " "
absolute error = 4.88498130835068900000000000000E-14 " "
relative error = 7.028952355968234000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = 0.6988449999999848 " "
y[1] (numeric) = 0.698844999999935 " "
absolute error = 4.98490138056695300000000000000E-14 " "
relative error = 7.1330572309554500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = 0.7027199999999862 " "
y[1] (numeric) = 0.7027199999999348 " "
absolute error = 5.14033260401447500000000000000E-14 " "
relative error = 7.31490864642329000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = 0.7066049999999875 " "
y[1] (numeric) = 0.7066049999999349 " "
absolute error = 5.26245713672324200000000000000E-14 " "
relative error = 7.447523208473383000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = 0.7104999999999888 " "
y[1] (numeric) = 0.7104999999999347 " "
absolute error = 5.406786129924512000000000000000E-14 " "
relative error = 7.609832695178885000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = 0.71440499999999 " "
y[1] (numeric) = 0.7144049999999348 " "
absolute error = 5.51780843238702800000000000000E-14 " "
relative error = 7.723641957135106000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = 0.7183199999999912 " "
y[1] (numeric) = 0.7183199999999347 " "
absolute error = 5.65103519534204700000000000000E-14 " "
relative error = 7.867016365049164000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = 0.7222449999999925 " "
y[1] (numeric) = 0.7222449999999347 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 7.993353679223635000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = 0.7261799999999938 " "
y[1] (numeric) = 0.7261799999999347 " "
absolute error = 5.91748872125208400000000000000E-14 " "
relative error = 8.148790549522342000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = 0.7301249999999953 " "
y[1] (numeric) = 0.7301249999999347 " "
absolute error = 6.05071548420710300000000000000E-14 " "
relative error = 8.287232301601976000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = 0.7340799999999965 " "
y[1] (numeric) = 0.7340799999999347 " "
absolute error = 6.18394224716212200000000000000E-14 " "
relative error = 8.424071282642424000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = 0.7380449999999978 " "
y[1] (numeric) = 0.7380449999999347 " "
absolute error = 6.31716901011714100000000000000E-14 " "
relative error = 8.559327696979396000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = 0.742019999999999 " "
y[1] (numeric) = 0.7420199999999346 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 8.678059274448015000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = 0.7460050000000005 " "
y[1] (numeric) = 0.7460049999999346 " "
absolute error = 6.58362253602717800000000000000E-14 " "
relative error = 8.825172131590504000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) - 0.3 ; "
Iterations = 4900
"Total Elapsed Time "= 46 Seconds
"Elapsed Time(since restart) "= 46 Seconds
"Time to Timeout "= 2 Minutes 13 Seconds
Percent Done = 100.0204081632654 "%"
(%o253) temp/diffeq.sub_lin_c.max