(%i1) batch("temp/diffeq.add_full_lin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.add_full_lin.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,40,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[40],convfloat)
(%i173) completearray(array_norms,[40],convfloat)
(%i174) completearray(array_fact_1,[40],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[40],convfloat)
(%i184) completearray(array_x,[40],convfloat)
(%i185) completearray(array_tmp0,[40],convfloat)
(%i186) completearray(array_tmp1,[40],convfloat)
(%i187) completearray(array_tmp2,[40],convfloat)
(%i188) completearray(array_tmp3_g,[40],convfloat)
(%i189) completearray(array_tmp3,[40],convfloat)
(%i190) completearray(array_tmp4,[40],convfloat)
(%i191) completearray(array_tmp5,[40],convfloat)
(%i192) completearray(array_tmp6,[40],convfloat)
(%i193) completearray(array_tmp7,[40],convfloat)
(%i194) completearray(array_m1,[40],convfloat)
(%i195) completearray(array_y_higher,[2,40],convfloat)
(%i196) completearray(array_y_higher_work,[2,40],convfloat)
(%i197) completearray(array_y_higher_work2,[2,40],convfloat)
(%i198) completearray(array_y_set_initial,[2,40],convfloat)
(%i199) completearray(array_given_rad_poles,[2,3],convfloat)
(%i200) completearray(array_given_ord_poles,[2,3],convfloat)
(%i201) completearray(array_rad_test_poles,[2,4],convfloat)
(%i202) completearray(array_ord_test_poles,[2,4],convfloat)
(%i203) completearray(array_fact_2,[40,40],convfloat)
(%i204) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i205) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i206) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i207) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (if vallen = 4
then printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel)
else printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel))
(%i208) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i209) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i210) logitem_time(fd,secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],convfloat]),
secs:secs_in,printf(fd,"
~%"),
if secs >= 0
then (years_int
:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int
:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if truncate(years_int) > 0.1
then printf(fd,
"~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(fd,
"~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(fd,
"~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(fd,
"~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(fd,"~d Seconds~%",
sec_int))
else printf(fd," 0.0 Seconds~%"),
printf(fd," | ~%")),0)
(%i211) omniout_timestr(secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],
convfloat]),secs:secs_in,
if secs >= 0
then (
years_int:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if years_int > 0
then printf(true,
"= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(true,
"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(true,
"= ~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(true,
"= ~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(true,"= ~d Seconds~%",
sec_int))
else printf(true,"= 0.0 Seconds~%")),0)
(%i212) zero_ats_ar(arr_a):=(
block(mode_declare([iii],fixnum),iii:1,
while iii <= ats_max_terms do
(arr_a[iii]:glob__0,iii:1+iii)),0)
(%i213) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:glob__0,
if jjj_ats <= mmm_ats
then (ma_ats:1+mmm_ats,iii_ats:jjj_ats,
while iii_ats <= mmm_ats do
(lll_ats:ma_ats-iii_ats,
if lll_ats <= ats_max_terms
and iii_ats <= ats_max_terms
then ret_ats
:c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i214) att(mmm_att,arr_aa,arr_bb,jjj_att):=block(
mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att],
fixnum]),ret_att:glob__0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= ats_max_terms do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= ats_max_terms
and iii_att <= ats_max_terms
then ret_att
:c(arr_aa[iii_att])*c(arr_bb[lll_att])
*c(al_att)
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/c(mmm_att)),ret_att)
(%i215) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i216) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i217) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i218) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i219) log_revs(file,revs):=printf(file,revs)
(%i220) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i221) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
elseif glob_h_reason = 7
then printf(file,"Opt Iter")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i222) logstart(file):=(printf(file,""),0)
(%i223) logend(file):=(printf(file,"
~%"),0)
(%i224) chk_data():=(
block(mode_declare([[errflag],boolean]),errflag:false,
if glob_max_iter < 2
then (omniout_str(always,"Illegal max_iter"),
errflag:true),if errflag then quit()),0)
(%i225) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:c(clock_sec2),
sub1:c(t_end2-t_start2),sub2:c(t2-t_start2),
if sub1 = glob__0 then sec_left:glob__0
else (if sub2 > glob__0
then (rrr:sub1/sub2,
sec_left:rrr*c(ms2)-c(ms2))
else sec_left:glob__0),sec_left)
(%i226) comp_percent(t_end2,t_start2,t2):=block(
mode_declare([[rrr,sub1,sub2],convfloat]),
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub2 > glob_small_float then rrr:glob__100*sub2/sub1
else rrr:0.0,rrr)
(%i227) comp_rad_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i228) comp_ord_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret
:abs(term2)*c(last_no)
*log(abs(term1*glob_h/term2))
/log(c(last_no))
+glob__1 else ret:glob_larger_float,ret)
(%i229) c(in_val):=(ret:in_val,ret)
(%i230) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3-term1*term3*c(last_no)
+glob__m2*term2*term2
+term2*term2*c(last_no)),
if abs(temp) > glob__0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i231) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*c(last_no*last_no)
+term2*term2*c(last_no*last_no)
+glob__4*term2*term2
-glob__4*term2*term2*c(last_no)
-glob__3*term1*term3
+glob__4*term1*term3*c(last_no))
/(term1*term3-term1*term3*c(last_no)
-glob__2*term2*term2
+term2*term2*c(last_no))),
ret)
(%i232) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # glob__0 and term4 # glob__0
and term3 # glob__0
and term2 # glob__0
and term1 # glob__0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:c(last_no-3)*rm2
-glob__2*c(last_no-2)*rm1
+c(last_no-1)*rm0,
nr2
:c(last_no-4)*rm3
-glob__2*c(last_no-3)*rm2
+c(last_no-2)*rm1,
dr1
:(-glob__1)/rm3+glob__2/rm2
+glob__m1/rm1,
dr2
:(-glob__1)/rm4+glob__2/rm3
+glob__m1/rm2,
ds1
:glob__5/rm3-glob__8/rm2
+glob__3/rm1,
ds2
:glob__5/rm4-glob__8/rm3
+glob__3/rm2,
if
abs(nr1*dr2-nr2*dr1) = glob__0
or abs(dr1) = glob__0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) > glob__0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(glob__2*dr1)
-c(last_no)/glob__2,
if abs(rcs) # glob__0
then (if rcs > glob__0
then rad_c
:sqrt(rcs)
*abs(glob_h)
else (
rad_c
:glob_larger_float,
ord_no
:glob_larger_float))
else (
rad_c:glob_larger_float,
ord_no:glob_larger_float))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float)))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float),
glob_six_term_ord_save:ord_no,rad_c)
(%i233) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i234) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i235) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms
then (if array_fact_1[nnn] = 0
then (ret:factorial_2(nnn),
array_fact_1[nnn]:ret)
else ret:array_fact_1[nnn])
else ret:factorial_2(nnn),ret)
(%i236) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i237) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i238) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms and mmm <= ats_max_terms
then (if array_fact_2[mmm,nnn] = 0
then (ret:factorial_1(mmm)/factorial_1(nnn),
array_fact_2[mmm,nnn]:ret)
else ret:array_fact_2[mmm,nnn])
else ret:factorial_2(mmm)/factorial_2(nnn),ret)
(%i239) log10(x):=log(x)/glob_log_10
(%i240) c(x):=x
(%i241) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y) else x^y
(%i242) estimated_needed_step_error(x_start,x_end,estimated_h,
estimated_answer):=block(
[desired_abs_gbl_error,range,
estimated_steps,step_error],
omniout_float(always,
"glob_desired_digits_correct",
32,
glob_desired_digits_correct,
32,""),
desired_abs_gbl_error
