(%i1) batch("temp/diffeq.div_c_exp.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.div_c_exp.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_m1,[30],convfloat)
(%i190) completearray(array_y_higher,[2,30],convfloat)
(%i191) completearray(array_y_higher_work,[2,30],convfloat)
(%i192) completearray(array_y_higher_work2,[2,30],convfloat)
(%i193) completearray(array_y_set_initial,[2,30],convfloat)
(%i194) completearray(array_given_rad_poles,[2,3],convfloat)
(%i195) completearray(array_given_ord_poles,[2,3],convfloat)
(%i196) completearray(array_rad_test_poles,[2,4],convfloat)
(%i197) completearray(array_ord_test_poles,[2,4],convfloat)
(%i198) completearray(array_fact_2,[30,30],convfloat)
(%i199) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i200) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i201) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i202) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (if vallen = 4
then printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel)
else printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel))
(%i203) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i204) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i205) logitem_time(fd,secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],convfloat]),
secs:secs_in,printf(fd,"| ~%"),
if secs >= 0
then (years_int
:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int
:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if truncate(years_int) > 0.1
then printf(fd,
"~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(fd,
"~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(fd,
"~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(fd,
"~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(fd,"~d Seconds~%",
sec_int))
else printf(fd," 0.0 Seconds~%"),
printf(fd," | ~%")),0)
(%i206) omniout_timestr(secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],
convfloat]),secs:secs_in,
if secs >= 0
then (
years_int:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if years_int > 0
then printf(true,
"= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(true,
"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(true,
"= ~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(true,
"= ~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(true,"= ~d Seconds~%",
sec_int))
else printf(true,"= 0.0 Seconds~%")),0)
(%i207) zero_ats_ar(arr_a):=(
block(mode_declare([iii],fixnum),iii:1,
while iii <= ats_max_terms do
(arr_a[iii]:glob__0,iii:1+iii)),0)
(%i208) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:glob__0,
if jjj_ats <= mmm_ats
then (ma_ats:1+mmm_ats,iii_ats:jjj_ats,
while iii_ats <= mmm_ats do
(lll_ats:ma_ats-iii_ats,
if lll_ats <= ats_max_terms
and iii_ats <= ats_max_terms
then ret_ats
:c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i209) att(mmm_att,arr_aa,arr_bb,jjj_att):=block(
mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att],
fixnum]),ret_att:glob__0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= ats_max_terms do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= ats_max_terms
and iii_att <= ats_max_terms
then ret_att
:c(arr_aa[iii_att])*c(arr_bb[lll_att])
*c(al_att)
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/c(mmm_att)),ret_att)
(%i210) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i211) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i212) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i213) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i214) log_revs(file,revs):=printf(file,revs)
(%i215) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i216) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
elseif glob_h_reason = 7
then printf(file,"Opt Iter")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i217) logstart(file):=(printf(file,""),0)
(%i218) logend(file):=(printf(file,"
~%"),0)
(%i219) chk_data():=(
block(mode_declare([[errflag],boolean]),errflag:false,
if glob_max_iter < 2
then (omniout_str(always,"Illegal max_iter"),
errflag:true),if errflag then quit()),0)
(%i220) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:c(clock_sec2),
sub1:c(t_end2-t_start2),sub2:c(t2-t_start2),
if sub1 = glob__0 then sec_left:glob__0
else (if sub2 > glob__0
then (rrr:sub1/sub2,
sec_left:rrr*c(ms2)-c(ms2))
else sec_left:glob__0),sec_left)
(%i221) comp_percent(t_end2,t_start2,t2):=block(
mode_declare([[rrr,sub1,sub2],convfloat]),
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub2 > glob_small_float then rrr:glob__100*sub2/sub1
else rrr:0.0,rrr)
(%i222) comp_rad_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i223) comp_ord_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret
:abs(term2)*c(last_no)
*log(abs(term1*glob_h/term2))
/log(c(last_no))
+glob__1 else ret:glob_larger_float,ret)
(%i224) c(in_val):=(ret:in_val,ret)
(%i225) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3-term1*term3*c(last_no)
+glob__m2*term2*term2
+term2*term2*c(last_no)),
if abs(temp) > glob__0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i226) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*c(last_no*last_no)
+term2*term2*c(last_no*last_no)
+glob__4*term2*term2
-glob__4*term2*term2*c(last_no)
-glob__3*term1*term3
+glob__4*term1*term3*c(last_no))
/(term1*term3-term1*term3*c(last_no)
-glob__2*term2*term2
+term2*term2*c(last_no))),
ret)
(%i227) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # glob__0 and term4 # glob__0
and term3 # glob__0
and term2 # glob__0
and term1 # glob__0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:c(last_no-3)*rm2
-glob__2*c(last_no-2)*rm1
+c(last_no-1)*rm0,
nr2
:c(last_no-4)*rm3
-glob__2*c(last_no-3)*rm2
+c(last_no-2)*rm1,
dr1
:(-glob__1)/rm3+glob__2/rm2
+glob__m1/rm1,
dr2
:(-glob__1)/rm4+glob__2/rm3
+glob__m1/rm2,
ds1
:glob__5/rm3-glob__8/rm2
+glob__3/rm1,
ds2
:glob__5/rm4-glob__8/rm3
+glob__3/rm2,
if
abs(nr1*dr2-nr2*dr1) = glob__0
or abs(dr1) = glob__0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) > glob__0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(glob__2*dr1)
-c(last_no)/glob__2,
if abs(rcs) # glob__0
then (if rcs > glob__0
then rad_c
:sqrt(rcs)
*abs(glob_h)
else (
rad_c
:glob_larger_float,
ord_no
:glob_larger_float))
else (
rad_c:glob_larger_float,
ord_no:glob_larger_float))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float)))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float),
glob_six_term_ord_save:ord_no,rad_c)
(%i228) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i229) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i230) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms
then (if array_fact_1[nnn] = 0
then (ret:factorial_2(nnn),
array_fact_1[nnn]:ret)
else ret:array_fact_1[nnn])
else ret:factorial_2(nnn),ret)
(%i231) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i232) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i233) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms and mmm <= ats_max_terms
then (if array_fact_2[mmm,nnn] = 0
then (ret:factorial_1(mmm)/factorial_1(nnn),
array_fact_2[mmm,nnn]:ret)
else ret:array_fact_2[mmm,nnn])
else ret:factorial_2(mmm)/factorial_2(nnn),ret)
(%i234) log10(x):=log(x)/glob_log_10
(%i235) c(x):=x
(%i236) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y) else x^y
(%i237) estimated_needed_step_error(x_start,x_end,estimated_h,
estimated_answer):=block(
[desired_abs_gbl_error,range,
estimated_steps,step_error],
omniout_float(always,
"glob_desired_digits_correct",
32,
glob_desired_digits_correct,
32,""),
desired_abs_gbl_error
:expt(glob__10,
c(-glob_desired_digits_correct))
*c(abs(c(estimated_answer))),
omniout_float(always,"estimated_h",32,
estimated_h,32,""),
omniout_float(always,"estimated_answer",
32,estimated_answer,32,""),
omniout_float(always,
"desired_abs_gbl_error",32,
desired_abs_gbl_error,32,
""),range:x_end-x_start,
omniout_float(always,"range",32,range,32,
""),
estimated_steps:range/estimated_h,
omniout_float(always,"estimated_steps",32,
estimated_steps,32,""),
step_error
:c(
abs(desired_abs_gbl_error)
/sqrt(c(estimated_steps))
/c(ats_max_terms)),
omniout_float(always,"step_error",32,
step_error,32,""),
step_error)
(%i238) exact_soln_y(x):=block(c(-2.0)/exp(c(x)))
c(- 2.0)
(%o238) exact_soln_y(x) := block(---------)
exp(c(x))
(%i239) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
omniout_float(always,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(always,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(always,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(always,
"SOME POLE (given) for Equation 1")
else omniout_str(always,
"NO info (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(always,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(always,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(always,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > glob__small
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(always,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(always,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > glob__small
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(always,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(always,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%i240) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i241) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(always,"min_size",32,min_size,
32,"")),
if min_size < glob__1
then (min_size:glob__1,
omniout_float(always,"min_size",32,min_size,
32,"")),min_size)
(%i242) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:glob__small,
no_terms:ats_max_terms,hn_div_ho:glob__0_5,
hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125,
omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(always,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i243) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:ats_max_terms,
hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25,
hn_div_ho_3:glob__0_125,
est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3)
+c(abs(array_y[no_terms-1]))
*c(hn_div_ho_2)
+c(abs(array_y[no_terms-2]))
*c(hn_div_ho)
+c(abs(array_y[no_terms-3])),
if glob_prec*c(abs(array_y[1])) > c(est_tmp)
then est_tmp
:c(glob_prec)*c(abs(array_y[1])),
if c(est_tmp) >= c(array_max_est_error[1])
then array_max_est_error[1]:c(est_tmp))
(%i244) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
-glob_h/glob__10 then ret:true else ret:false,
return(ret))
(%i245) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(19)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i246) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
clock_sec1:elapsed_time_seconds(),
total_clock_sec:clock_sec1-glob_orig_start_sec,
glob_clock_sec:clock_sec1-glob_clock_start_sec,
left_sec:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
clock_sec1
-glob_orig_start_sec),
opt_clock_sec:clock_sec1
-glob_optimal_clock_start_sec,
glob_optimal_expect_sec
:comp_expect_sec(x_end,x_start,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:c(total_clock_sec)+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
glob_percent_done:percent_done,
omniout_str_noeol(info,
"Total Elapsed Time "),
omniout_timestr(total_clock_sec),
omniout_str_noeol(info,
"Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec),
if c(percent_done) < glob__100
then (omniout_str_noeol(info,
"Expected Time Remaining "),
omniout_timestr(expect_sec),
omniout_str_noeol(info,
"Optimized Time Remaining "),
omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(info,
"Expected Total Time "),
omniout_timestr(glob_total_exp_sec)),
omniout_str_noeol(info,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(info,
"Percent Done ",33,
percent_done,4,"%")),0)
(%i247) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i248) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),array_tmp1[1]:exp(array_x[1]),
array_tmp2[1]:array_const_2D0[1]/array_tmp1[1],
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp3[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_tmp1[1]*array_x[2]/c(1),
array_tmp2[2]:neg(ats(2,array_tmp1,array_tmp2,2))
/array_tmp1[1],
array_tmp3[2]:array_tmp2[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp3[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_tmp1[2]*array_x[2]/c(2),
array_tmp2[3]:neg(ats(3,array_tmp1,array_tmp2,2))
/array_tmp1[1],
array_tmp3[3]:array_tmp2[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp3[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_tmp1[3]*array_x[2]/c(3),
array_tmp2[4]:neg(ats(4,array_tmp1,array_tmp2,2))
/array_tmp1[1],
array_tmp3[4]:array_tmp2[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp3[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_tmp1[4]*array_x[2]/c(4),
array_tmp2[5]:neg(ats(5,array_tmp1,array_tmp2,2))
/array_tmp1[1],
array_tmp3[5]:array_tmp2[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp3[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp1[kkk]
:array_tmp1[kkk-1]*array_x[2]/c(kkk-1),
array_tmp2[kkk]
:neg(ats(kkk,array_tmp1,array_tmp2,2))
/array_tmp1[1],array_tmp3[kkk]:array_tmp2[kkk],
order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp3[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i249) exact_soln_y(x):=block(c(-2.0)/exp(c(x)))
c(- 2.0)
(%o249) exact_soln_y(x) := block(---------)
exp(c(x))
(%i250) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms: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_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_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_2D0),
array_const_2D0[1]:c(2.0),zero_ats_ar(array_m1),
array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,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/div_c_exppostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(1.0),"),
omniout_str(always,""),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,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (c(-2.0)/exp(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(1.0),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 ) = 2.0 / exp ( x ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:42:25-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"div_c_exp"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"div_c_exp diffeq.max"),
logitem_str(html_log_file,
"div_c_exp maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i251) main():=(glob_iolevel:2,compile(all),main_prog())