:expt(glob__10,
c(-glob_desired_digits_correct))
*c(abs(c(estimated_answer))),
omniout_float(always,"estimated_h",32,
estimated_h,32,""),
omniout_float(always,"estimated_answer",
32,estimated_answer,32,""),
omniout_float(always,
"desired_abs_gbl_error",32,
desired_abs_gbl_error,32,
""),range:x_end-x_start,
omniout_float(always,"range",32,range,32,
""),
estimated_steps:range/estimated_h,
omniout_float(always,"estimated_steps",32,
estimated_steps,32,""),
step_error
:c(
abs(desired_abs_gbl_error)
/sqrt(c(estimated_steps))
/c(ats_max_terms)),
omniout_float(always,"step_error",32,
step_error,32,""),
step_error)
(%i243) exact_soln_y(x):=block(
(-cos(c(0.1)+c(0.3)*c(x)))/c(0.3)
+c(0.2)*c(x)+c(0.05)*c(x)*c(x))
- cos(c(0.1) + c(0.3) c(x))
(%o243) exact_soln_y(x) := block(--------------------------- + c(0.2) c(x)
c(0.3)
+ c(0.05) c(x) c(x))
(%i244) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
omniout_float(always,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(always,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(always,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(always,
"SOME POLE (given) for Equation 1")
else omniout_str(always,
"NO info (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(always,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(always,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(always,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > glob__small
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(always,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(always,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > glob__small
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(always,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(always,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%i245) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i246) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(always,"min_size",32,min_size,
32,"")),
if min_size < glob__1
then (min_size:glob__1,
omniout_float(always,"min_size",32,min_size,
32,"")),min_size)
(%i247) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:glob__small,
no_terms:ats_max_terms,hn_div_ho:glob__0_5,
hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125,
omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(always,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i248) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:ats_max_terms,
hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25,
hn_div_ho_3:glob__0_125,
est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3)
+c(abs(array_y[no_terms-1]))
*c(hn_div_ho_2)
+c(abs(array_y[no_terms-2]))
*c(hn_div_ho)
+c(abs(array_y[no_terms-3])),
if glob_prec*c(abs(array_y[1])) > c(est_tmp)
then est_tmp
:c(glob_prec)*c(abs(array_y[1])),
if c(est_tmp) >= c(array_max_est_error[1])
then array_max_est_error[1]:c(est_tmp))
(%i249) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
-glob_h/glob__10 then ret:true else ret:false,
return(ret))
(%i250) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(29)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i251) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
clock_sec1:elapsed_time_seconds(),
total_clock_sec:clock_sec1-glob_orig_start_sec,
glob_clock_sec:clock_sec1-glob_clock_start_sec,
left_sec:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
clock_sec1
-glob_orig_start_sec),
opt_clock_sec:clock_sec1
-glob_optimal_clock_start_sec,
glob_optimal_expect_sec
:comp_expect_sec(x_end,x_start,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:c(total_clock_sec)+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
glob_percent_done:percent_done,
omniout_str_noeol(info,
"Total Elapsed Time "),
omniout_timestr(total_clock_sec),
omniout_str_noeol(info,
"Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec),
if c(percent_done) < glob__100
then (omniout_str_noeol(info,
"Expected Time Remaining "),
omniout_timestr(expect_sec),
omniout_str_noeol(info,
"Optimized Time Remaining "),
omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(info,
"Expected Total Time "),
omniout_timestr(glob_total_exp_sec)),
omniout_str_noeol(info,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(info,
"Percent Done ",33,
percent_done,4,"%")),0)
(%i252) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i253) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D3[1]*array_x[1],
array_tmp2[1]:array_const_0D1[1]+array_tmp1[1],
array_tmp3[1]:sin(array_tmp2[1]),
array_tmp3_g[1]:cos(array_tmp2[1]),
array_tmp4[1]:array_tmp3[1]+array_const_0D0[1],
array_tmp5[1]:array_const_0D1[1]*array_x[1],
array_tmp6[1]:array_const_0D2[1]+array_tmp5[1],
array_tmp7[1]:array_tmp6[1]+array_tmp4[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp7[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_const_0D3[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:array_tmp3_g[1]*array_tmp2[2]/c(1),
array_tmp3_g[2]:neg(array_tmp3[1])*array_tmp2[2]/c(1),
array_tmp4[2]:array_tmp3[2],
array_tmp5[2]:array_const_0D1[1]*array_x[2],
array_tmp6[2]:array_tmp5[2],
array_tmp7[2]:array_tmp6[2]+array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp7[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp3[3]:array_tmp3_g[2]*array_tmp2[2]/c(2),
array_tmp3_g[3]:neg(array_tmp3[2])*array_tmp2[2]/c(2),
array_tmp4[3]:array_tmp3[3],array_tmp7[3]:array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp7[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp3[4]:array_tmp3_g[3]*array_tmp2[2]/c(3),
array_tmp3_g[4]:neg(array_tmp3[3])*array_tmp2[2]/c(3),
array_tmp4[4]:array_tmp3[4],array_tmp7[4]:array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp7[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp3[5]:array_tmp3_g[4]*array_tmp2[2]/c(4),
array_tmp3_g[5]:neg(array_tmp3[4])*array_tmp2[2]/c(4),
array_tmp4[5]:array_tmp3[5],array_tmp7[5]:array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp7[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp3[kkk]
:array_tmp3_g[kkk-1]*array_tmp2[2]/c(kkk-1),
array_tmp3_g[kkk]
:neg(array_tmp3[kkk-1])*array_tmp2[2]/c(kkk-1),
array_tmp4[kkk]:array_tmp3[kkk],
array_tmp7[kkk]:array_tmp4[kkk],order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp7[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i254) exact_soln_y(x):=block(
(-cos(c(0.1)+c(0.3)*c(x)))/c(0.3)
+c(0.2)*c(x)+c(0.05)*c(x)*c(x))
- cos(c(0.1) + c(0.3) c(x))
(%o254) exact_soln_y(x) := block(--------------------------- + c(0.2) c(x)
c(0.3)
+ c(0.05) c(x) c(x))
(%i255) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp6[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp7[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3_g),
zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4),
zero_ats_ar(array_tmp5),zero_ats_ar(array_tmp6),
zero_ats_ar(array_tmp7),zero_ats_ar(array_m1),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_0D3),array_const_0D3[1]:c(0.3),
zero_ats_ar(array_const_0D1),array_const_0D1[1]:c(0.1),
zero_ats_ar(array_const_0D2),array_const_0D2[1]:c(0.2),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/add_full_linpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(1.0),"),
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_display_interval:c(0.1),"),
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,""),omniout_str(always,""),
omniout_str(always,
" (c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)) "),
omniout_str(always,""),omniout_str(always,"));"),
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_display_interval:c(0.1),glob_look_poles:true,
glob_type_given_pole:3,glob_desired_digits_correct:8,
glob_max_minutes:3.0,glob_subiter_method:3,
glob_max_iter:100000,glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:09:47-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"add_full_lin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"add_full_lin diffeq.max"),
logitem_str(html_log_file,
"add_full_lin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i256) main():=(glob_iolevel:2,compile(all),main_prog())
(%i257) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_const_0D3 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D1 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp3_g in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp6 in translation.
warning: encountered undefined variable array_tmp7 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
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: 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/add_full_linpostode.ode#################"
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(1.0),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_display_interval:c(0.1),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
""
""
" (c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)) "
""
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1. " "
y[1] (closed_form) = -2.8202033133429505 " "
y[1] (numeric) = -2.8202033133429505 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.009999999999999 " "
y[1] (closed_form) = -2.8132903198565886 " "
y[1] (numeric) = -2.813290319856588 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 1.57854028329611100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999978 " "
y[1] (closed_form) = -2.8063397297330464 " "
y[1] (numeric) = -2.8063397297330455 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 3.16489985260841300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999967 " "
y[1] (closed_form) = -2.7993515783926073 " "
y[1] (numeric) = -2.799351578392605 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 7.93200134770244500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999956 " "
y[1] (closed_form) = -2.7923259015036064 " "
y[1] (numeric) = -2.7923259015036037 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 9.54235054606477600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999945 " "
y[1] (closed_form) = -2.7852627349821097 " "
y[1] (numeric) = -2.7852627349821066 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.11609738999017810000000000000E-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) = -2.7781621149915883 " "
y[1] (numeric) = -2.7781621149915834 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 1.75834998324620070000000000000E-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) = -2.7710240779425943 " "
y[1] (numeric) = -2.771024077942589 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 1.92314118113236800000000000000E-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) = -2.763848660492435 " "
y[1] (numeric) = -2.763848660492428 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 2.4101674751482552000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.08999999999999 " "
y[1] (closed_form) = -2.756635899544838 " "
y[1] (numeric) = -2.7566358995448303 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 2.73867019169909350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.099999999999989 " "
y[1] (closed_form) = -2.7493858322496254 " "
y[1] (numeric) = -2.749385832249617 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 3.0689381199899574000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999879 " "
y[1] (closed_form) = -2.7420984960023738 " "
y[1] (numeric) = -2.742098496002365 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 3.23904637632446500000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999868 " "
y[1] (closed_form) = -2.734773928444082 " "
y[1] (numeric) = -2.734773928444072 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.7348797720777620000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999857 " "
y[1] (closed_form) = -2.727412167460829 " "
y[1] (numeric) = -2.7274121674608187 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 3.74496086378485860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999846 " "
y[1] (closed_form) = -2.7200132511834356 " "
y[1] (numeric) = -2.7200132511834245 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 4.0816824114445610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999835 " "
y[1] (closed_form) = -2.71257721798712 " "
y[1] (numeric) = -2.7125772179871075 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 4.5840161870226230000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999824 " "
y[1] (closed_form) = -2.7051041064911496 " "
y[1] (numeric) = -2.7051041064911363 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 4.9250142586131435000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999813 " "
y[1] (closed_form) = -2.697593955558502 " "
y[1] (numeric) = -2.697593955558487 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 5.5972223335502210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999802 " "
y[1] (closed_form) = -2.690046804295504 " "
y[1] (numeric) = -2.690046804295488 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 5.9430979152755450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999979 " "
y[1] (closed_form) = -2.682462692051488 " "
y[1] (numeric) = -2.6824626920514714 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 6.1254536039366210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.199999999999978 " "
y[1] (closed_form) = -2.6748416584184342 " "
y[1] (numeric) = -2.6748416584184174 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 6.3089304449820660000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999769 " "
y[1] (closed_form) = -2.6671837432306162 " "
y[1] (numeric) = -2.667183743230599 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 6.4935455714701860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999758 " "
y[1] (closed_form) = -2.6594889865642406 " "
y[1] (numeric) = -2.659488986564222 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 7.0132822162195070000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999747 " "
y[1] (closed_form) = -2.6517574287370866 " "
y[1] (numeric) = -2.6517574287370675 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 7.2012001613010220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999736 " "
y[1] (closed_form) = -2.6439891103081443 " "
y[1] (numeric) = -2.643989110308125 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 7.390319860706790000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999725 " "
y[1] (closed_form) = -2.6361840720772487 " "
y[1] (numeric) = -2.6361840720772283 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 7.7491188378989150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999714 " "
y[1] (closed_form) = -2.6283423550847145 " "
y[1] (numeric) = -2.628342355084693 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 8.1101619169074950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999703 " "
y[1] (closed_form) = -2.6204640006109616 " "
y[1] (numeric) = -2.6204640006109403 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 8.1345449003814240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999692 " "
y[1] (closed_form) = -2.612549050176151 " "
y[1] (numeric) = -2.6125490501761295 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 8.1591892299077630000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999968 " "
y[1] (closed_form) = -2.604597545539804 " "
y[1] (numeric) = -2.6045975455397814 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 8.6956043328602880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.299999999999967 " "
y[1] (closed_form) = -2.5966095287004314 " "
y[1] (numeric) = -2.596609528700408 " "
absolute error = 2.35367281220533200000000000000E-14 " "
relative error = 9.0644079758242050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999659 " "
y[1] (closed_form) = -2.5885850418951533 " "
y[1] (numeric) = -2.588585041895129 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 9.4356206755608460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999648 " "
y[1] (closed_form) = -2.5805241275993183 " "
y[1] (numeric) = -2.5805241275992934 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 9.637187843207390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999637 " "
y[1] (closed_form) = -2.5724268285261234 " "
y[1] (numeric) = -2.572426828526098 " "
absolute error = 2.53130849614535700000000000000E-14 " "
relative error = 9.8401574267349510000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999626 " "
y[1] (closed_form) = -2.564293187626229 " "
y[1] (numeric) = -2.5642931876262023 " "
absolute error = 2.664535259100375700000000000000E-14 " "
relative error = 1.0390915016885964000000000000E-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) = -2.5561232480873692 " "
y[1] (numeric) = -2.5561232480873413 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.0945333031765321000000000000E-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) = -2.5479170533339683 " "
y[1] (numeric) = -2.5479170533339395 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 1.1329175179577748000000000000E-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) = -2.539674647026746 " "
y[1] (numeric) = -2.5396746470267164 " "
absolute error = 2.975397705995419500000000000000E-14 " "
relative error = 1.171566487651788100000000000E-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) = -2.5313960730623264 " "
y[1] (numeric) = -2.5313960730622957 " "
absolute error = 3.06421554796543200000000000000E-14 " "
relative error = 1.2104844360679337000000000000E-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) = -2.5230813755728416 " "
y[1] (numeric) = -2.5230813755728096 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 1.2672767283197522000000000000E-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) = -2.5147305989255364 " "
y[1] (numeric) = -2.5147305989255035 " "