(%i252) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_2D0 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 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/div_c_exppostode.ode#################"
"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(1.0),"
""
"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(-2.0)/exp(c(x))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1. " "
y[1] (closed_form) = -0.7357588823428847 " "
y[1] (numeric) = -0.7357588823428847 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.009999999999999 " "
y[1] (closed_form) = -0.7284379591430474 " "
y[1] (numeric) = -0.7284379591430465 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 1.2192917853223910000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999978 " "
y[1] (closed_form) = -0.7211898803461582 " "
y[1] (numeric) = -0.7211898803461563 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.6170349769146206000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999967 " "
y[1] (closed_form) = -0.7140139211382971 " "
y[1] (numeric) = -0.7140139211382944 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.7317693398085480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999956 " "
y[1] (closed_form) = -0.7069093639175634 " "
y[1] (numeric) = -0.70690936391756 " "
absolute error = 3.4416913763379850000000000000000E-15 " "
relative error = 4.868645900041210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999945 " "
y[1] (closed_form) = -0.6998754982223147 " "
y[1] (numeric) = -0.6998754982223104 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 6.0279971284771040000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0599999999999934 " "
y[1] (closed_form) = -0.6929116206601195 " "
y[1] (numeric) = -0.6929116206601145 " "
absolute error = 4.9960036108132044000000000000000E-15 " "
relative error = 7.2101599422645520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0699999999999923 " "
y[1] (closed_form) = -0.6860170348374186 " "
y[1] (numeric) = -0.6860170348374128 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 8.4154757606259930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999912 " "
y[1] (closed_form) = -0.6791910512898842 " "
y[1] (numeric) = -0.6791910512898777 " "
absolute error = 6.5503158452884240000000000000000E-15 " "
relative error = 9.6442905613205680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.08999999999999 " "
y[1] (closed_form) = -0.6724329874134733 " "
y[1] (numeric) = -0.6724329874134659 " "
absolute error = 7.438494264988549000000000000000E-15 " "
relative error = 1.1062060315632138000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.099999999999989 " "
y[1] (closed_form) = -0.6657421673961664 " "
y[1] (numeric) = -0.6657421673961583 " "
absolute error = 8.104628079763643000000000000000E-15 " "
relative error = 1.2173824156973946000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999879 " "
y[1] (closed_form) = -0.6591179221503861 " "
y[1] (numeric) = -0.6591179221503772 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 1.3475258217868274000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999868 " "
y[1] (closed_form) = -0.6525595892460876 " "
y[1] (numeric) = -0.6525595892460779 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 1.4801621910725407000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999857 " "
y[1] (closed_form) = -0.6460665128445151 " "
y[1] (numeric) = -0.6460665128445048 " "
absolute error = 1.032507412901395600000000000000E-14 " "
relative error = 1.5981441420875547000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999846 " "
y[1] (closed_form) = -0.6396380436326177 " "
y[1] (numeric) = -0.6396380436326066 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 1.735705115849588100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999835 " "
y[1] (closed_form) = -0.6332735387581169 " "
y[1] (numeric) = -0.6332735387581052 " "
absolute error = 1.165734175856414400000000000000E-14 " "
relative error = 1.840806704386356000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999824 " "
y[1] (closed_form) = -0.6269723617652216 " "
y[1] (numeric) = -0.6269723617652093 " "
absolute error = 1.232347557333923800000000000000E-14 " "
relative error = 1.965553240439956000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999813 " "
y[1] (closed_form) = -0.6207338825309816 " "
y[1] (numeric) = -0.6207338825309686 " "
absolute error = 1.298960938811433200000000000000E-14 " "
relative error = 2.0926212912932143000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999802 " "
y[1] (closed_form) = -0.6145574772022746 " "
y[1] (numeric) = -0.6145574772022612 " "
absolute error = 1.343369859796439400000000000000E-14 " "
relative error = 2.18591410833048000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999979 " "
y[1] (closed_form) = -0.6084425281334208 " "
y[1] (numeric) = -0.6084425281334067 " "
absolute error = 1.409983241273948800000000000000E-14 " "
relative error = 2.317364707558319000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.199999999999978 " "
y[1] (closed_form) = -0.6023884238244175 " "
y[1] (numeric) = -0.6023884238244026 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 2.4696670688866695000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999769 " "
y[1] (closed_form) = -0.5963945588597885 " "
y[1] (numeric) = -0.5963945588597731 " "
absolute error = 1.543210004228967600000000000000E-14 " "
relative error = 2.5875655324209185000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999758 " "
y[1] (closed_form) = -0.5904603338480428 " "
y[1] (numeric) = -0.5904603338480265 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 2.745189681733778000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999747 " "
y[1] (closed_form) = -0.5845851553617336 " "
y[1] (numeric) = -0.5845851553617168 " "
absolute error = 1.676436767183986400000000000000E-14 " "
relative error = 2.867737491805842000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999736 " "
y[1] (closed_form) = -0.5787684358781165 " "
y[1] (numeric) = -0.5787684358780991 " "
absolute error = 1.743050148661495800000000000000E-14 " "
relative error = 3.0116537817355443000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999725 " "
y[1] (closed_form) = -0.5730095937203961 " "
y[1] (numeric) = -0.5730095937203777 " "
absolute error = 1.831867990631508300000000000000E-14 " "
relative error = 3.196923770050141000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999714 " "
y[1] (closed_form) = -0.567308052999557 " "
y[1] (numeric) = -0.5673080529995381 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 3.3269034907640205000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999703 " "
y[1] (closed_form) = -0.5616632435567762 " "
y[1] (numeric) = -0.5616632435567568 " "
absolute error = 1.94289029309402400000000000000E-14 " "
relative error = 3.459172939269659000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999692 " "
y[1] (closed_form) = -0.5560746009064054 " "
y[1] (numeric) = -0.5560746009063854 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 3.593765011147558000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999968 " "
y[1] (closed_form) = -0.5505415661795222 " "
y[1] (numeric) = -0.5505415661795017 " "
absolute error = 2.053912595556539600000000000000E-14 " "
relative error = 3.7307130319144590000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.299999999999967 " "
y[1] (closed_form) = -0.5450635860680433 " "
y[1] (numeric) = -0.5450635860680219 " "
absolute error = 2.14273043752655200000000000000E-14 " "
relative error = 3.931156827011121000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999659 " "
y[1] (closed_form) = -0.5396401127693922 " "
y[1] (numeric) = -0.5396401127693702 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 4.0735325946705490000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999648 " "
y[1] (closed_form) = -0.5342706039317195 " "
y[1] (numeric) = -0.5342706039316969 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 4.239153255987055400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999637 " "
y[1] (closed_form) = -0.5289545225996671 " "
y[1] (numeric) = -0.5289545225996439 " "
absolute error = 2.320366121466577200000000000000E-14 " "
relative error = 4.38670249015475000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999626 " "
y[1] (closed_form) = -0.5236913371606716 " "
y[1] (numeric) = -0.5236913371606476 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 4.579189234238932300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999615 " "
y[1] (closed_form) = -0.518480521291803 " "
y[1] (numeric) = -0.5184805212917785 " "
absolute error = 2.45359288442159600000000000000E-14 " "
relative error = 4.732275917151965000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3599999999999604 " "
y[1] (closed_form) = -0.5133215539071321 " "
y[1] (numeric) = -0.5133215539071071 " "
absolute error = 2.498001805406602200000000000000E-14 " "
relative error = 4.8663489510485850000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3699999999999593 " "
y[1] (closed_form) = -0.5082139191056213 " "
y[1] (numeric) = -0.5082139191055959 " "
absolute error = 2.542410726391608500000000000000E-14 " "
relative error = 5.0026389101382000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999581 " "
y[1] (closed_form) = -0.5031571061195341 " "
y[1] (numeric) = -0.503157106119508 " "
absolute error = 2.60902410786911800000000000000E-14 " "
relative error = 5.1853070862707770000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.389999999999957 " "
y[1] (closed_form) = -0.49815060926335775 " "
y[1] (numeric) = -0.49815060926333116 " "
absolute error = 2.6589841439772500000000000000E-14 " "
relative error = 5.3377113156786740000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.399999999999956 " "
y[1] (closed_form) = -0.4931939278832347 " "
y[1] (numeric) = -0.49319392788320754 " "
absolute error = 2.714495295208508000000000000000E-14 " "
relative error = 5.503910615564541000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999548 " "
y[1] (closed_form) = -0.48828656630689615 " "
y[1] (numeric) = -0.48828656630686856 " "
absolute error = 2.75890421619351400000000000000E-14 " "
relative error = 5.650174316816035000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999537 " "
y[1] (closed_form) = -0.48342803379409527 " "
y[1] (numeric) = -0.48342803379406696 " "
absolute error = 2.831068712794149000000000000000E-14 " "
relative error = 5.856236119728166000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999526 " "
y[1] (closed_form) = -0.47861784448753175 " "
y[1] (numeric) = -0.4786178444875029 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 6.031074472612155000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999515 " "
y[1] (closed_form) = -0.4738555173642665 " "
y[1] (numeric) = -0.4738555173642372 " "
absolute error = 2.93098878501041300000000000000E-14 " "
relative error = 6.18540605227833000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4499999999999504 " "
y[1] (closed_form) = -0.46914057618761856 " "
y[1] (numeric) = -0.46914057618758875 " "
absolute error = 2.98094882111854530000000000000E-14 " "
relative error = 6.354063094142608000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4599999999999493 " "
y[1] (closed_form) = -0.4644725494595412 " "
y[1] (numeric) = -0.4644725494595108 " "
absolute error = 3.04201108747292900000000000000E-14 " "
relative error = 6.549388313717578000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4699999999999482 " "
y[1] (closed_form) = -0.4598509703734715 " "
y[1] (numeric) = -0.45985097037344064 " "
absolute error = 3.08642000845793500000000000000E-14 " "
relative error = 6.711783180431858000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999471 " "
y[1] (closed_form) = -0.45527537676764956 " "
y[1] (numeric) = -0.4552753767676182 " "
absolute error = 3.13638004456606700000000000000E-14 " "
relative error = 6.888973585247777000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.489999999999946 " "
y[1] (closed_form) = -0.45074531107890176 " "
y[1] (numeric) = -0.45074531107886995 " "
absolute error = 3.180788965551073500000000000000E-14 " "
relative error = 7.056732232971105000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.499999999999945 " "
y[1] (closed_form) = -0.4462603202968843 " "
y[1] (numeric) = -0.44626032029685203 " "
absolute error = 3.2251978865360800000000000000E-14 " "
relative error = 7.227167058882689000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999438 " "
y[1] (closed_form) = -0.44181995591878115 " "
y[1] (numeric) = -0.4418199559187486 " "
absolute error = 3.252953462151708700000000000000E-14 " "
relative error = 7.362622304796238000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999427 " "
y[1] (closed_form) = -0.4374237739044545 " "
y[1] (numeric) = -0.43742377390442144 " "
absolute error = 3.308464613382966500000000000000E-14 " "
relative error = 7.563522631272499000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999416 " "
y[1] (closed_form) = -0.4330713346320394 " "
y[1] (numeric) = -0.4330713346320058 " "
absolute error = 3.358424649491098500000000000000E-14 " "
relative error = 7.754899437859575000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999405 " "
y[1] (closed_form) = -0.4287622028539814 " "
y[1] (numeric) = -0.4287622028539473 " "
absolute error = 3.413935800722356400000000000000E-14 " "
relative error = 7.962305860913308000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5499999999999394 " "
y[1] (closed_form) = -0.42449594765351184 " "
y[1] (numeric) = -0.42449594765347715 " "
absolute error = 3.46944695195361400000000000000E-14 " "
relative error = 8.173097932104397000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5599999999999383 " "
y[1] (closed_form) = -0.4202721424015554 " "
y[1] (numeric) = -0.4202721424015203 " "
absolute error = 3.513855872938620500000000000000E-14 " "
relative error = 8.360905990245848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5699999999999372 " "
y[1] (closed_form) = -0.4160903647140671 " "
y[1] (numeric) = -0.4160903647140315 " "
absolute error = 3.55826479392362670000000000000E-14 " "
relative error = 8.551663522342867000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999361 " "
y[1] (closed_form) = -0.41195019640979325 " "
y[1] (numeric) = -0.4119501964097573 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 8.731935634780518000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.589999999999935 " "