absolute error = 3.286260152890463400000000000000E-14 " "
relative error = 1.3068040585717516000000000000E-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) = -2.506343787722367 " "
y[1] (numeric) = -2.506343787722333 " "
absolute error = 3.41948691584548200000000000000E-14 " "
relative error = 1.3643327513951830000000000000E-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) = -2.4979209867996 " "
y[1] (numeric) = -2.497920986799565 " "
absolute error = 3.508304757815494700000000000000E-14 " "
relative error = 1.4044898843299378000000000000E-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) = -2.48946224122741 " "
y[1] (numeric) = -2.4894622412273746 " "
absolute error = 3.55271367880050100000000000000E-14 " "
relative error = 1.4271008493179085000000000000E-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) = -2.4809675963094744 " "
y[1] (numeric) = -2.480967596309437 " "
absolute error = 3.73034936274052600000000000000E-14 " "
relative error = 1.503586491129328000000000000E-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) = -2.4724370975825614 " "
y[1] (numeric) = -2.4724370975825236 " "
absolute error = 3.77475828372553200000000000000E-14 " "
relative error = 1.5267358216782630000000000000E-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) = -2.4638707908161264 " "
y[1] (numeric) = -2.463870790816088 " "
absolute error = 3.819167204710538500000000000000E-14 " "
relative error = 1.5500679739157455000000000000E-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) = -2.455268722011896 " "
y[1] (numeric) = -2.455268722011856 " "
absolute error = 3.996802888650563500000000000000E-14 " "
relative error = 1.6278474338953433000000000000E-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) = -2.4466309374034543 " "
y[1] (numeric) = -2.446630937403413 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 1.6880476693344992000000000000E-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) = -2.437957483455828 " "
y[1] (numeric) = -2.4379574834557856 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.7487000669582614000000000000E-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) = -2.4292484068650673 " "
y[1] (numeric) = -2.4292484068650246 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.7549693158232063000000000000E-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) = -2.4205037545578265 " "
y[1] (numeric) = -2.420503754557783 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 1.7980035140766154000000000000E-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) = -2.4117235736909417 " "
y[1] (numeric) = -2.411723573690897 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 1.8597906776775636000000000000E-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) = -2.4029079116510044 " "
y[1] (numeric) = -2.4029079116509586 " "
absolute error = 4.57411886145564500000000000000E-14 " "
relative error = 1.9035764289081025000000000000E-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) = -2.394056816053937 " "
y[1] (numeric) = -2.39405681605389 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 1.947713467849713800000000000E-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) = -2.3851703347445645 " "
y[1] (numeric) = -2.3851703347445175 " "
absolute error = 4.70734562441066400000000000000E-14 " "
relative error = 1.973588869456901200000000000E-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) = -2.376248515796183 " "
y[1] (numeric) = -2.376248515796135 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 2.0183762070751593000000000000E-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) = -2.367291407510126 " "
y[1] (numeric) = -2.3672914075100775 " "
absolute error = 4.840572387365682500000000000000E-14 " "
relative error = 2.0447725075202755000000000000E-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) = -2.3582990584153327 " "
y[1] (numeric) = -2.3582990584152825 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 2.1278930055112305000000000000E-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) = -2.349271517267907 " "
y[1] (numeric) = -2.3492715172678555 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 2.1927796750592726000000000000E-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) = -2.340208833050683 " "
y[1] (numeric) = -2.3402088330506308 " "
absolute error = 5.24025267623073900000000000000E-14 " "
relative error = 2.2392243812701002000000000E-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) = -2.3311110549727823 " "
y[1] (numeric) = -2.3311110549727294 " "
absolute error = 5.28466159721574500000000000000E-14 " "
relative error = 2.2670140858121612000000000000E-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) = -2.3219782324691707 " "
y[1] (numeric) = -2.3219782324691165 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 2.333307127694056700000000000E-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) = -2.312810415200212 " "
y[1] (numeric) = -2.3128104152001567 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 2.3809587530174110000000000000E-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) = -2.303607653051226 " "
y[1] (numeric) = -2.3036076530511695 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 2.4483044921410405000000000000E-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) = -2.2943699961320334 " "
y[1] (numeric) = -2.2943699961319757 " "
absolute error = 5.77315972805081400000000000000E-14 " "
relative error = 2.51622874156457000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6599999999999273 " "
y[1] (closed_form) = -2.2850974947765086 " "
y[1] (numeric) = -2.2850974947764504 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 2.5458732777634946000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999262 " "
y[1] (closed_form) = -2.2757901995421266 " "
y[1] (numeric) = -2.2757901995420675 " "
absolute error = 5.90638649100583300000000000000E-14 " "
relative error = 2.5953123852076340000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.679999999999925 " "
y[1] (closed_form) = -2.2664481612095058 " "
y[1] (numeric) = -2.2664481612094454 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 2.664792143641075000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.689999999999924 " "
y[1] (closed_form) = -2.257071430781954 " "
y[1] (numeric) = -2.257071430781892 " "
absolute error = 6.1728400169158700000000000000E-14 " "
relative error = 2.734889083584436400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.699999999999923 " "
y[1] (closed_form) = -2.2476600594850042 " "
y[1] (numeric) = -2.2476600594849416 " "
absolute error = 6.26165785888588300000000000000E-14 " "
relative error = 2.7858562652577396000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999218 " "
y[1] (closed_form) = -2.2382140987659627 " "
y[1] (numeric) = -2.2382140987658983 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 2.876978366982947000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999207 " "
y[1] (closed_form) = -2.2287336002934346 " "
y[1] (numeric) = -2.22873360029337 " "
absolute error = 6.43929354282590800000000000000E-14 " "
relative error = 2.8892163432983253000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999196 " "
y[1] (closed_form) = -2.219218615956869 " "
y[1] (numeric) = -2.219218615956803 " "
absolute error = 6.61692922676593300000000000000E-14 " "
relative error = 2.9816482158126120000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999185 " "
y[1] (closed_form) = -2.209669197866085 " "
y[1] (numeric) = -2.2096691978660177 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 3.0548264854484514000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7499999999999174 " "
y[1] (closed_form) = -2.2000853983508057 " "
y[1] (numeric) = -2.200085398350738 " "
absolute error = 6.79456491070595800000000000000E-14 " "
relative error = 3.0883187151731456000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7599999999999163 " "
y[1] (closed_form) = -2.1904672699601884 " "
y[1] (numeric) = -2.190467269960119 " "
absolute error = 6.92779167366097700000000000000E-14 " "
relative error = 3.1627003830040745000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999152 " "
y[1] (closed_form) = -2.1808148654623487 " "
y[1] (numeric) = -2.180814865462278 " "
absolute error = 7.06101843661599600000000000000E-14 " "
relative error = 3.2377890248464575000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.779999999999914 " "
y[1] (closed_form) = -2.171128237843887 " "
y[1] (numeric) = -2.171128237843815 " "
absolute error = 7.23865412055602100000000000000E-14 " "
relative error = 3.334051851190795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.789999999999913 " "
y[1] (closed_form) = -2.161407440309412 " "
y[1] (numeric) = -2.161407440309339 " "
absolute error = 7.32747196252603300000000000000E-14 " "
relative error = 3.390139140761486000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.799999999999912 " "
y[1] (closed_form) = -2.1516525262810617 " "
y[1] (numeric) = -2.151652526280987 " "
absolute error = 7.46069872548105200000000000000E-14 " "
relative error = 3.4674273073153683000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999108 " "
y[1] (closed_form) = -2.141863549398022 " "
y[1] (numeric) = -2.1418635493979465 " "
absolute error = 7.54951656745106400000000000000E-14 " "
relative error = 3.5247420731226700000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999097 " "
y[1] (closed_form) = -2.1320405635160444 " "
y[1] (numeric) = -2.1320405635159676 " "
absolute error = 7.68274333040608300000000000000E-14 " "
relative error = 3.6034695877155937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999086 " "
y[1] (closed_form) = -2.1221836227069617 " "
y[1] (numeric) = -2.122183622706883 " "
absolute error = 7.86037901434610800000000000000E-14 " "
relative error = 3.703910882282544000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999075 " "
y[1] (closed_form) = -2.1122927812582 " "
y[1] (numeric) = -2.1122927812581196 " "
absolute error = 8.03801469828613300000000000000E-14 " "
relative error = 3.805350645329688700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8499999999999064 " "
y[1] (closed_form) = -2.102368093672291 " "
y[1] (numeric) = -2.1023680936722102 " "
absolute error = 8.0824236192711400000000000000E-14 " "
relative error = 3.84443791912445000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8599999999999053 " "
y[1] (closed_form) = -2.092409614666384 " "
y[1] (numeric) = -2.092409614666302 " "
absolute error = 8.21565038222615800000000000000E-14 " "
relative error = 3.92640634254401000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999042 " "
y[1] (closed_form) = -2.082417399171746 " "
y[1] (numeric) = -2.082417399171663 " "
absolute error = 8.30446822419617100000000000000E-14 " "
relative error = 3.987898020588554000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.879999999999903 " "
y[1] (closed_form) = -2.072391502333277 " "
y[1] (numeric) = -2.0723915023331925 " "
absolute error = 8.4376949871511900000000000000E-14 " "
relative error = 4.071477313843116500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.889999999999902 " "
y[1] (closed_form) = -2.0623319795090067 " "
y[1] (numeric) = -2.0623319795089214 " "
absolute error = 8.52651282912120200000000000000E-14 " "
relative error = 4.13440363328466950000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999009 " "
y[1] (closed_form) = -2.052238886269598 " "
y[1] (numeric) = -2.052238886269512 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 4.198015508200168600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999998998 " "
y[1] (closed_form) = -2.0421122783978496 " "
y[1] (numeric) = -2.0421122783977617 " "
absolute error = 8.7929663550312400000000000000E-14 " "
relative error = 4.305819248062996000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998987 " "
y[1] (closed_form) = -2.0319522118881888 " "
y[1] (numeric) = -2.0319522118881004 " "
absolute error = 8.83737527601624600000000000000E-14 " "
relative error = 4.349204289506458000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998976 " "
y[1] (closed_form) = -2.0217587429461736 " "
y[1] (numeric) = -2.0217587429460826 " "
absolute error = 9.10382880192628400000000000000E-14 " "
relative error = 4.5029254027905846000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998965 " "
y[1] (closed_form) = -2.0115319279879813 " "
y[1] (numeric) = -2.011531927987889 " "
absolute error = 9.23705556488130200000000000000E-14 " "
relative error = 4.592050186407229000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9499999999998954 " "
y[1] (closed_form) = -2.001271823639904 " "
y[1] (numeric) = -2.001271823639811 " "
absolute error = 9.28146448586630900000000000000E-14 " "
relative error = 4.6377830218911614000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9599999999998943 " "
y[1] (closed_form) = -1.990978486737838 " "
y[1] (numeric) = -1.990978486737744 " "
absolute error = 9.39248678832882400000000000000E-14 " "
relative error = 4.717522992284135000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998932 " "
y[1] (closed_form) = -1.9806519743267739 " "
y[1] (numeric) = -1.980651974326678 " "
absolute error = 9.59232693276135300000000000000E-14 " "
relative error = 4.843014854248585000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.979999999999892 " "
y[1] (closed_form) = -1.9702923436602782 " "
y[1] (numeric) = -1.970292343660182 " "
absolute error = 9.61453139325385600000000000000E-14 " "
relative error = 4.879748644504509000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.989999999999891 " "
y[1] (closed_form) = -1.9598996521999865 " "
y[1] (numeric) = -1.9598996521998888 " "
absolute error = 9.76996261670137800000000000000E-14 " "
relative error = 4.984930022174655000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998899 " "
y[1] (closed_form) = -1.949473957615077 " "
y[1] (numeric) = -1.9494739576149775 " "
absolute error = 9.94759830064140300000000000000E-14 " "
relative error = 5.102708995821094000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998888 " "
y[1] (closed_form) = -1.9390153177817573 " "
y[1] (numeric) = -1.9390153177816574 " "
absolute error = 9.99200722162640900000000000000E-14 " "
relative error = 5.153134753498138000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998877 " "
y[1] (closed_form) = -1.9285237907827435 " "
y[1] (numeric) = -1.9285237907826422 " "
absolute error = 1.01252339845814280000000000000E-13 " "
relative error = 5.2502510121857660000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998866 " "
y[1] (closed_form) = -1.9179994349067342 " "
y[1] (numeric) = -1.9179994349066318 " "
absolute error = 1.02362562870439430000000000000E-13 " "
relative error = 5.336944370654467000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998855 " "
y[1] (closed_form) = -1.9074423086478889 " "
y[1] (numeric) = -1.907442308647785 " "
absolute error = 1.03916875104914650000000000000E-13 " "
relative error = 5.447969494740696000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998844 " "
y[1] (closed_form) = -1.8968524707052992 " "
y[1] (numeric) = -1.896852470705194 " "
absolute error = 1.05249142734464840000000000000E-13 " "
relative error = 5.548620378227437000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0599999999998833 " "
y[1] (closed_form) = -1.8862299799824627 " "
y[1] (numeric) = -1.8862299799823565 " "
absolute error = 1.06137321154164970000000000000E-13 " "
relative error = 5.626955476296256000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999882 " "
y[1] (closed_form) = -1.8755748955867517 " "
y[1] (numeric) = -1.8755748955866445 " "
absolute error = 1.07247544178790120000000000000E-13 " "
relative error = 5.718115785786255000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999881 " "
y[1] (closed_form) = -1.8648872768288811 " "
y[1] (numeric) = -1.8648872768287728 " "
absolute error = 1.08357767203415280000000000000E-13 " "
relative error = 5.810419136306757000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.08999999999988 " "
y[1] (closed_form) = -1.8541671832223754 " "
y[1] (numeric) = -1.8541671832222657 " "
absolute error = 1.09690034832965470000000000000E-13 " "
relative error = 5.915865399059327000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999879 " "
y[1] (closed_form) = -1.8434146744830324 " "
y[1] (numeric) = -1.8434146744829212 " "
absolute error = 1.11244347067440690000000000000E-13 " "
relative error = 6.034689243137228000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998778 " "
y[1] (closed_form) = -1.8326298105283847 " "
y[1] (numeric) = -1.8326298105282728 " "
absolute error = 1.11910480882215780000000000000E-13 " "
relative error = 6.1065513743853000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998766 " "
y[1] (closed_form) = -1.8218126514771638 " "
y[1] (numeric) = -1.821812651477051 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 6.1915619704614730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998755 " "
y[1] (closed_form) = -1.8109632576487562 " "
y[1] (numeric) = -1.8109632576486416 " "
absolute error = 1.14575016141316150000000000000E-13 " "
relative error = 6.326744380781825000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998744 " "
y[1] (closed_form) = -1.80008168956266 " "
y[1] (numeric) = -1.8000816895625444 " "
absolute error = 1.15463194561016280000000000000E-13 " "
relative error = 6.41433081790131000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998733 " "
y[1] (closed_form) = -1.7891680079379433 " "
y[1] (numeric) = -1.7891680079378263 " "
absolute error = 1.1701750679549150000000000000E-13 " "
relative error = 6.540330828425489000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1599999999998722 " "
y[1] (closed_form) = -1.7782222736926943 " "
y[1] (numeric) = -1.7782222736925761 " "
absolute error = 1.18127729820116660000000000000E-13 " "
relative error = 6.64302385408828000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999871 " "
y[1] (closed_form) = -1.7672445479434757 " "
y[1] (numeric) = -1.7672445479433565 " "
absolute error = 1.1923795284474181000000000000E-13 " "
relative error = 6.747111087907884000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.17999999999987 " "
y[1] (closed_form) = -1.756234892004773 " "
y[1] (numeric) = -1.7562348920046529 " "
absolute error = 1.20126131264441940000000000000E-13 " "
relative error = 6.839980905248719000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999869 " "
y[1] (closed_form) = -1.745193367388444 " "
y[1] (numeric) = -1.7451933673883229 " "
absolute error = 1.2123635428906710000000000000E-13 " "
relative error = 6.946872281006232000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999868 " "