y[1] (closed_form) = -0.4078512234684534 " "
y[1] (numeric) = -0.407851223468417 " "
absolute error = 3.641531520770513500000000000000E-14 " "
relative error = 8.92857814622242900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.599999999999934 " "
y[1] (closed_form) = -0.4037930359893375 " "
y[1] (numeric) = -0.4037930359893007 " "
absolute error = 3.68038932663239400000000000000E-14 " "
relative error = 9.114543834603372000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999328 " "
y[1] (closed_form) = -0.3997752281503159 " "
y[1] (numeric) = -0.39977522815027866 " "
absolute error = 3.724798247617400000000000000E-14 " "
relative error = 9.317231247296975000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999317 " "
y[1] (closed_form) = -0.3957973981672564 " "
y[1] (numeric) = -0.39579739816721876 " "
absolute error = 3.763656053479280700000000000000E-14 " "
relative error = 9.509046979355918000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999306 " "
y[1] (closed_form) = -0.3918591482538459 " "
y[1] (numeric) = -0.39185914825380785 " "
absolute error = 3.80251385934116100000000000000E-14 " "
relative error = 9.703777176787761000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999295 " "
y[1] (closed_form) = -0.38796008458181114 " "
y[1] (numeric) = -0.38796008458177267 " "
absolute error = 3.846922780326167400000000000000E-14 " "
relative error = 9.915769516528566000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6499999999999284 " "
y[1] (closed_form) = -0.38409981724153575 " "
y[1] (numeric) = -0.3840998172414968 " "
absolute error = 3.896882816434299500000000000000E-14 " "
relative error = 1.014549510702786700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6599999999999273 " "
y[1] (closed_form) = -0.3802779602030687 " "
y[1] (numeric) = -0.3802779602030293 " "
absolute error = 3.94129173741930570000000000000E-14 " "
relative error = 1.036423918786840300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999262 " "
y[1] (closed_form) = -0.3764941312775213 " "
y[1] (numeric) = -0.37649413127748155 " "
absolute error = 3.974598428158060400000000000000E-14 " "
relative error = 1.055686688839328800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.679999999999925 " "
y[1] (closed_form) = -0.37274795207884787 " "
y[1] (numeric) = -0.37274795207880773 " "
absolute error = 4.01345623401994100000000000000E-14 " "
relative error = 1.076721203064039700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.689999999999924 " "
y[1] (closed_form) = -0.36903904798600656 " "
y[1] (numeric) = -0.369039047985966 " "
absolute error = 4.05786515500494700000000000000E-14 " "
relative error = 1.099576095578594500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.699999999999923 " "
y[1] (closed_form) = -0.36536704810549747 " "
y[1] (numeric) = -0.36536704810545634 " "
absolute error = 4.11337630623620500000000000000E-14 " "
relative error = 1.125820275135620100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999218 " "
y[1] (closed_form) = -0.36173158523427246 " "
y[1] (numeric) = -0.36173158523423093 " "
absolute error = 4.152234112098085500000000000000E-14 " "
relative error = 1.147877122593241500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999207 " "
y[1] (closed_form) = -0.3581322958230148 " "
y[1] (numeric) = -0.35813229582297285 " "
absolute error = 4.19664303308309200000000000000E-14 " "
relative error = 1.17181362363282300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999196 " "
y[1] (closed_form) = -0.3545688199397841 " "
y[1] (numeric) = -0.3545688199397418 " "
absolute error = 4.229949723821846400000000000000E-14 " "
relative error = 1.192984122106453800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999185 " "
y[1] (closed_form) = -0.35104080123402237 " "
y[1] (numeric) = -0.3510408012339796 " "
absolute error = 4.274358644806852700000000000000E-14 " "
relative error = 1.21762445555647500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7499999999999174 " "
y[1] (closed_form) = -0.3475478869009189 " "
y[1] (numeric) = -0.3475478869008758 " "
absolute error = 4.31321645066873300000000000000E-14 " "
relative error = 1.241042346460409100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7599999999999163 " "
y[1] (closed_form) = -0.3440897276461299 " "
y[1] (numeric) = -0.3440897276460863 " "
absolute error = 4.357625371653739400000000000000E-14 " "
relative error = 1.266421233049777300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999152 " "
y[1] (closed_form) = -0.3406659776508478 " "
y[1] (numeric) = -0.3406659776508038 " "
absolute error = 4.3964831775156200000000000000E-14 " "
relative error = 1.290555402048872400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.779999999999914 " "
y[1] (closed_form) = -0.33727629453721997 " "
y[1] (numeric) = -0.3372762945371757 " "
absolute error = 4.42423875313124900000000000000E-14 " "
relative error = 1.311755028381638700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.789999999999913 " "
y[1] (closed_form) = -0.33392033933411047 " "
y[1] (numeric) = -0.33392033933406584 " "
absolute error = 4.46309655899312930000000000000E-14 " "
relative error = 1.33657523464825300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.799999999999912 " "
y[1] (closed_form) = -0.3305977764432022 " "
y[1] (numeric) = -0.3305977764431572 " "
absolute error = 4.5019543648550100000000000000E-14 " "
relative error = 1.361761840412275300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999108 " "
y[1] (closed_form) = -0.32730827360543735 " "
y[1] (numeric) = -0.32730827360539194 " "
absolute error = 4.5408121707168900000000000000E-14 " "
relative error = 1.387319703439802200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999097 " "
y[1] (closed_form) = -0.3240515018677908 " "
y[1] (numeric) = -0.3240515018677451 " "
absolute error = 4.56856774633251900000000000000E-14 " "
relative error = 1.409827672453263800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999086 " "
y[1] (closed_form) = -0.32082713555037484 " "
y[1] (numeric) = -0.3208271355503289 " "
absolute error = 4.59632332194814800000000000000E-14 " "
relative error = 1.432647931747797500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999075 " "
y[1] (closed_form) = -0.3176348522138708 " "
y[1] (numeric) = -0.31763485221382454 " "
absolute error = 4.62407889756377700000000000000E-14 " "
relative error = 1.455784485025679600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8499999999999064 " "
y[1] (closed_form) = -0.3144743326272847 " "
y[1] (numeric) = -0.31447433262723806 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.482771793955017500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8599999999999053 " "
y[1] (closed_form) = -0.31134526073602414 " "
y[1] (numeric) = -0.31134526073597735 " "
absolute error = 4.67959004879503500000000000000E-14 " "
relative error = 1.503022733582783400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999042 " "
y[1] (closed_form) = -0.3082473236302924 " "
y[1] (numeric) = -0.3082473236302454 " "
absolute error = 4.70179450928753800000000000000E-14 " "
relative error = 1.52533181923967200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.879999999999903 " "
y[1] (closed_form) = -0.3051802115137973 " "
y[1] (numeric) = -0.30518021151374997 " "
absolute error = 4.735101200026292600000000000000E-14 " "
relative error = 1.55157543686682220000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.889999999999902 " "
y[1] (closed_form) = -0.3021436176727713 " "
y[1] (numeric) = -0.3021436176727236 " "
absolute error = 4.77395900588817300000000000000E-14 " "
relative error = 1.58002973640783080000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999009 " "
y[1] (closed_form) = -0.29913723844529977 " "
y[1] (numeric) = -0.2991372384452517 " "
absolute error = 4.80726569662692800000000000000E-14 " "
relative error = 1.607043550181728500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999998998 " "
y[1] (closed_form) = -0.29616077319095463 " "
y[1] (numeric) = -0.29616077319090633 " "
absolute error = 4.82947015711943100000000000000E-14 " "
relative error = 1.630692041044054200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998987 " "
y[1] (closed_form) = -0.29321392426073 " "
y[1] (numeric) = -0.29321392426068144 " "
absolute error = 4.8572257327350600000000000000E-14 " "
relative error = 1.65654674994764080000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998976 " "
y[1] (closed_form) = -0.2902963969672772 " "
y[1] (numeric) = -0.2902963969672283 " "
absolute error = 4.890532423473814600000000000000E-14 " "
relative error = 1.684668660915238600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998965 " "
y[1] (closed_form) = -0.2874078995554356 " "
y[1] (numeric) = -0.28740789955538637 " "
absolute error = 4.92383911421256900000000000000E-14 " "
relative error = 1.713188510764246700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9499999999998954 " "
y[1] (closed_form) = -0.2845481431730569 " "
y[1] (numeric) = -0.28454814317300736 " "
absolute error = 4.95159468982819800000000000000E-14 " "
relative error = 1.740160605025185800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9599999999998943 " "
y[1] (closed_form) = -0.28171684184211976 " "
y[1] (numeric) = -0.2817168418420699 " "
absolute error = 4.98490138056695300000000000000E-14 " "
relative error = 1.769472264409594800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998932 " "
y[1] (closed_form) = -0.27891371243013163 " "
y[1] (numeric) = -0.27891371243008156 " "
absolute error = 5.00710584105945600000000000000E-14 " "
relative error = 1.7952168064572102000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.979999999999892 " "
y[1] (closed_form) = -0.2761384746218154 " "
y[1] (numeric) = -0.2761384746217651 " "
absolute error = 5.02931030155195900000000000000E-14 " "
relative error = 1.82130009533797680000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.989999999999891 " "
y[1] (closed_form) = -0.2733908508910775 " "
y[1] (numeric) = -0.2733908508910269 " "
absolute error = 5.06261699229071400000000000000E-14 " "
relative error = 1.851787276637039400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998899 " "
y[1] (closed_form) = -0.27067056647325516 " "
y[1] (numeric) = -0.2706705664732043 " "
absolute error = 5.08482145278321700000000000000E-14 " "
relative error = 1.878601548382855300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998888 " "
y[1] (closed_form) = -0.2679773493376397 " "
y[1] (numeric) = -0.2679773493375886 " "
absolute error = 5.11257702839884600000000000000E-14 " "
relative error = 1.90783924127752390000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998877 " "
y[1] (closed_form) = -0.26531093016027324 " "
y[1] (numeric) = -0.26531093016022184 " "
absolute error = 5.14033260401447500000000000000E-14 " "
relative error = 1.93747487180766400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998866 " "
y[1] (closed_form) = -0.26267104229701593 " "
y[1] (numeric) = -0.2626710422969642 " "
absolute error = 5.173639294753230000000000000000E-14 " "
relative error = 1.969626818971207400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998855 " "
y[1] (closed_form) = -0.2600574217568816 " "
y[1] (numeric) = -0.26005742175682955 " "
absolute error = 5.20694598549198400000000000000E-14 " "
relative error = 2.002229334704307000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998844 " "
y[1] (closed_form) = -0.2574698071756382 " "
y[1] (numeric) = -0.25746980717558593 " "
absolute error = 5.22915044598448700000000000000E-14 " "
relative error = 2.030976176720137600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0599999999998833 " "
y[1] (closed_form) = -0.25490793978967125 " "
y[1] (numeric) = -0.25490793978961873 " "
absolute error = 5.251354906476990000000000000000E-14 " "
relative error = 2.06009860297406620000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999882 " "
y[1] (closed_form) = -0.25237156341010725 " "
y[1] (numeric) = -0.25237156341005457 " "
absolute error = 5.26800825184636800000000000000E-14 " "
relative error = 2.08740167896245200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999881 " "
y[1] (closed_form) = -0.24986042439719455 " "
y[1] (numeric) = -0.24986042439714168 " "
absolute error = 5.28743715477730800000000000000E-14 " "
relative error = 2.116156317085274300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.08999999999988 " "
y[1] (closed_form) = -0.24737427163493936 " "
y[1] (numeric) = -0.24737427163488615 " "
absolute error = 5.32074384551606300000000000000E-14 " "
relative error = 2.150888130099523300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999879 " "
y[1] (closed_form) = -0.2449128565059935 " "
y[1] (numeric) = -0.24491285650594002 " "
absolute error = 5.348499421131692000000000000000E-14 " "
relative error = 2.18383775251129100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998778 " "
y[1] (closed_form) = -0.24247593286679298 " "
y[1] (numeric) = -0.24247593286673924 " "
absolute error = 5.373479439185758000000000000000E-14 " "
relative error = 2.216087747618953600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998766 " "
y[1] (closed_form) = -0.24006325702294307 " "
y[1] (numeric) = -0.24006325702288908 " "
absolute error = 5.398459457239824000000000000000E-14 " "
relative error = 2.24876539799836500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998755 " "
y[1] (closed_form) = -0.2376745877048489 " "
y[1] (numeric) = -0.23767458770479455 " "
absolute error = 5.43454170554014100000000000000E-14 " "
relative error = 2.28654723166656400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998744 " "
y[1] (closed_form) = -0.23530968604358793 " "
y[1] (numeric) = -0.2353096860435334 " "
absolute error = 5.453970608471082000000000000000E-14 " "
relative error = 2.31778415082361200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998733 " "
y[1] (closed_form) = -0.23296831554702344 " "
y[1] (numeric) = -0.2329683155469686 " "
absolute error = 5.48450174164827300000000000000E-14 " "
relative error = 2.354183541555999700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1599999999998722 " "
y[1] (closed_form) = -0.2306502420761545 " "
y[1] (numeric) = -0.23065024207609938 " "
absolute error = 5.51225731726390200000000000000E-14 " "
relative error = 2.389877100343082700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999871 " "
y[1] (closed_form) = -0.2283552338217024 " "
y[1] (numeric) = -0.22835523382164702 " "
absolute error = 5.53723733531796800000000000000E-14 " "
relative error = 2.42483486918517100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.17999999999987 " "
y[1] (closed_form) = -0.22608306128092912 " "
y[1] (numeric) = -0.22608306128087344 " "
absolute error = 5.5677684684951600000000000000E-14 " "
relative error = 2.462709252497555800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999869 " "
y[1] (closed_form) = -0.22383349723468707 " "
y[1] (numeric) = -0.22383349723463114 " "
absolute error = 5.59274848654922600000000000000E-14 " "
relative error = 2.49861998121098380000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999868 " "
y[1] (closed_form) = -0.22160631672469705 " "
y[1] (numeric) = -0.22160631672464087 " "
absolute error = 5.61772850460329200000000000000E-14 " "
relative error = 2.535003779509693000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998667 " "
y[1] (closed_form) = -0.21940129703105202 " "
y[1] (numeric) = -0.21940129703099556 " "
absolute error = 5.64548408021892100000000000000E-14 " "
relative error = 2.57313158883464200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998656 " "
y[1] (closed_form) = -0.21721821764994514 " "
y[1] (numeric) = -0.2172182176498884 " "
absolute error = 5.6732396558345500000000000000E-14 " "
relative error = 2.611769729635281500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998645 " "
y[1] (closed_form) = -0.21505686027161902 " "
y[1] (numeric) = -0.21505686027156204 " "
absolute error = 5.69821967388861600000000000000E-14 " "
relative error = 2.64963399293177900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998634 " "
y[1] (closed_form) = -0.21291700875853473 " "
y[1] (numeric) = -0.21291700875847752 " "
absolute error = 5.72042413438111900000000000000E-14 " "
relative error = 2.686691949945881300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2499999999998623 " "
y[1] (closed_form) = -0.2107984491237577 " "
y[1] (numeric) = -0.21079844912370027 " "
absolute error = 5.74262859487362200000000000000E-14 " "
relative error = 2.724227155723608600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2599999999998612 " "
y[1] (closed_form) = -0.20870096950955896 " "
y[1] (numeric) = -0.20870096950950132 " "
absolute error = 5.76483305536612500000000000000E-14 " "
relative error = 2.762245460053832000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.26999999999986 " "
y[1] (closed_form) = -0.2066243601662293 " "
y[1] (numeric) = -0.20662436016617144 " "
absolute error = 5.78426195829706600000000000000E-14 " "
relative error = 2.799409495397167700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999859 " "
y[1] (closed_form) = -0.20456841343110377 " "
y[1] (numeric) = -0.2045684134310457 " "
absolute error = 5.80646641878956900000000000000E-14 " "
relative error = 2.83839832425797200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999858 " "
y[1] (closed_form) = -0.2025329237077956 " "
y[1] (numeric) = -0.20253292370773734 " "
absolute error = 5.82589532172050900000000000000E-14 " "
relative error = 2.87651766195101200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999857 " "
y[1] (closed_form) = -0.20051768744563617 " "
y[1] (numeric) = -0.2005176874455777 " "
absolute error = 5.84532422465144900000000000000E-14 " "
relative error = 2.9151165162106800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998557 " "
y[1] (closed_form) = -0.19852250311931996 " "
y[1] (numeric) = -0.19852250311926126 " "
absolute error = 5.87030424270551500000000000000E-14 " "
relative error = 2.956996889756738400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998546 " "
y[1] (closed_form) = -0.19654717120875165 " "
y[1] (numeric) = -0.19654717120869272 " "
absolute error = 5.89250870319801800000000000000E-14 " "
relative error = 2.99801247047184300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998535 " "
y[1] (closed_form) = -0.19459149417909405 " "
y[1] (numeric) = -0.19459149417903487 " "
absolute error = 5.91748872125208400000000000000E-14 " "
relative error = 3.040980154973202400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998524 " "
y[1] (closed_form) = -0.19265527646101446 " "
y[1] (numeric) = -0.19265527646095504 " "
absolute error = 5.9424687393061500000000000000E-14 " "
relative error = 3.08450868746834600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3499999999998513 " "
y[1] (closed_form) = -0.1907383244311276 " "
y[1] (numeric) = -0.19073832443106792 " "
absolute error = 5.96744875736021600000000000000E-14 " "
relative error = 3.128605001201509000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.35999999999985 " "
y[1] (closed_form) = -0.18884044639263298 " "
y[1] (numeric) = -0.18884044639257308 " "
absolute error = 5.9896532178527200000000000000E-14 " "
relative error = 3.17180632235912140000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.369999999999849 " "
y[1] (closed_form) = -0.18696145255614516 " "
y[1] (numeric) = -0.18696145255608507 " "
absolute error = 6.0090821207836600000000000000E-14 " "
relative error = 3.21407543567255500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999848 " "
y[1] (closed_form) = -0.1851011550207147 " "
y[1] (numeric) = -0.1851011550206544 " "
absolute error = 6.028511023714600000000000000E-14 " "
relative error = 3.25687380126825700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999847 " "
y[1] (closed_form) = -0.18325936775503776 " "
y[1] (numeric) = -0.18325936775497725 " "
absolute error = 6.05071548420710300000000000000E-14 " "
relative error = 3.301722339397719600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999846 " "
y[1] (closed_form) = -0.181435906578853 " "
y[1] (numeric) = -0.18143590657879227 " "
absolute error = 6.07291994469960600000000000000E-14 " "
relative error = 3.34714338479648400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998447 " "
y[1] (closed_form) = -0.17963058914452318 " "
y[1] (numeric) = -0.17963058914446225 " "
absolute error = 6.09234884763054700000000000000E-14 " "
relative error = 3.39159876758456770000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998436 " "
y[1] (closed_form) = -0.17784323491880047 " "
y[1] (numeric) = -0.17784323491873938 " "
absolute error = 6.10900219299992400000000000000E-14 " "
relative error = 3.43504896083855370000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998425 " "
y[1] (closed_form) = -0.17607366516477285 " "
y[1] (numeric) = -0.17607366516471162 " "
absolute error = 6.12287998080773800000000000000E-14 " "
relative error = 3.47745358459928600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998414 " "
y[1] (closed_form) = -0.17432170292399024 " "
y[1] (numeric) = -0.1743217029239288 " "
absolute error = 6.14508444130024100000000000000E-14 " "
relative error = 3.52514020814705560000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999998403 " "
y[1] (closed_form) = -0.17258717299876858 " "
y[1] (numeric) = -0.17258717299870696 " "
absolute error = 6.16173778666961900000000000000E-14 " "
relative error = 3.57021769324281300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.459999999999839 " "
y[1] (closed_form) = -0.17086990193466992 " "
y[1] (numeric) = -0.17086990193460813 " "
absolute error = 6.17839113203899600000000000000E-14 " "
relative error = 3.615845191039689400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999838 " "
y[1] (closed_form) = -0.1691697180031568 " "
y[1] (numeric) = -0.16916971800309483 " "
absolute error = 6.19782003496993600000000000000E-14 " "
relative error = 3.6636698979744600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999837 " "
y[1] (closed_form) = -0.16748645118441924 " "
y[1] (numeric) = -0.16748645118435707 " "
absolute error = 6.21724893790087700000000000000E-14 " "
relative error = 3.712090675952688000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999836 " "
y[1] (closed_form) = -0.16581993315037258 " "
y[1] (numeric) = -0.16581993315031027 " "
absolute error = 6.23112672570869100000000000000E-14 " "
relative error = 3.75776699901213900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.499999999999835 " "
y[1] (closed_form) = -0.16416999724782472 " "
y[1] (numeric) = -0.16416999724776218 " "
absolute error = 6.25333118620119400000000000000E-14 " "
relative error = 3.80905847050810700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998337 " "
y[1] (closed_form) = -0.1625364784818104 " "
y[1] (numeric) = -0.16253647848174768 " "
absolute error = 6.27276008913213400000000000000E-14 " "
relative error = 3.859293709155956500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998326 " "
y[1] (closed_form) = -0.1609192134990918 " "
y[1] (numeric) = -0.1609192134990289 " "
absolute error = 6.28941343450151200000000000000E-14 " "
relative error = 3.908429141394609300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998315 " "
y[1] (closed_form) = -0.15931804057182292 " "
y[1] (numeric) = -0.15931804057175983 " "
absolute error = 6.30884233743245200000000000000E-14 " "
relative error = 3.95990454991086400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998304 " "
y[1] (closed_form) = -0.15773279958137665 " "
y[1] (numeric) = -0.1577327995813134 " "
absolute error = 6.3254956828018290000000000000E-14 " "
relative error = 4.01026019926718800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999998293 " "
y[1] (closed_form) = -0.15616333200233296 " "
y[1] (numeric) = -0.1561633320022695 " "
absolute error = 6.3449245857327700000000000000E-14 " "
relative error = 4.06300538313179800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999828 " "
y[1] (closed_form) = -0.15460948088662604 " "
y[1] (numeric) = -0.15460948088656243 " "
absolute error = 6.36157793110214700000000000000E-14 " "
relative error = 4.11461049776568600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999827 " "
y[1] (closed_form) = -0.15307109084784948 " "
y[1] (numeric) = -0.15307109084778567 " "
absolute error = 6.38100683403308700000000000000E-14 " "
relative error = 4.16865575249327660000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999826 " "
y[1] (closed_form) = -0.15154800804571733 " "
y[1] (numeric) = -0.15154800804565335 " "
absolute error = 6.39766017940246500000000000000E-14 " "
relative error = 4.22154026430521500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.589999999999825 " "
y[1] (closed_form) = -0.1500400801706802 " "
y[1] (numeric) = -0.15004008017061607 " "
absolute error = 6.41431352477184200000000000000E-14 " "
relative error = 4.27506671382416600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.599999999999824 " "
y[1] (closed_form) = -0.14854715642869393 " "
y[1] (numeric) = -0.14854715642862962 " "
absolute error = 6.43096687014121900000000000000E-14 " "
relative error = 4.32924266256704300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998227 " "
y[1] (closed_form) = -0.14706908752614026 " "
y[1] (numeric) = -0.14706908752607578 " "
absolute error = 6.44762021551059700000000000000E-14 " "
relative error = 4.38407575920030600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998216 " "
y[1] (closed_form) = -0.14560572565489716 " "
y[1] (numeric) = -0.1456057256548325 " "
absolute error = 6.46427356087997400000000000000E-14 " "
relative error = 4.43957374052794400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998205 " "
y[1] (closed_form) = -0.14415692447755807 " "
y[1] (numeric) = -0.14415692447749326 " "
absolute error = 6.48092690624935100000000000000E-14 " "
relative error = 4.495744432490500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998194 " "
y[1] (closed_form) = -0.1427225391127979 " "
y[1] (numeric) = -0.14272253911273292 " "
absolute error = 6.49758025161872900000000000000E-14 " "
relative error = 4.5525957511752896000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999998183 " "
y[1] (closed_form) = -0.14130242612088487 " "
y[1] (numeric) = -0.14130242612081972 " "
absolute error = 6.51423359698810600000000000000E-14 " "
relative error = 4.610135703837915400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999817 " "
y[1] (closed_form) = -0.1398964434893363 " "
y[1] (numeric) = -0.139896443489271 " "
absolute error = 6.53088694235748300000000000000E-14 " "
relative error = 4.668372389935205300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999816 " "
y[1] (closed_form) = -0.13850445061871744 " "
y[1] (numeric) = -0.13850445061865196 " "
absolute error = 6.54754028772686100000000000000E-14 " "
relative error = 4.727314002169709700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999815 " "
y[1] (closed_form) = -0.13712630830858122 " "
y[1] (numeric) = -0.13712630830851558 " "
absolute error = 6.56419363309623800000000000000E-14 " "
relative error = 4.786968827545879400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.689999999999814 " "
y[1] (closed_form) = -0.13576187874354814 " "
y[1] (numeric) = -0.13576187874348236 " "
absolute error = 6.57807142090405300000000000000E-14 " "
relative error = 4.84530081771328200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998128 " "
y[1] (closed_form) = -0.1344110254795247 " "
y[1] (numeric) = -0.13441102547945874 " "
absolute error = 6.5947247662734300000000000000E-14 " "
relative error = 4.906386766075248600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998117 " "
y[1] (closed_form) = -0.13307361343005877 " "
y[1] (numeric) = -0.1330736134299927 " "
absolute error = 6.60860255408124400000000000000E-14 " "
relative error = 4.96612542767887900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998106 " "
y[1] (closed_form) = -0.13174950885283088 " "
y[1] (numeric) = -0.13174950885276465 " "
absolute error = 6.62248034188905900000000000000E-14 " "
relative error = 5.02656928253646600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998095 " "
y[1] (closed_form) = -0.1304385793362799 " "
y[1] (numeric) = -0.13043857933621353 " "
absolute error = 6.63635812969687300000000000000E-14 " "
relative error = 5.0877264713132700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998084 " "
y[1] (closed_form) = -0.12914069378636173 " "
y[1] (numeric) = -0.12914069378629522 " "
absolute error = 6.65023591750468800000000000000E-14 " "