y[1] (closed_form) = -1.7341200358031639 " "
y[1] (numeric) = -1.7341200358030415 " "
absolute error = 1.22346577313692250000000000000E-13 " "
relative error = 7.055254237751022000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998667 " "
y[1] (closed_form) = -1.7230149591538706 " "
y[1] (numeric) = -1.7230149591537467 " "
absolute error = 1.23900889548167470000000000000E-13 " "
relative error = 7.190935220261354000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998656 " "
y[1] (closed_form) = -1.7118781995412071 " "
y[1] (numeric) = -1.7118781995410817 " "
absolute error = 1.2545520178264270000000000000E-13 " "
relative error = 7.32851214626515900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998645 " "
y[1] (closed_form) = -1.7007098192609629 " "
y[1] (numeric) = -1.700709819260836 " "
absolute error = 1.26787469412192880000000000000E-13 " "
relative error = 7.454973680771002000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998634 " "
y[1] (closed_form) = -1.6895098808035138 " "
y[1] (numeric) = -1.6895098808033862 " "
absolute error = 1.276756478318930000000000000E-13 " "
relative error = 7.556963666360551000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2499999999998623 " "
y[1] (closed_form) = -1.6782784468532599 " "
y[1] (numeric) = -1.6782784468531304 " "
absolute error = 1.29452004671293250000000000000E-13 " "
relative error = 7.713380632040725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2599999999998612 " "
y[1] (closed_form) = -1.6670155802880584 " "
y[1] (numeric) = -1.6670155802879276 " "
absolute error = 1.30784272300843440000000000000E-13 " "
relative error = 7.84541391498237000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.26999999999986 " "
y[1] (closed_form) = -1.655721344178661 " "
y[1] (numeric) = -1.6557213441785295 " "
absolute error = 1.31450406115618530000000000000E-13 " "
relative error = 7.939162382473602000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999859 " "
y[1] (closed_form) = -1.6443958017881464 " "
y[1] (numeric) = -1.6443958017880134 " "
absolute error = 1.33004718350093750000000000000E-13 " "
relative error = 8.08836401828939000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999858 " "
y[1] (closed_form) = -1.6330390165713475 " "
y[1] (numeric) = -1.6330390165712134 " "
absolute error = 1.3411494137471890000000000000E-13 " "
relative error = 8.2125987201641000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999857 " "
y[1] (closed_form) = -1.6216510521742842 " "
y[1] (numeric) = -1.6216510521741487 " "
absolute error = 1.3544720900426910000000000000E-13 " "
relative error = 8.352426301741279000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998557 " "
y[1] (closed_form) = -1.6102319724335876 " "
y[1] (numeric) = -1.6102319724334506 " "
absolute error = 1.37001521238744320000000000000E-13 " "
relative error = 8.508185378513518000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998546 " "
y[1] (closed_form) = -1.5987818413759276 " "
y[1] (numeric) = -1.5987818413757895 " "
absolute error = 1.38111744263369470000000000000E-13 " "
relative error = 8.63856097743198900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998535 " "
y[1] (closed_form) = -1.5873007232174352 " "
y[1] (numeric) = -1.5873007232172962 " "
absolute error = 1.3899992268306960000000000000E-13 " "
relative error = 8.756999896107829000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998524 " "
y[1] (closed_form) = -1.5757886823631262 " "
y[1] (numeric) = -1.5757886823629859 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 8.905520891428862000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3499999999998513 " "
y[1] (closed_form) = -1.5642457834063195 " "
y[1] (numeric) = -1.5642457834061776 " "
absolute error = 1.418865025470950000000000000E-13 " "
relative error = 9.070601567365029000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.35999999999985 " "
y[1] (closed_form) = -1.5526720911280574 " "
y[1] (numeric) = -1.5526720911279142 " "
absolute error = 1.4321877017664520000000000000E-13 " "
relative error = 9.224019095531818000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.369999999999849 " "
y[1] (closed_form) = -1.5410676704965212 " "
y[1] (numeric) = -1.5410676704963768 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 9.365519500825592000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999848 " "
y[1] (closed_form) = -1.5294325866664482 " "
y[1] (numeric) = -1.5294325866663023 " "
absolute error = 1.45883305435745570000000000000E-13 " "
relative error = 9.538393957834577000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999847 " "
y[1] (closed_form) = -1.517766904978543 " "
y[1] (numeric) = -1.5177669049783962 " "
absolute error = 1.4677148385544570000000000000E-13 " "
relative error = 9.670225604077238000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999846 " "
y[1] (closed_form) = -1.5060706909588926 " "
y[1] (numeric) = -1.5060706909587445 " "
absolute error = 1.48103751484995880000000000000E-13 " "
relative error = 9.833784853133318000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998447 " "
y[1] (closed_form) = -1.4943440103183736 " "
y[1] (numeric) = -1.4943440103182242 " "
absolute error = 1.49436019114546070000000000000E-13 " "
relative error = 1.000010828046939300000000000E-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) = -1.4825869289520623 " "
y[1] (numeric) = -1.4825869289519116 " "
absolute error = 1.50768286744096260000000000000E-13 " "
relative error = 1.016927127845811100000000000E-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) = -1.4707995129386415 " "
y[1] (numeric) = -1.4707995129384897 " "
absolute error = 1.51878509768721410000000000000E-13 " "
relative error = 1.032625510361162700000000000E-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) = -1.4589818285398057 " "
y[1] (numeric) = -1.458981828539652 " "
absolute error = 1.53654866608121670000000000000E-13 " "
relative error = 1.053165047037660500000000000E-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) = -1.4471339421996643 " "
y[1] (numeric) = -1.4471339421995089 " "
absolute error = 1.55431223447521920000000000000E-13 " "
relative error = 1.074062454863468000000000000E-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) = -1.4352559205441442 " "
y[1] (numeric) = -1.435255920543988 " "
absolute error = 1.560973572622970000000000000E-13 " "
relative error = 1.087592498507975500000000000E-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) = -1.4233478303803913 " "
y[1] (numeric) = -1.4233478303802336 " "
absolute error = 1.57651669496772230000000000000E-13 " "
relative error = 1.107611689369278500000000000E-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) = -1.4114097386961655 " "
y[1] (numeric) = -1.411409738696007 " "
absolute error = 1.58539847916472350000000000000E-13 " "
relative error = 1.123273019661381700000000000E-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) = -1.3994417126592427 " "
y[1] (numeric) = -1.3994417126590826 " "
absolute error = 1.60094160150947570000000000000E-13 " "
relative error = 1.14398591025798400000000000E-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) = -1.387443819616806 " "
y[1] (numeric) = -1.3874438196166445 " "
absolute error = 1.61426427780497760000000000000E-13 " "
relative error = 1.163480823498004200000000000E-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) = -1.3754161270948424 " "
y[1] (numeric) = -1.3754161270946796 " "
absolute error = 1.62758695410047950000000000000E-13 " "
relative error = 1.183341479017170600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998326 " "
y[1] (closed_form) = -1.3633587027975338 " "
y[1] (numeric) = -1.36335870279737 " "
absolute error = 1.6386891843467310000000000000E-13 " "
relative error = 1.201950140476042700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998315 " "
y[1] (closed_form) = -1.351271614606648 " "
y[1] (numeric) = -1.351271614606483 " "
absolute error = 1.64979141459298260000000000000E-13 " "
relative error = 1.220917687280238800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998304 " "
y[1] (closed_form) = -1.3391549305809276 " "
y[1] (numeric) = -1.3391549305807608 " "
absolute error = 1.6675549829869850000000000000E-13 " "
relative error = 1.245229319555726800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999998293 " "
y[1] (closed_form) = -1.3270087189554776 " "
y[1] (numeric) = -1.3270087189553097 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 1.264993356301796200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999828 " "
y[1] (closed_form) = -1.3148330481411512 " "
y[1] (numeric) = -1.3148330481409825 " "
absolute error = 1.6875389974302380000000000000E-13 " "
relative error = 1.283462565696839600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999827 " "
y[1] (closed_form) = -1.302627986723935 " "
y[1] (numeric) = -1.3026279867237645 " "
absolute error = 1.70530256582424040000000000000E-13 " "
relative error = 1.309124771772344800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999826 " "
y[1] (closed_form) = -1.2903936034643295 " "
y[1] (numeric) = -1.2903936034641577 " "
absolute error = 1.71862524211974230000000000000E-13 " "
relative error = 1.33186125342355720000000000E-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) = -1.2781299672967326 " "
y[1] (numeric) = -1.2781299672965594 " "