relative error = 5.14960522707599500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999998073 " "
y[1] (closed_form) = -0.1278557224134398 " "
y[1] (numeric) = -0.12785572241337317 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 5.21004302506738700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999806 " "
y[1] (closed_form) = -0.126583536719306 " "
y[1] (numeric) = -0.12658353671923925 " "
absolute error = 6.67521593555875400000000000000E-14 " "
relative error = 5.273368171376648000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999805 " "
y[1] (closed_form) = -0.12532400948433073 " "
y[1] (numeric) = -0.12532400948426384 " "
absolute error = 6.68909372336656800000000000000E-14 " "
relative error = 5.33743992941983400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999804 " "
y[1] (closed_form) = -0.12407701475474095 " "
y[1] (numeric) = -0.1240770147546739 " "
absolute error = 6.70435928995516400000000000000E-14 " "
relative error = 5.40338539189345900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.789999999999803 " "
y[1] (closed_form) = -0.12284242783002448 " "
y[1] (numeric) = -0.12284242782995729 " "
absolute error = 6.7196248565437600000000000000E-14 " "
relative error = 5.47011726749785500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998018 " "
y[1] (closed_form) = -0.12162012525046004 " "
y[1] (numeric) = -0.12162012525039272 " "
absolute error = 6.73211486557079300000000000000E-14 " "
relative error = 5.53536254933706300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998007 " "
y[1] (closed_form) = -0.12040998478477109 " "
y[1] (numeric) = -0.12040998478470365 " "
absolute error = 6.74460487459782600000000000000E-14 " "
relative error = 5.60136676925388400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999997996 " "
y[1] (closed_form) = -0.1192118854179026 " "
y[1] (numeric) = -0.11921188541783505 " "
absolute error = 6.75570710484407800000000000000E-14 " "
relative error = 5.66697446413303800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997985 " "
y[1] (closed_form) = -0.11802570733891947 " "
y[1] (numeric) = -0.1180257073388518 " "
absolute error = 6.76680933509032900000000000000E-14 " "
relative error = 5.733335124744425000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997974 " "
y[1] (closed_form) = -0.11685133192902533 " "
y[1] (numeric) = -0.1168513319289575 " "
absolute error = 6.78346268045970600000000000000E-14 " "
relative error = 5.80520783843519600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8499999999997963 " "
y[1] (closed_form) = -0.11568864174970049 " "
y[1] (numeric) = -0.11568864174963255 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 5.87314779389183100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999795 " "
y[1] (closed_form) = -0.11453752053095817 " "
y[1] (numeric) = -0.11453752053089009 " "
absolute error = 6.80844269851377200000000000000E-14 " "
relative error = 5.94429027881176100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999794 " "
y[1] (closed_form) = -0.11339785315971719 " "
y[1] (numeric) = -0.11339785315964898 " "
absolute error = 6.82093270754080500000000000000E-14 " "
relative error = 6.01504571513690300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999793 " "
y[1] (closed_form) = -0.1122695256682907 " "
y[1] (numeric) = -0.11226952566822238 " "
absolute error = 6.83203493778705700000000000000E-14 " "
relative error = 6.08538683771841400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.889999999999792 " "
y[1] (closed_form) = -0.11115242522298927 " "
y[1] (numeric) = -0.11115242522292082 " "
absolute error = 6.8445249468140900000000000000E-14 " "
relative error = 6.1577828221767500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997907 " "
y[1] (closed_form) = -0.11004644011283748 " "
y[1] (numeric) = -0.11004644011276891 " "
absolute error = 6.85701495584112300000000000000E-14 " "
relative error = 6.23101933039378400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997896 " "
y[1] (closed_form) = -0.10895145973840266 " "
y[1] (numeric) = -0.10895145973833398 " "
absolute error = 6.86811718608737500000000000000E-14 " "
relative error = 6.30383218598266800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997885 " "
y[1] (closed_form) = -0.10786737460073484 " "
y[1] (numeric) = -0.10786737460066605 " "
absolute error = 6.87921941633362600000000000000E-14 " "
relative error = 6.37747923484434400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997874 " "
y[1] (closed_form) = -0.10679407629041687 " "
y[1] (numeric) = -0.10679407629034796 " "
absolute error = 6.89170942536065900000000000000E-14 " "
relative error = 6.45326938042825100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997863 " "
y[1] (closed_form) = -0.10573145747672331 " "
y[1] (numeric) = -0.10573145747665427 " "
absolute error = 6.90419943438769200000000000000E-14 " "
relative error = 6.52993877050039300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9499999999997852 " "
y[1] (closed_form) = -0.10467941189688727 " "
y[1] (numeric) = -0.10467941189681813 " "
absolute error = 6.91391388585316200000000000000E-14 " "
relative error = 6.60484593920302100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999784 " "
y[1] (closed_form) = -0.10363783434547404 " "
y[1] (numeric) = -0.1036378343454048 " "
absolute error = 6.92362833731863200000000000000E-14 " "
relative error = 6.68059920495723300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999783 " "
y[1] (closed_form) = -0.1026066206638605 " "
y[1] (numeric) = -0.10260662066379116 " "
absolute error = 6.93473056756488400000000000000E-14 " "
relative error = 6.75856053215423200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999782 " "
y[1] (closed_form) = -0.10158566772981914 " "
y[1] (numeric) = -0.1015856677297497 " "
absolute error = 6.94444501903035400000000000000E-14 " "
relative error = 6.83604801171366800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.989999999999781 " "
y[1] (closed_form) = -0.10057487344720578 " "
y[1] (numeric) = -0.10057487344713621 " "
absolute error = 6.95693502805738700000000000000E-14 " "
relative error = 6.91717005411819200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997797 " "
y[1] (closed_form) = -9.95741367357498200E-2 " "
y[1] (numeric) = -9.95741367356801200E-2 " "
absolute error = 6.9694250370844200000000000000E-14 " "
relative error = 6.99923219578584400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997786 " "
y[1] (closed_form) = -9.85833575209461500E-2 " "
y[1] (numeric) = -9.85833575208763400E-2 " "
absolute error = 6.98052726733067200000000000000E-14 " "
relative error = 7.0808374180677600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997775 " "
y[1] (closed_form) = -9.76024367240476300E-2 " "
y[1] (numeric) = -9.76024367239777300E-2 " "
absolute error = 6.99024171879614200000000000000E-14 " "
relative error = 7.16195410014170400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997764 " "
y[1] (closed_form) = -9.66312762521571600E-2 " "
y[1] (numeric) = -9.66312762520871300E-2 " "
absolute error = 7.00273172782317500000000000000E-14 " "
relative error = 7.24685836659106400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0399999999997753 " "
y[1] (closed_form) = -9.56697789884182300E-2 " "
y[1] (numeric) = -9.56697789883480800E-2 " "
absolute error = 7.01522173685020800000000000000E-14 " "
relative error = 7.33274583784652600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0499999999997742 " "
y[1] (closed_form) = -9.47178487823032300E-2 " "
y[1] (numeric) = -9.47178487822329700E-2 " "
absolute error = 7.0263239670964600000000000000E-14 " "
relative error = 7.41816252947800700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999773 " "
y[1] (closed_form) = -9.37753904399982500E-2 " "
y[1] (numeric) = -9.37753904399278900E-2 " "
absolute error = 7.0360384185619300000000000000E-14 " "
relative error = 7.50307557830314300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999772 " "
y[1] (closed_form) = -9.28423097148837000E-2 " "
y[1] (numeric) = -9.28423097148132300E-2 " "
absolute error = 7.045752870027400000000000000E-14 " "
relative error = 7.5889461299107300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999771 " "
y[1] (closed_form) = -9.19185132981094700E-2 " "
y[1] (numeric) = -9.19185132980389200E-2 " "
absolute error = 7.0554673214928700000000000000E-14 " "
relative error = 7.67578485371127400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.08999999999977 " "
y[1] (closed_form) = -9.10039088092640800E-2 " "
y[1] (numeric) = -9.10039088091934100E-2 " "
absolute error = 7.06656955173912100000000000000E-14 " "
relative error = 7.76512750298452500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997687 " "
y[1] (closed_form) = -9.00984047871364400E-2 " "
y[1] (numeric) = -9.00984047870656800E-2 " "
absolute error = 7.07628400320459100000000000000E-14 " "
relative error = 7.85395037783719800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997676 " "
y[1] (closed_form) = -8.92019106805698000E-2 " "
y[1] (numeric) = -8.92019106804989200E-2 " "
absolute error = 7.08738623345084300000000000000E-14 " "
relative error = 7.94533007127014100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997665 " "
y[1] (closed_form) = -8.83143368394063600E-2 " "
y[1] (numeric) = -8.83143368393353700E-2 " "
absolute error = 7.09848846369709500000000000000E-14 " "
relative error = 8.03775323207738600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997654 " "
y[1] (closed_form) = -8.74355945055223800E-2 " "
y[1] (numeric) = -8.74355945054513100E-2 " "
absolute error = 7.10681513638178300000000000000E-14 " "
relative error = 8.12805720207337400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1399999999997643 " "
y[1] (closed_form) = -8.6565595803952200E-2 " "
y[1] (numeric) = -8.65655958038810100E-2 " "
absolute error = 7.11930514540881600000000000000E-14 " "
relative error = 8.22417391030511500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999763 " "
y[1] (closed_form) = -8.57042537341006700E-2 " "
y[1] (numeric) = -8.57042537340293700E-2 " "
absolute error = 7.12901959687428600000000000000E-14 " "
relative error = 8.31816308557125600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999762 " "
y[1] (closed_form) = -8.48514821610429700E-2 " "
y[1] (numeric) = -8.4851482160971600E-2 " "
absolute error = 7.13595849077819400000000000000E-14 " "
relative error = 8.4099397076347790000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999761 " "
y[1] (closed_form) = -8.40071958069111800E-2 " "
y[1] (numeric) = -8.40071958068397300E-2 " "
absolute error = 7.14567294224366400000000000000E-14 " "
relative error = 8.50602483942904900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.17999999999976 " "
y[1] (closed_form) = -8.3171310242366300E-2 " "
y[1] (numeric) = -8.31713102422947600E-2 " "
absolute error = 7.15399961492835200000000000000E-14 " "
relative error = 8.60152328258525400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.189999999999759 " "
y[1] (closed_form) = -8.23437418781553400E-2 " "
y[1] (numeric) = -8.23437418780836900E-2 " "
absolute error = 7.16510184517460400000000000000E-14 " "
relative error = 8.70145281444321600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997577 " "
y[1] (closed_form) = -8.15244079567521900E-2 " "
y[1] (numeric) = -8.15244079566804600E-2 " "
absolute error = 7.17342851785929300000000000000E-14 " "
relative error = 8.7991175865572900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997566 " "
y[1] (closed_form) = -8.07132265440819500E-2 " "
y[1] (numeric) = -8.07132265440101400E-2 " "
absolute error = 7.180367411763200000000000000E-14 " "
relative error = 8.8961471610128310000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997555 " "
y[1] (closed_form) = -7.99101165213273500E-2 " "
y[1] (numeric) = -7.99101165212554600E-2 " "
absolute error = 7.18869408444788900000000000000E-14 " "
relative error = 8.99597497461949700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997544 " "
y[1] (closed_form) = -7.91149975768168800E-2 " "
y[1] (numeric) = -7.9114997576744890E-2 " "
absolute error = 7.19840853591335900000000000000E-14 " "
relative error = 9.09866492623481100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2399999999997533 " "
y[1] (closed_form) = -7.83277901979934600E-2 " "
y[1] (numeric) = -7.8327790197921400E-2 " "
absolute error = 7.20673520859804700000000000000E-14 " "
relative error = 9.20073857615692500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999752 " "
y[1] (closed_form) = -7.75484156634632400E-2 " "
y[1] (numeric) = -7.75484156633910600E-2 " "
absolute error = 7.21783743884429900000000000000E-14 " "
relative error = 9.30752405073952700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999751 " "
y[1] (closed_form) = -7.67767960351232300E-2 " "
y[1] (numeric) = -7.67767960350509600E-2 " "
absolute error = 7.22616411152898800000000000000E-14 " "
relative error = 9.41191152105802800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.26999999999975 " "
y[1] (closed_form) = -7.60128541503676400E-2 " "
y[1] (numeric) = -7.60128541502952500E-2 " "
absolute error = 7.23865412055602100000000000000E-14 " "
relative error = 9.52293424772158800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999749 " "
y[1] (closed_form) = -7.52565136143713100E-2 " "
y[1] (numeric) = -7.52565136142988500E-2 " "
absolute error = 7.24698079324070900000000000000E-14 " "
relative error = 9.62970571607345100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.289999999999748 " "
y[1] (closed_form) = -7.45076987924504000E-2 " "
y[1] (numeric) = -7.45076987923778400E-2 " "
absolute error = 7.2566952447061790000000000000E-14 " "
relative error = 9.73952405230031600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997467 " "
y[1] (closed_form) = -7.3766334802498700E-2 " "
y[1] (numeric) = -7.37663348024260600E-2 " "
absolute error = 7.26363413861008700000000000000E-14 " "
relative error = 9.84681448259246400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997456 " "
y[1] (closed_form) = -7.30323475074993800E-2 " "
y[1] (numeric) = -7.30323475074266600E-2 " "
absolute error = 7.27196081129477500000000000000E-14 " "
relative error = 9.95717796220099400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997445 " "
y[1] (closed_form) = -7.23056635081113100E-2 " "
y[1] (numeric) = -7.23056635080385200E-2 " "
absolute error = 7.27889970519868300000000000000E-14 " "
relative error = 1.00668458763014170000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997434 " "
y[1] (closed_form) = -7.15862101353289600E-2 " "
y[1] (numeric) = -7.15862101352561200E-2 " "
absolute error = 7.28445082032180800000000000000E-14 " "
relative error = 1.01757738069259970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999997423 " "
y[1] (closed_form) = -7.08739154432155300E-2 " "
y[1] (numeric) = -7.08739154431426100E-2 " "
absolute error = 7.29138971422571600000000000000E-14 " "
relative error = 1.02878325102097780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999741 " "
y[1] (closed_form) = -7.01687082017082200E-2 " "
y[1] (numeric) = -7.01687082016352200E-2 " "
absolute error = 7.29971638691040400000000000000E-14 " "
relative error = 1.04030935925548310000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.35999999999974 " "
y[1] (closed_form) = -6.94705178894951600E-2 " "
y[1] (numeric) = -6.94705178894221100E-2 " "
absolute error = 7.3052675020335300000000000000E-14 " "
relative error = 1.05156370269958510000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999739 " "
y[1] (closed_form) = -6.87792746869633800E-2 " "
y[1] (numeric) = -6.87792746868902600E-2 " "
absolute error = 7.31220639593743700000000000000E-14 " "
relative error = 1.06314095768204050000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.379999999999738 " "
y[1] (closed_form) = -6.80949094692165400E-2 " "
y[1] (numeric) = -6.80949094691433300E-2 " "
absolute error = 7.32053306862212600000000000000E-14 " "
relative error = 1.07504850592855220000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.389999999999737 " "
y[1] (closed_form) = -6.74173537991625600E-2 " "
y[1] (numeric) = -6.74173537990892900E-2 " "
absolute error = 7.32747196252603300000000000000E-14 " "
relative error = 1.08688216751353030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997357 " "
y[1] (closed_form) = -6.6746539920669800E-2 " "
y[1] (numeric) = -6.67465399205964700E-2 " "
absolute error = 7.33302307764915900000000000000E-14 " "
relative error = 1.09863718574246250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997346 " "
y[1] (closed_form) = -6.60824007517914100E-2 " "
y[1] (numeric) = -6.608240075171801E-2 " "
absolute error = 7.34134975033384800000000000000E-14 " "
relative error = 1.11093871693740350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997335 " "
y[1] (closed_form) = -6.54248698780570700E-2 " "
y[1] (numeric) = -6.54248698779835700E-2 " "
absolute error = 7.34967642301853600000000000000E-14 " "
relative error = 1.12337654422810770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997324 " "
y[1] (closed_form) = -6.47738815458314100E-2 " "
y[1] (numeric) = -6.47738815457578500E-2 " "
absolute error = 7.35661531692244400000000000000E-14 " "
relative error = 1.13573791493677840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999997313 " "
y[1] (closed_form) = -6.41293706557387700E-2 " "
y[1] (numeric) = -6.41293706556651400E-2 " "
absolute error = 7.36355421082635100000000000000E-14 " "
relative error = 1.14823428571529340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.44999999999973 " "
y[1] (closed_form) = -6.34912727561530200E-2 " "
y[1] (numeric) = -6.34912727560793100E-2 " "
absolute error = 7.37049310473025800000000000000E-14 " "
relative error = 1.16086712153931020000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.459999999999729 " "
y[1] (closed_form) = -6.28595240367524500E-2 " "
y[1] (numeric) = -6.28595240366786900E-2 " "
absolute error = 7.37604421985338400000000000000E-14 " "
relative error = 1.17341712857080950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999728 " "
y[1] (closed_form) = -6.223406132213866000E-2 " "
y[1] (numeric) = -6.22340613220648500E-2 " "
absolute error = 7.38090144558611900000000000000E-14 " "
relative error = 1.1859906438342141000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.479999999999727 " "
y[1] (closed_form) = -6.16148220655189800E-2 " "
y[1] (numeric) = -6.1614822065445100E-2 " "
absolute error = 7.38784033949002600000000000000E-14 " "
relative error = 1.199036220803180000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997258 " "
y[1] (closed_form) = -6.1001744342451700E-2 " "
y[1] (numeric) = -6.10017443423777600E-2 " "
absolute error = 7.39408534400354300000000000000E-14 " "
relative error = 1.21211047711924660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997247 " "
y[1] (closed_form) = -6.039476684465364000E-2 " "
y[1] (numeric) = -6.03947668445796100E-2 " "
absolute error = 7.40241201668823100000000000000E-14 " "
relative error = 1.22567109758509170000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997236 " "
y[1] (closed_form) = -5.979382887386917000E-2 " "
y[1] (numeric) = -5.97938288737950700E-2 " "
absolute error = 7.40935091059213800000000000000E-14 " "
relative error = 1.23914976681316700000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997225 " "
y[1] (closed_form) = -5.91988703358004200E-2 " "
y[1] (numeric) = -5.919887033572627000E-2 " "
absolute error = 7.41559591510565500000000000000E-14 " "
relative error = 1.25265834855316230000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997214 " "
y[1] (closed_form) = -5.86098317340978400E-2 " "
y[1] (numeric) = -5.86098317340236200E-2 " "
absolute error = 7.42184091961917100000000000000E-14 " "
relative error = 1.2663132959143641000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999997203 " "
y[1] (closed_form) = -5.802665416441034000E-2 " "
y[1] (numeric) = -5.802665416433606000E-2 " "
absolute error = 7.42808592413268800000000000000E-14 " "
relative error = 1.28011618644877480000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.549999999999719 " "
y[1] (closed_form) = -5.74492793084949900E-2 " "
y[1] (numeric) = -5.74492793084206400E-2 " "
absolute error = 7.43502481803659500000000000000E-14 " "
relative error = 1.29418939759217870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999718 " "
y[1] (closed_form) = -5.68776494283850500E-2 " "
y[1] (numeric) = -5.687764942831065000E-2 " "
absolute error = 7.44057593315972100000000000000E-14 " "
relative error = 1.30817219205378560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999717 " "
y[1] (closed_form) = -5.631170736061615000E-2 " "
y[1] (numeric) = -5.631170736054167000E-2 " "
absolute error = 7.44682093767323700000000000000E-14 " "
relative error = 1.322428547581469800000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.579999999999716 " "
y[1] (closed_form) = -5.57513965105098800E-2 " "
y[1] (numeric) = -5.57513965104353500E-2 " "
absolute error = 7.45306594218675400000000000000E-14 " "
relative error = 1.3368393275640642000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997148 " "
y[1] (closed_form) = -5.51966608465143100E-2 " "
y[1] (numeric) = -5.519666084643973000E-2 " "
absolute error = 7.4586170573098800000000000000E-14 " "
relative error = 1.3512804838050080000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997137 " "
y[1] (closed_form) = -5.46474448946007700E-2 " "
y[1] (numeric) = -5.46474448945261300E-2 " "
absolute error = 7.46416817243300600000000000000E-14 " "
relative error = 1.3658768835083218000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997125 " "
y[1] (closed_form) = -5.410369373271637000E-2 " "
y[1] (numeric) = -5.41036937326416700E-2 " "
absolute error = 7.47041317694652200000000000000E-14 " "
relative error = 1.38075844023735880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997114 " "
y[1] (closed_form) = -5.35653529852918100E-2 " "
y[1] (numeric) = -5.35653529852170500E-2 " "
absolute error = 7.47596429206964800000000000000E-14 " "
relative error = 1.39567161895160600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997103 " "
y[1] (closed_form) = -5.303236881780372000E-2 " "
y[1] (numeric) = -5.3032368817728900E-2 " "
absolute error = 7.48220929658316400000000000000E-14 " "
relative error = 1.41087593546665780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999997092 " "
y[1] (closed_form) = -5.25046879313911900E-2 " "
y[1] (numeric) = -5.25046879313163200E-2 " "
absolute error = 7.487066522315899000000000000E-14 " "
relative error = 1.42598057760087660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999708 " "
y[1] (closed_form) = -5.198225755752586000E-2 " "
y[1] (numeric) = -5.19822575574509200E-2 " "
absolute error = 7.49331152682941600000000000000E-14 " "
relative error = 1.44151329298020330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999707 " "
y[1] (closed_form) = -5.14650254527349700E-2 " "
y[1] (numeric) = -5.146502545265997000E-2 " "
absolute error = 7.49955653134293200000000000000E-14 " "
relative error = 1.45721418873686560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999706 " "
y[1] (closed_form) = -5.095293989337701000E-2 " "
y[1] (numeric) = -5.09529398933019700E-2 " "
absolute error = 7.50371986768527700000000000000E-14 " "
relative error = 1.4726765292419620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.679999999999705 " "
y[1] (closed_form) = -5.044594967046931000E-2 " "
y[1] (numeric) = -5.04459496703942300E-2 " "
absolute error = 7.50857709341801200000000000000E-14 " "
relative error = 1.48844003184927200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997037 " "
y[1] (closed_form) = -4.994400408456710600E-2 " "
y[1] (numeric) = -4.99440040844919600E-2 " "
absolute error = 7.51412820854113800000000000000E-14 " "
relative error = 1.50451057064185880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997026 " "
y[1] (closed_form) = -4.94470529406934870E-2 " "
y[1] (numeric) = -4.944705294061827500E-2 " "
absolute error = 7.52106710244504500000000000000E-14 " "
relative error = 1.5210344510249720000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997015 " "
y[1] (closed_form) = -4.89550465433199470E-2 " "
y[1] (numeric) = -4.89550465432446850E-2 " "
absolute error = 7.5259243281777800000000000000E-14 " "
relative error = 1.53731328220026220000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997004 " "
y[1] (closed_form) = -4.846793569139676000E-2 " "
y[1] (numeric) = -4.846793569132143400E-2 " "
absolute error = 7.53216933269129600000000000000E-14 " "
relative error = 1.55405201918436260000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999996993 " "
y[1] (closed_form) = -4.79856716734327840E-2 " "
y[1] (numeric) = -4.7985671673357400E-2 " "
absolute error = 7.53841433720481300000000000000E-14 " "
relative error = 1.57097193272767060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7399999999996982 " "
y[1] (closed_form) = -4.750820626262433600E-2 " "
y[1] (numeric) = -4.750820626254890000E-2 " "
absolute error = 7.54327156293754800000000000000E-14 " "
relative error = 1.58778286034174930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999697 " "
y[1] (closed_form) = -4.703549171203247000E-2 " "
y[1] (numeric) = -4.703549171195698400E-2 " "
absolute error = 7.54812878867028300000000000000E-14 " "
relative error = 1.60477301584993240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999696 " "
y[1] (closed_form) = -4.65674807498081660E-2 " "
y[1] (numeric) = -4.65674807497326300E-2 " "
absolute error = 7.55367990379340900000000000000E-14 " "
relative error = 1.6220933110762120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999695 " "
y[1] (closed_form) = -4.61041265744652100E-2 " "
y[1] (numeric) = -4.610412657438963700E-2 " "
absolute error = 7.55714935074536200000000000000E-14 " "
relative error = 1.6391481440472389000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.779999999999694 " "
y[1] (closed_form) = -4.56453828501999300E-2 " "
y[1] (numeric) = -4.56453828501243100E-2 " "
absolute error = 7.56200657647809700000000000000E-14 " "
relative error = 1.65668597879773870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996927 " "
y[1] (closed_form) = -4.51912037022576200E-2 " "
y[1] (numeric) = -4.51912037021819500E-2 " "
absolute error = 7.56686380221083300000000000000E-14 " "
relative error = 1.67441076632194570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996916 " "
y[1] (closed_form) = -4.47415437123449900E-2 " "
y[1] (numeric) = -4.47415437122692700E-2 " "
absolute error = 7.57172102794356800000000000000E-14 " "
relative error = 1.69232449300903200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996905 " "
y[1] (closed_form) = -4.42963579140883400E-2 " "
y[1] (numeric) = -4.429635791401257400E-2 " "
absolute error = 7.57657825367630300000000000000E-14 " "
relative error = 1.71042916629192940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996894 " "
y[1] (closed_form) = -4.385560178853686000E-2 " "
y[1] (numeric) = -4.38556017884610460E-2 " "
absolute error = 7.58074159001864700000000000000E-14 " "
relative error = 1.72856859348812540000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8299999999996883 " "
y[1] (closed_form) = -4.34192312597106800E-2 " "
y[1] (numeric) = -4.34192312596348200E-2 " "
absolute error = 7.58559881575138200000000000000E-14 " "
relative error = 1.74705967739925580000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999687 " "
y[1] (closed_form) = -4.29872026901932900E-2 " "
y[1] (numeric) = -4.29872026901173800E-2 " "
absolute error = 7.59045604148411700000000000000E-14 " "
relative error = 1.7657478427215120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999686 " "
y[1] (closed_form) = -4.255947287676769600E-2 " "
y[1] (numeric) = -4.25594728766917400E-2 " "
absolute error = 7.59531326721685200000000000000E-14 " "
relative error = 1.78463518314931300000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999685 " "
y[1] (closed_form) = -4.213599904609613400E-2 " "
y[1] (numeric) = -4.213599904602012300E-2 " "
absolute error = 7.60086438233997800000000000000E-14 " "
relative error = 1.80388849307328620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999684 " "
y[1] (closed_form) = -4.17167388504426250E-2 " "
y[1] (numeric) = -4.17167388503665750E-2 " "
absolute error = 7.60502771868232200000000000000E-14 " "
relative error = 1.82301587522142340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.879999999999683 " "
y[1] (closed_form) = -4.130165036343822500E-2 " "
y[1] (numeric) = -4.130165036336213600E-2 " "
absolute error = 7.60919105502466700000000000000E-14 " "