absolute error = 1.73194791841524420000000000000E-13 " "
relative error = 1.355064009709704700000000000E-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) = -1.2658371473288181 " "
y[1] (numeric) = -1.265837147328643 " "
absolute error = 1.7519319328584970000000000000E-13 " "
relative error = 1.384010523435373000000000000E-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) = -1.2535152128409128 " "
y[1] (numeric) = -1.2535152128407365 " "
absolute error = 1.76303416310474860000000000000E-13 " "
relative error = 1.406472091478717700000000000E-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) = -1.241164233285376 " "
y[1] (numeric) = -1.2411642332851989 " "
absolute error = 1.77191594730174980000000000000E-13 " "
relative error = 1.427624080506628700000000000E-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) = -1.2287842782859717 " "
y[1] (numeric) = -1.228784278285793 " "
absolute error = 1.7874590696465020000000000000E-13 " "
relative error = 1.454656526155937200000000000E-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) = -1.2163754176372414 " "
y[1] (numeric) = -1.2163754176370618 " "
absolute error = 1.79634085384350330000000000000E-13 " "
relative error = 1.476798057406340000000000000E-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) = -1.20393772130388 " "
y[1] (numeric) = -1.2039377213036986 " "
absolute error = 1.81410442223750580000000000000E-13 " "
relative error = 1.506809189658753800000000000E-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) = -1.1914712594201007 " "
y[1] (numeric) = -1.1914712594199173 " "
absolute error = 1.83408843668075860000000000000E-13 " "
relative error = 1.53934761093056100000000000E-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) = -1.1789761022890077 " "
y[1] (numeric) = -1.1789761022888232 " "
absolute error = 1.84519066692701020000000000000E-13 " "
relative error = 1.565078938703280000000000000E-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) = -1.166452320381963 " "
y[1] (numeric) = -1.1664523203817774 " "
absolute error = 1.85629289717326170000000000000E-13 " "
relative error = 1.591400578264018000000000000E-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) = -1.1538999843379503 " "
y[1] (numeric) = -1.1538999843377633 " "
absolute error = 1.86961557346876360000000000000E-13 " "
relative error = 1.62025790696362220000000000E-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) = -1.1413191649629413 " "
y[1] (numeric) = -1.1413191649627532 " "
absolute error = 1.88071780371501520000000000000E-13 " "
relative error = 1.647845634639879500000000000E-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) = -1.1287099332292565 " "
y[1] (numeric) = -1.1287099332290675 " "
absolute error = 1.88959958791201640000000000000E-13 " "
relative error = 1.674123290920141700000000000E-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) = -1.116072360274929 " "
y[1] (numeric) = -1.1160723602747384 " "
absolute error = 1.90514271025676860000000000000E-13 " "
relative error = 1.707006443370269500000000000E-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) = -1.1034065174030614 " "
y[1] (numeric) = -1.1034065174028693 " "
absolute error = 1.92068583260152080000000000000E-13 " "
relative error = 1.74068740967923520000000000E-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) = -1.090712476081186 " "
y[1] (numeric) = -1.0907124760809928 " "
absolute error = 1.93178806284777240000000000000E-13 " "
relative error = 1.771124934582651300000000000E-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) = -1.0779903079406208 " "
y[1] (numeric) = -1.0779903079404263 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 1.80438611072412100000000000E-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) = -1.0652400847758257 " "
y[1] (numeric) = -1.0652400847756296 " "
absolute error = 1.96065386148802650000000000000E-13 " "
relative error = 1.840574617411844800000000000E-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) = -1.0524618785437547 " "
y[1] (numeric) = -1.0524618785435569 " "
absolute error = 1.9784174298820290000000000000E-13 " "
relative error = 1.879799611002992700000000000E-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) = -1.0396557613632103 " "
y[1] (numeric) = -1.039655761363011 " "
absolute error = 1.99174010617753080000000000000E-13 " "
relative error = 1.915768834451448700000000000E-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) = -1.0268218055141922 " "
y[1] (numeric) = -1.0268218055139917 " "
absolute error = 2.00506278247303270000000000000E-13 " "
relative error = 1.952688160404789700000000000E-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) = -1.0139600834372497 " "
y[1] (numeric) = -1.0139600834370477 " "
absolute error = 2.0206059048177850000000000000E-13 " "
relative error = 1.9927864398449300000000000E-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) = -1.001070667732826 " "
y[1] (numeric) = -1.001070667732623 " "
absolute error = 2.02948768901478620000000000000E-13 " "
relative error = 2.0273171060051800000000000E-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) = -0.9881536311606087 " "
y[1] (numeric) = -0.9881536311604044 " "
absolute error = 2.0428103653102880000000000000E-13 " "
relative error = 2.067300367971082700000000000E-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) = -0.9752090466388716 " "
y[1] (numeric) = -0.9752090466386659 " "
absolute error = 2.0572432646304150000000000000E-13 " "
relative error = 2.109540792018749200000000000E-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) = -0.9622369872438215 " "
y[1] (numeric) = -0.962236987243614 " "
absolute error = 2.07500683302441760000000000000E-13 " "
relative error = 2.156440524041746700000000000E-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) = -0.9492375262089368 " "
y[1] (numeric) = -0.9492375262087281 " "
absolute error = 2.08610906327066910000000000000E-13 " "
relative error = 2.197668134341641500000000000E-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) = -0.9362107369243129 " "
y[1] (numeric) = -0.9362107369241025 " "
absolute error = 2.10387263166467160000000000000E-13 " "
relative error = 2.247221217069589300000000000E-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) = -0.9231566929359977 " "
y[1] (numeric) = -0.9231566929357858 " "
absolute error = 2.11830553098479870000000000000E-13 " "
relative error = 2.294632695829526600000000000E-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) = -0.9100754679453313 " "
y[1] (numeric) = -0.9100754679451185 " "
absolute error = 2.1282975382064250000000000000E-13 " "
relative error = 2.338594559648401500000000000E-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) = -0.8969671358082842 " "
y[1] (numeric) = -0.8969671358080701 " "
absolute error = 2.1416202145019270000000000000E-13 " "
relative error = 2.387623948531902300000000000E-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) = -0.8838317705347898 " "
y[1] (numeric) = -0.8838317705345741 " "
absolute error = 2.15716333684667920000000000000E-13 " "
relative error = 2.4406944949958300000000000E-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) = -0.8706694462880795 " "
y[1] (numeric) = -0.8706694462878624 " "
absolute error = 2.17159623616680620000000000000E-13 " "
relative error = 2.494168418824114200000000000E-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) = -0.8574802373840162 " "
y[1] (numeric) = -0.8574802373837977 " "
absolute error = 2.1849189124623080000000000000E-13 " "
relative error = 2.54806911833678600000000000E-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) = -0.8442642182904241 " "
y[1] (numeric) = -0.8442642182902041 " "
absolute error = 2.1993518117824350000000000000E-13 " "
relative error = 2.605051551558076000000000000E-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) = -0.8310214636264193 " "
y[1] (numeric) = -0.8310214636261977 " "
absolute error = 2.21600515715181250000000000000E-13 " "
relative error = 2.666603997785555000000000000E-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) = -0.8177520481617373 " "
y[1] (numeric) = -0.8177520481615141 " "
absolute error = 2.23154827949656460000000000000E-13 " "
relative error = 2.72888130884290100000000000E-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) = -0.8044560468160613 " "
y[1] (numeric) = -0.8044560468158366 " "
absolute error = 2.24709140184131680000000000000E-13 " "
relative error = 2.793305377882396300000000000E-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) = -0.791133534658347 " "
y[1] (numeric) = -0.7911335346581209 " "
absolute error = 2.26152430116144400000000000000E-13 " "
relative error = 2.858587333348331400000000000E-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) = -0.7777845869061477 " "
y[1] (numeric) = -0.77778458690592 " "
absolute error = 2.2770674235061960000000000000E-13 " "
relative error = 2.927632485703861600000000000E-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) = -0.7644092789249362 " "
y[1] (numeric) = -0.764409278924707 " "
absolute error = 2.2915003228263230000000000000E-13 " "
relative error = 2.997740066746815700000000000E-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) = -0.7510076862274282 " "
y[1] (numeric) = -0.7510076862271975 " "
absolute error = 2.30704344517107530000000000000E-13 " "