relative error = 1.84234552083676760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996817 " "
y[1] (closed_form) = -4.08906920758883300E-2 " "
y[1] (numeric) = -4.08906920758121900E-2 " "
absolute error = 7.61404828075740200000000000000E-14 " "
relative error = 1.8620492572311130000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996806 " "
y[1] (closed_form) = -4.04838228916217100E-2 " "
y[1] (numeric) = -4.04838228915455200E-2 " "
absolute error = 7.61890550649013700000000000000E-14 " "
relative error = 1.88196295762051160000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996795 " "
y[1] (closed_form) = -4.00810021233808800E-2 " "
y[1] (numeric) = -4.00810021233046500E-2 " "
absolute error = 7.62306884283248100000000000000E-14 " "
relative error = 1.90191573039178940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996784 " "
y[1] (closed_form) = -3.968218948875334000E-2 " "
y[1] (numeric) = -3.96821894886770550E-2 " "
absolute error = 7.62792606856521600000000000000E-14 " "
relative error = 1.92225433294881870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9299999999996773 " "
y[1] (closed_form) = -3.92873451061432700E-2 " "
y[1] (numeric) = -3.92873451060669400E-2 " "
absolute error = 7.63278329429795100000000000000E-14 " "
relative error = 1.94280964358277050000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999676 " "
y[1] (closed_form) = -3.889642949078337400E-2 " "
y[1] (numeric) = -3.889642949070700E-2 " "
absolute error = 7.63764052003068600000000000000E-14 " "
relative error = 1.96358396388039870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999675 " "
y[1] (closed_form) = -3.85094035507863600E-2 " "
y[1] (numeric) = -3.850940355070993000E-2 " "
absolute error = 7.64249774576342100000000000000E-14 " "
relative error = 1.98457961980233330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999674 " "
y[1] (closed_form) = -3.8126228583235700E-2 " "
y[1] (numeric) = -3.81262285831592300E-2 " "
absolute error = 7.64735497149615600000000000000E-14 " "
relative error = 2.0057989619405310000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999673 " "
y[1] (closed_form) = -3.77468662703153200E-2 " "
y[1] (numeric) = -3.774686627023881600E-2 " "
absolute error = 7.6508244184481100000000000000E-14 " "
relative error = 2.02687671174039350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.979999999999672 " "
y[1] (closed_form) = -3.737127867547780400E-2 " "
y[1] (numeric) = -3.73712786754012400E-2 " "
absolute error = 7.65637553357123600000000000000E-14 " "
relative error = 2.04873255744261630000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996707 " "
y[1] (closed_form) = -3.699942823965068000E-2 " "
y[1] (numeric) = -3.69994282395740600E-2 " "
absolute error = 7.66123275930397100000000000000E-14 " "
relative error = 2.07063544595366550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996696 " "
y[1] (closed_form) = -3.66312777774804600E-2 " "
y[1] (numeric) = -3.66312777774038150E-2 " "
absolute error = 7.66470220625592400000000000000E-14 " "
relative error = 2.09239280508197200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999673 " "
y[1] (closed_form) = -3.626679047361400E-2 " "
y[1] (numeric) = -3.62667904735374800E-2 " "
absolute error = 7.65221219722889100000000000000E-14 " "
relative error = 2.10997777782301360000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999676 " "
y[1] (closed_form) = -3.590592987901733400E-2 " "
y[1] (numeric) = -3.59059298789409300E-2 " "
absolute error = 7.64041607759224900000000000000E-14 " "
relative error = 2.1278981224928940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.02999999999968 " "
y[1] (closed_form) = -3.554865990733028000E-2 " "
y[1] (numeric) = -3.554865990725400E-2 " "
absolute error = 7.62861995795560700000000000000E-14 " "
relative error = 2.1459655519623550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999683 " "
y[1] (closed_form) = -3.51949448312579460E-2 " "
y[1] (numeric) = -3.51949448311817850E-2 " "
absolute error = 7.61612994892857400000000000000E-14 " "
relative error = 2.1639840566433860000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999686 " "
y[1] (closed_form) = -3.48447492789979550E-2 " "
y[1] (numeric) = -3.48447492789219050E-2 " "
absolute error = 7.60502771868232200000000000000E-14 " "
relative error = 2.18254625906179640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.05999999999969 " "
y[1] (closed_form) = -3.44980382307032500E-2 " "
y[1] (numeric) = -3.449803823062732600E-2 " "
absolute error = 7.59253770965528900000000000000E-14 " "
relative error = 2.20086071529074140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999693 " "
y[1] (closed_form) = -3.415477701498008700E-2 " "
y[1] (numeric) = -3.41547770149042640E-2 " "
absolute error = 7.58212936879942800000000000000E-14 " "
relative error = 2.21993232907770150000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999696 " "
y[1] (closed_form) = -3.38149313054208260E-2 " "
y[1] (numeric) = -3.381493130534512500E-2 " "
absolute error = 7.57033324916278600000000000000E-14 " "
relative error = 2.2387545847089138000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997 " "
y[1] (closed_form) = -3.34784671171713200E-2 " "
y[1] (numeric) = -3.34784671170957300E-2 " "
absolute error = 7.55923101891653500000000000000E-14 " "
relative error = 2.25793821218276620000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999703 " "
y[1] (closed_form) = -3.314535080353233600E-2 " "
y[1] (numeric) = -3.314535080345685000E-2 " "
absolute error = 7.54812878867028300000000000000E-14 " "
relative error = 2.27728130965078570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999706 " "
y[1] (closed_form) = -3.28155490525949400E-2 " "
y[1] (numeric) = -3.28155490525195500E-2 " "
absolute error = 7.53910822659520400000000000000E-14 " "
relative error = 2.29741949906489100000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.11999999999971 " "
y[1] (closed_form) = -3.24890288839091770E-2 " "
y[1] (numeric) = -3.24890288838338900E-2 " "
absolute error = 7.52869988573934300000000000000E-14 " "
relative error = 2.31730530101134450000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999713 " "
y[1] (closed_form) = -3.216575764518609400E-2 " "
y[1] (numeric) = -3.216575764511090400E-2 " "
absolute error = 7.51898543427387300000000000000E-14 " "
relative error = 2.3375744843986782000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999716 " "
y[1] (closed_form) = -3.18457030090324170E-2 " "
y[1] (numeric) = -3.184570300895734300E-2 " "
absolute error = 7.5071893146372300000000000000E-14 " "
relative error = 2.3573633505619150000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.14999999999972 " "
y[1] (closed_form) = -3.15288329697178200E-2 " "
y[1] (numeric) = -3.15288329696428600E-2 " "
absolute error = 7.49608708439097900000000000000E-14 " "
relative error = 2.37753395172941250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999723 " "
y[1] (closed_form) = -3.121511583997431700E-2 " "
y[1] (numeric) = -3.12151158398994500E-2 " "
absolute error = 7.48637263292550900000000000000E-14 " "
relative error = 2.39831646670950470000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999726 " "
y[1] (closed_form) = -3.090452024782748000E-2 " "
y[1] (numeric) = -3.09045202477527300E-2 " "
absolute error = 7.47561734737445200000000000000E-14 " "
relative error = 2.4189397820857520000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.17999999999973 " "
y[1] (closed_form) = -3.059701513345930000E-2 " "
y[1] (numeric) = -3.059701513338465000E-2 " "
absolute error = 7.46520900651859200000000000000E-14 " "
relative error = 2.4398487806593358000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999733 " "
y[1] (closed_form) = -3.029256974610205500E-2 " "
y[1] (numeric) = -3.029256974602750300E-2 " "
absolute error = 7.45514761035792600000000000000E-14 " "
relative error = 2.46104826128764780000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999736 " "
y[1] (closed_form) = -2.99911536409633200E-2 " "
y[1] (numeric) = -2.999115364088886000E-2 " "
absolute error = 7.44578010358765100000000000000E-14 " "
relative error = 2.48265878422824550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20999999999974 " "
y[1] (closed_form) = -2.96927366761813900E-2 " "
y[1] (numeric) = -2.969273667610703400E-2 " "
absolute error = 7.43571870742698600000000000000E-14 " "
relative error = 2.504221415667520000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999743 " "
y[1] (closed_form) = -2.93972890098111100E-2 " "
y[1] (numeric) = -2.939728900973685400E-2 " "
absolute error = 7.4256573112663200000000000000E-14 " "
relative error = 2.52596670012260900000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999746 " "
y[1] (closed_form) = -2.91047810968396400E-2 " "
y[1] (numeric) = -2.910478109676547500E-2 " "
absolute error = 7.41663674919124100000000000000E-14 " "
relative error = 2.54825374721563600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.23999999999975 " "
y[1] (closed_form) = -2.88151836862319200E-2 " "
y[1] (numeric) = -2.881518368615784700E-2 " "
absolute error = 7.40726924242096600000000000000E-14 " "
relative error = 2.57061323053797030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999753 " "
y[1] (closed_form) = -2.852846781800555400E-2 " "
y[1] (numeric) = -2.85284678179315800E-2 " "
absolute error = 7.39755479095549600000000000000E-14 " "
relative error = 2.59304314488511660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999756 " "
y[1] (closed_form) = -2.824460482033479500E-2 " "
y[1] (numeric) = -2.824460482026091600E-2 " "
absolute error = 7.38818728418522100000000000000E-14 " "
relative error = 2.61578709675062360000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.26999999999976 " "
y[1] (closed_form) = -2.79635663066833200E-2 " "
y[1] (numeric) = -2.79635663066095330E-2 " "
absolute error = 7.37881977741494700000000000000E-14 " "
relative error = 2.63872629710016700000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999763 " "
y[1] (closed_form) = -2.768532417296556400E-2 " "
y[1] (numeric) = -2.76853241728918730E-2 " "
absolute error = 7.36945227064467200000000000000E-14 " "
relative error = 2.661862373221140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2899999999997664 " "
y[1] (closed_form) = -2.740985059473629600E-2 " "
y[1] (numeric) = -2.740985059466269400E-2 " "
absolute error = 7.36008476387439700000000000000E-14 " "
relative error = 2.6851969653887153000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.29999999999977 " "
y[1] (closed_form) = -2.71371180244081100E-2 " "
y[1] (numeric) = -2.713711802433460000E-2 " "
absolute error = 7.35071725710412200000000000000E-14 " "
relative error = 2.7087317269625390000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999773 " "
y[1] (closed_form) = -2.686709918849671000E-2 " "
y[1] (numeric) = -2.686709918842329300E-2 " "
absolute error = 7.34169669502904300000000000000E-14 " "
relative error = 2.7325974581477813000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3199999999997765 " "
y[1] (closed_form) = -2.659976708489349000E-2 " "
y[1] (numeric) = -2.659976708482016000E-2 " "
absolute error = 7.33302307764915900000000000000E-14 " "
relative error = 2.7567997322103327000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.32999999999978 " "
y[1] (closed_form) = -2.633509498016530000E-2 " "
y[1] (numeric) = -2.633509498009206000E-2 " "
absolute error = 7.3240025155740800000000000000E-14 " "
relative error = 2.7810807293804213000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999783 " "
y[1] (closed_form) = -2.607305640688112300E-2 " "
y[1] (numeric) = -2.607305640680796500E-2 " "
absolute error = 7.31567584288939100000000000000E-14 " "
relative error = 2.80583746252267560000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3499999999997865 " "
y[1] (closed_form) = -2.58136251609652530E-2 " "
y[1] (numeric) = -2.58136251608921840E-2 " "
absolute error = 7.30700222550950700000000000000E-14 " "
relative error = 2.830676505119080000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.35999999999979 " "
y[1] (closed_form) = -2.5556775299076900E-2 " "
y[1] (numeric) = -2.555677529900392500E-2 " "
absolute error = 7.29728777404403700000000000000E-14 " "
relative error = 2.8553241512858674000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999793 " "
y[1] (closed_form) = -2.530248113601585000E-2 " "
y[1] (numeric) = -2.530248113594295600E-2 " "
absolute error = 7.28930804605454300000000000000E-14 " "
relative error = 2.88086690268443970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3799999999997965 " "
y[1] (closed_form) = -2.505071724215386400E-2 " "
y[1] (numeric) = -2.505071724208105500E-2 " "
absolute error = 7.28098137336985500000000000000E-14 " "
relative error = 2.90649617054391200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3899999999998 " "
y[1] (closed_form) = -2.48014584408917700E-2 " "
y[1] (numeric) = -2.480145844081904400E-2 " "
absolute error = 7.27265470068516600000000000000E-14 " "
relative error = 2.932349610817350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999803 " "
y[1] (closed_form) = -2.455467980614171600E-2 " "
y[1] (numeric) = -2.45546798060690690E-2 " "
absolute error = 7.26467497269567300000000000000E-14 " "
relative error = 2.9585704354729980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4099999999998065 " "
y[1] (closed_form) = -2.43103566598345800E-2 " "
y[1] (numeric) = -2.431035665976201400E-2 " "
absolute error = 7.2566952447061790000000000000E-14 " "
relative error = 2.98502212297676650000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999981 " "
y[1] (closed_form) = -2.406846456945212200E-2 " "
y[1] (numeric) = -2.406846456937963600E-2 " "
absolute error = 7.24871551671668600000000000000E-14 " "
relative error = 3.01170666529214760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999813 " "
y[1] (closed_form) = -2.38289793455837400E-2 " "
y[1] (numeric) = -2.382897934551132500E-2 " "
absolute error = 7.24142967811758400000000000000E-14 " "
relative error = 3.0389172667018360000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4399999999998165 " "
y[1] (closed_form) = -2.35918770395074600E-2 " "
y[1] (numeric) = -2.35918770394351300E-2 " "
absolute error = 7.23310300543289500000000000000E-14 " "
relative error = 3.06592942703125600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.44999999999982 " "
y[1] (closed_form) = -2.335713394079509700E-2 " "
y[1] (numeric) = -2.335713394072284600E-2 " "
absolute error = 7.22512327744340200000000000000E-14 " "
relative error = 3.0933261314326527000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999823 " "
y[1] (closed_form) = -2.31247265749411600E-2 " "
y[1] (numeric) = -2.312472657486898400E-2 " "
absolute error = 7.21749049414910400000000000000E-14 " "
relative error = 3.1211138738264060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999827 " "
y[1] (closed_form) = -2.28946317010153900E-2 " "
y[1] (numeric) = -2.28946317009432900E-2 " "
absolute error = 7.20985771085480600000000000000E-14 " "
relative error = 3.1491477150667790000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.47999999999983 " "
y[1] (closed_form) = -2.26668263093386400E-2 " "
y[1] (numeric) = -2.26668263092666200E-2 " "
absolute error = 7.20187798286531200000000000000E-14 " "
relative error = 3.17727673233996900000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999833 " "
y[1] (closed_form) = -2.244128761918191600E-2 " "
y[1] (numeric) = -2.244128761910997300E-2 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 3.20580767095630550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.499999999999837 " "
y[1] (closed_form) = -2.221799307648824600E-2 " "
y[1] (numeric) = -2.22179930764163790E-2 " "
absolute error = 7.18661241627671600000000000000E-14 " "
relative error = 3.2345911674091790000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50999999999984 " "
y[1] (closed_form) = -2.19969203516172800E-2 " "
y[1] (numeric) = -2.199692035154549300E-2 " "
absolute error = 7.17863268828722300000000000000E-14 " "
relative error = 3.26347169219050660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999843 " "
y[1] (closed_form) = -2.177804733711230500E-2 " "
y[1] (numeric) = -2.17780473370405900E-2 " "
absolute error = 7.1713468496881200000000000000E-14 " "
relative error = 3.2929246312488810000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999847 " "
y[1] (closed_form) = -2.156135214548947600E-2 " "
y[1] (numeric) = -2.156135214541783600E-2 " "
absolute error = 7.16406101108901800000000000000E-14 " "
relative error = 3.322639954464870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.53999999999985 " "
y[1] (closed_form) = -2.134681310704905600E-2 " "
y[1] (numeric) = -2.134681310697748600E-2 " "
absolute error = 7.15712211718511100000000000000E-14 " "
relative error = 3.35278248855878000000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999853 " "
y[1] (closed_form) = -2.113440876770840700E-2 " "
y[1] (numeric) = -2.11344087676369090E-2 " "
absolute error = 7.14983627858600800000000000000E-14 " "
relative error = 3.38303113049954600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999857 " "
y[1] (closed_form) = -2.0924117886856602E-2 " "
y[1] (numeric) = -2.092411788678517000E-2 " "
absolute error = 7.14289738468210100000000000000E-14 " "
relative error = 3.4137149404844840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.56999999999986 " "
y[1] (closed_form) = -2.0715919435230298E-2 " "
y[1] (numeric) = -2.071591943515894700E-2 " "
absolute error = 7.13526460138780300000000000000E-14 " "
relative error = 3.4443388446729010000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999863 " "
y[1] (closed_form) = -2.05097925928108520E-2 " "
y[1] (numeric) = -2.050979259273956500E-2 " "
absolute error = 7.12867265217909100000000000000E-14 " "
relative error = 3.475740975887710000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999867 " "
y[1] (closed_form) = -2.030571674674223000E-2 " "
y[1] (numeric) = -2.030571674667101800E-2 " "
absolute error = 7.12138681357998800000000000000E-14 " "
relative error = 3.5070846808313310000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.59999999999987 " "
y[1] (closed_form) = -2.010367148926977800E-2 " "
y[1] (numeric) = -2.01036714891986300E-2 " "
absolute error = 7.11479486437127700000000000000E-14 " "
relative error = 3.5390524900731485000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999873 " "
y[1] (closed_form) = -1.990363661569936600E-2 " "
y[1] (numeric) = -1.990363661562828700E-2 " "
absolute error = 7.1078559704673690000000000000E-14 " "
relative error = 3.5711343146512810000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999877 " "
y[1] (closed_form) = -1.970559212237694700E-2 " "
y[1] (numeric) = -1.970559212230592600E-2 " "
absolute error = 7.10195791064904800000000000000E-14 " "
relative error = 3.6040317218300310000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.62999999999988 " "
y[1] (closed_form) = -1.950951820468814500E-2 " "
y[1] (numeric) = -1.950951820461719300E-2 " "
absolute error = 7.09501901674514100000000000000E-14 " "
relative error = 3.63669617173847200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999883 " "
y[1] (closed_form) = -1.9315395255077802E-2 " "
y[1] (numeric) = -1.931539525500691500E-2 " "
absolute error = 7.08877401223162500000000000000E-14 " "
relative error = 3.6700124013087770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999887 " "
y[1] (closed_form) = -1.91232038610891800E-2 " "
y[1] (numeric) = -1.912320386101836700E-2 " "
absolute error = 7.08148817363252200000000000000E-14 " "
relative error = 3.7030866925188910000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.65999999999989 " "
y[1] (closed_form) = -1.89329248034227320E-2 " "
y[1] (numeric) = -1.893292480335197200E-2 " "
absolute error = 7.07593705850939600000000000000E-14 " "
relative error = 3.7373713422398390000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999893 " "
y[1] (closed_form) = -1.87445390540141100E-2 " "
y[1] (numeric) = -1.874453905394341300E-2 " "
absolute error = 7.0696920539958800000000000000E-14 " "
relative error = 3.77160090926958100000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999897 " "
y[1] (closed_form) = -1.8558027774131400E-2 " "
y[1] (numeric) = -1.855802777406076500E-2 " "
absolute error = 7.06344704948236300000000000000E-14 " "
relative error = 3.80614100563440140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6899999999999 " "
y[1] (closed_form) = -1.83733723124911700E-2 " "
y[1] (numeric) = -1.837337231242060500E-2 " "
absolute error = 7.05650815557845600000000000000E-14 " "
relative error = 3.84061675535801200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999903 " "
y[1] (closed_form) = -1.81905542033933900E-2 " "
y[1] (numeric) = -1.81905542033228900E-2 " "
absolute error = 7.04991620636974400000000000000E-14 " "
relative error = 3.87559176457339840000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999907 " "
y[1] (closed_form) = -1.800955516487479600E-2 " "
y[1] (numeric) = -1.800955516480435800E-2 " "
absolute error = 7.04401814655142300000000000000E-14 " "
relative error = 3.91126714794701240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.71999999999991 " "
y[1] (closed_form) = -1.783035709688070600E-2 " "
y[1] (numeric) = -1.78303570968103230E-2 " "
absolute error = 7.03846703142829700000000000000E-14 " "
relative error = 3.94746274187611550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999913 " "
y[1] (closed_form) = -1.765294207945498000E-2 " "
y[1] (numeric) = -1.765294207938465600E-2 " "
absolute error = 7.03256897160997600000000000000E-14 " "
relative error = 3.9837942819710986000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999917 " "
y[1] (closed_form) = -1.74772923709480420E-2 " "
y[1] (numeric) = -1.74772923708777780E-2 " "
absolute error = 7.0263239670964600000000000000E-14 " "
relative error = 4.0202588696039090000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.74999999999992 " "
y[1] (closed_form) = -1.73033904062426500E-2 " "
y[1] (numeric) = -1.730339040617244800E-2 " "
absolute error = 7.02007896258294300000000000000E-14 " "
relative error = 4.05705402107223200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999923 " "
y[1] (closed_form) = -1.71312187949974300E-2 " "
y[1] (numeric) = -1.713121879492729000E-2 " "
absolute error = 7.01418090276462200000000000000E-14 " "
relative error = 4.094385219581030000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999927 " "
y[1] (closed_form) = -1.69607603199077700E-2 " "
y[1] (numeric) = -1.696076031983768700E-2 " "
absolute error = 7.00828284294630100000000000000E-14 " "
relative error = 4.13205700143070600000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.77999999999993 " "
y[1] (closed_form) = -1.67919979349841200E-2 " "
y[1] (numeric) = -1.679199793491408800E-2 " "
absolute error = 7.00342561721356600000000000000E-14 " "
relative error = 4.1706922811268130000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999933 " "
y[1] (closed_form) = -1.662491476384734300E-2 " "
y[1] (numeric) = -1.66249147637773680E-2 " "
absolute error = 6.99752755739524400000000000000E-14 " "
relative error = 4.2090607120657947000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999937 " "
y[1] (closed_form) = -1.645949409804109700E-2 " "
y[1] (numeric) = -1.645949409797117800E-2 " "
absolute error = 6.99197644227211900000000000000E-14 " "
relative error = 4.247989883907950000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.80999999999994 " "
y[1] (closed_form) = -1.62957193953609500E-2 " "
y[1] (numeric) = -1.629571939529108600E-2 " "
absolute error = 6.98642532714899300000000000000E-14 " "
relative error = 4.28727640532266530000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999943 " "
y[1] (closed_form) = -1.613357427820014400E-2 " "
y[1] (numeric) = -1.61335742781303400E-2 " "
absolute error = 6.98052726733067200000000000000E-14 " "
relative error = 4.326708481928170000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999947 " "
y[1] (closed_form) = -1.597304253191185500E-2 " "
y[1] (numeric) = -1.597304253184209700E-2 " "
absolute error = 6.97567004159793700000000000000E-14 " "
relative error = 4.36715173559548530000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.83999999999995 " "
y[1] (closed_form) = -1.58141081031876700E-2 " "
y[1] (numeric) = -1.581410810311796300E-2 " "
absolute error = 6.97081281586520200000000000000E-14 " "
relative error = 4.40797088927202040000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8499999999999535 " "
y[1] (closed_form) = -1.565675509845227000E-2 " "
y[1] (numeric) = -1.565675509838261600E-2 " "
absolute error = 6.96560864543727100000000000000E-14 " "
relative error = 4.4489478194149230000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999957 " "
y[1] (closed_form) = -1.550096778227405800E-2 " "
y[1] (numeric) = -1.550096778220445300E-2 " "
absolute error = 6.96057794735693800000000000000E-14 " "
relative error = 4.4904150793195130000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.86999999999996 " "
y[1] (closed_form) = -1.534673057579159000E-2 " "
y[1] (numeric) = -1.534673057572204000E-2 " "
absolute error = 6.9552003045814100000000000000E-14 " "
relative error = 4.5320404044577150000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8799999999999635 " "
y[1] (closed_form) = -1.519402805515569000E-2 " "
y[1] (numeric) = -1.519402805508619000E-2 " "
absolute error = 6.9499961341534800000000000000E-14 " "
relative error = 4.57416302571271360000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999967 " "
y[1] (closed_form) = -1.504284494998703600E-2 " "
y[1] (numeric) = -1.504284494991758600E-2 " "
absolute error = 6.9447919637255500000000000000E-14 " "
relative error = 4.6166745630995387000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999997 " "
y[1] (closed_form) = -1.489316614184912300E-2 " "
y[1] (numeric) = -1.489316614177973000E-2 " "
absolute error = 6.93958779329761900000000000000E-14 " "
relative error = 4.6595785793308850000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9099999999999735 " "
y[1] (closed_form) = -1.474497666273641400E-2 " "
y[1] (numeric) = -1.474497666266706700E-2 " "
absolute error = 6.93473056756488400000000000000E-14 " "
relative error = 4.7031139663247973000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999977 " "
y[1] (closed_form) = -1.459826169357750200E-2 " "
y[1] (numeric) = -1.459826169350820200E-2 " "
absolute error = 6.93004681417974700000000000000E-14 " "
relative error = 4.7471726152358384000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.92999999999998 " "
y[1] (closed_form) = -1.445300656275320700E-2 " "
y[1] (numeric) = -1.445300656268395400E-2 " "
absolute error = 6.92536306079460900000000000000E-14 " "
relative error = 4.7916418156495816000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9399999999999835 " "
y[1] (closed_form) = -1.4309196744629400E-2 " "
y[1] (numeric) = -1.430919674456019600E-2 " "
absolute error = 6.92033236271427700000000000000E-14 " "
relative error = 4.8362829068736170000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999987 " "
y[1] (closed_form) = -1.416681785810442700E-2 " "
y[1] (numeric) = -1.416681785803527200E-2 " "
absolute error = 6.91564860932913900000000000000E-14 " "
relative error = 4.8815822145781995000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.95999999999999 " "
y[1] (closed_form) = -1.402585566517098300E-2 " "
y[1] (numeric) = -1.402585566510187700E-2 " "
absolute error = 6.91079138359640400000000000000E-14 " "
relative error = 4.9271798801960340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999935 " "
y[1] (closed_form) = -1.388629606949231500E-2 " "
y[1] (numeric) = -1.388629606942325400E-2 " "
absolute error = 6.90628110255886400000000000000E-14 " "
relative error = 4.9734508525507465000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999997 " "
y[1] (closed_form) = -1.374812511499254600E-2 " "
y[1] (numeric) = -1.374812511492353000E-2 " "
absolute error = 6.90177082152132500000000000000E-14 " "
relative error = 5.0201542128786970000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.99 " "
y[1] (closed_form) = -1.361132898446108800E-2 " "
y[1] (numeric) = -1.361132898439211300E-2 " "
absolute error = 6.8976074851789800000000000000E-14 " "
relative error = 5.0675488727466660000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = 2.0 / exp ( x ) ; "
Iterations = 4000
"Total Elapsed Time "= 1 Minutes 22 Seconds
"Elapsed Time(since restart) "= 1 Minutes 22 Seconds
"Time to Timeout "= 1 Minutes 37 Seconds
Percent Done = 100.02500000000009 "%"
(%o252) temp/diffeq.div_c_exp.max