relative error = 3.071930537435846300000000000E-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) = -0.7375798844729007 " "
y[1] (numeric) = -0.7375798844726684 " "
absolute error = 2.32258656751582750000000000000E-13 " "
relative error = 3.148928836604086300000000000E-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) = -0.7241259494665129 " "
y[1] (numeric) = -0.7241259494662792 " "
absolute error = 2.33701946683595450000000000000E-13 " "
relative error = 3.22736599697568200000000000E-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) = -0.7106459571586228 " "
y[1] (numeric) = -0.7106459571583877 " "
absolute error = 2.35034214313145640000000000000E-13 " "
relative error = 3.30733203989344300000000000E-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) = -0.6971399836441046 " "
y[1] (numeric) = -0.6971399836438679 " "
absolute error = 2.36699548850083370000000000000E-13 " "
relative error = 3.39529440863228900000000000E-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) = -0.683608105161662 " "
y[1] (numeric) = -0.6836081051614241 " "
absolute error = 2.37920794177171050000000000000E-13 " "
relative error = 3.48036824579349700000000000E-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) = -0.6700503980931445 " "
y[1] (numeric) = -0.670050398092905 " "
absolute error = 2.39475106411646270000000000000E-13 " "
relative error = 3.57398648061629130000000000E-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) = -0.6564669389628581 " "
y[1] (numeric) = -0.6564669389626173 " "
absolute error = 2.40807374041196450000000000000E-13 " "
relative error = 3.668233078449377000000000000E-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) = -0.6428578044368778 " "
y[1] (numeric) = -0.6428578044366354 " "
absolute error = 2.42361686275671670000000000000E-13 " "
relative error = 3.770066795532995300000000000E-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) = -0.6292230713223563 " "
y[1] (numeric) = -0.6292230713221124 " "
absolute error = 2.4391599851014690000000000000E-13 " "
relative error = 3.876463048272218400000000000E-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) = -0.6155628165668345 " "
y[1] (numeric) = -0.6155628165665888 " "
absolute error = 2.45692355349547140000000000000E-13 " "
relative error = 3.99134497304177500000000000E-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) = -0.6018771172575468 " "
y[1] (numeric) = -0.6018771172572995 " "
absolute error = 2.47246667584022360000000000000E-13 " "
relative error = 4.107926028332857000000000000E-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) = -0.5881660506207287 " "
y[1] (numeric) = -0.5881660506204802 " "
absolute error = 2.48467912911110030000000000000E-13 " "
relative error = 4.22445179637427500000000000E-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) = -0.5744296940209235 " "
y[1] (numeric) = -0.5744296940206732 " "
absolute error = 2.5024426975051030000000000000E-13 " "
relative error = 4.35639508812361630000000000E-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) = -0.5606681249602807 " "
y[1] (numeric) = -0.5606681249600292 " "
absolute error = 2.51576537380060470000000000000E-13 " "
relative error = 4.487084715184813700000000000E-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) = -0.5468814210778647 " "
y[1] (numeric) = -0.5468814210776117 " "
absolute error = 2.5301982731207320000000000000E-13 " "
relative error = 4.62659394816135700000000000E-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) = -0.533069660148952 " "
y[1] (numeric) = -0.5330696601486975 " "
absolute error = 2.5446311724408590000000000000E-13 " "
relative error = 4.77354342719454370000000000E-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) = -0.519232920084332 " "
y[1] (numeric) = -0.5192329200840761 " "
absolute error = 2.5590640717609860000000000000E-13 " "
relative error = 4.92854742597089500000000000E-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) = -0.5053712789296074 " "
y[1] (numeric) = -0.5053712789293499 " "
absolute error = 2.5757174171303630000000000000E-13 " "
relative error = 5.09668341775538800000000000E-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) = -0.49148481486448947 " "
y[1] (numeric) = -0.4914848148642304 " "
absolute error = 2.5907054279628030000000000000E-13 " "
relative error = 5.271181020469785000000000000E-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) = -0.4775736062020963 " "
y[1] (numeric) = -0.4775736062018355 " "
absolute error = 2.60846899635680530000000000000E-13 " "
relative error = 5.46192034585129800000000000E-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) = -0.4636377313882467 " "
y[1] (numeric) = -0.4636377313879845 " "
absolute error = 2.622346784164620000000000000E-13 " "
relative error = 5.656025397917165000000000000E-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) = -0.44967726900075533 " "
y[1] (numeric) = -0.4496772690004917 " "
absolute error = 2.6362245719724340000000000000E-13 " "
relative error = 5.8624812809206200000000000E-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) = -0.43569229774872476 " "
y[1] (numeric) = -0.4356922977484595 " "
absolute error = 2.6523228058294990000000000000E-13 " "
relative error = 6.08760544892433100000000000E-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) = -0.4216828964718369 " "
y[1] (numeric) = -0.4216828964715701 " "
absolute error = 2.6678659281742510000000000000E-13 " "
relative error = 6.32671125743045500000000000E-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) = -0.40764914413964415 " "
y[1] (numeric) = -0.4076491441393758 " "
absolute error = 2.68340905051900340000000000000E-13 " "
relative error = 6.58264365103088700000000000E-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) = -0.39359111985085815 " "
y[1] (numeric) = -0.3935911198505882 " "
absolute error = 2.6995072843760680000000000000E-13 " "
relative error = 6.85865902004847300000000000E-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) = -0.37950890283263794 " "
y[1] (numeric) = -0.37950890283236643 " "
absolute error = 2.71505040672082030000000000000E-13 " "
relative error = 7.15411519059448200000000000E-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) = -0.3654025724398773 " "
y[1] (numeric) = -0.3654025724396043 " "
absolute error = 2.730038417553260000000000000E-13 " "
relative error = 7.4713169076073100000000000E-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) = -0.3512722081544901 " "
y[1] (numeric) = -0.35127220815421556 " "
absolute error = 2.7455815398980120000000000000E-13 " "
relative error = 7.81610806708198500000000000E-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) = -0.33711788958469535 " "
y[1] (numeric) = -0.3371178895844192 " "
absolute error = 2.7616797737550770000000000000E-13 " "
relative error = 8.19202972929518800000000000E-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) = -0.3229396964643003 " "
y[1] (numeric) = -0.3229396964640224 " "
absolute error = 2.77944334214907940000000000000E-13 " "
relative error = 8.60669460143725600000000000E-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) = -0.3087377086519827 " "
y[1] (numeric) = -0.3087377086517035 " "
absolute error = 2.7916557954199560000000000000E-13 " "
relative error = 9.04216011581139400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997434 " "
y[1] (closed_form) = -0.2945120061305737 " "
y[1] (numeric) = -0.2945120061302928 " "
absolute error = 2.8088642523016460000000000000E-13 " "
relative error = 9.53735057937270900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999997423 " "
y[1] (closed_form) = -0.28026266900633456 " "
y[1] (numeric) = -0.280262669006053 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 1.00460243257933140000000000E-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) = -0.26598977750824115 " "
y[1] (numeric) = -0.2659897775079579 " "
absolute error = 2.8327340473310870000000000000E-13 " "
relative error = 1.06497853935131780000000000E-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) = -0.2516934119872556 " "
y[1] (numeric) = -0.2516934119869707 " "
absolute error = 2.84883228118815170000000000000E-13 " "
relative error = 1.13186605032490920000000000E-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) = -0.23737365291560697 " "
y[1] (numeric) = -0.2373736529153208 " "
absolute error = 2.8615998459713410000000000000E-13 " "
relative error = 1.20552547042308890000000000E-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) = -0.2230305808860673 " "
y[1] (numeric) = -0.22303058088577937 " "
absolute error = 2.87936341436534350000000000000E-13 " "
relative error = 1.29101731382578160000000000E-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) = -0.20866427661122366 " "
y[1] (numeric) = -0.2086642766109341 " "
absolute error = 2.89573920397856450000000000000E-13 " "
relative error = 1.38775033801008970000000000E-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) = -0.19427482092275405 " "
y[1] (numeric) = -0.1942748209224629 " "
absolute error = 2.9115598820794730000000000000E-13 " "
relative error = 1.49868102734586670000000000E-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) = -0.17986229477069893 " "
y[1] (numeric) = -0.17986229477040627 " "
absolute error = 2.92654789291191260000000000000E-13 " "
relative error = 1.62710472288974260000000000E-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) = -0.1654267792227333 " "
y[1] (numeric) = -0.16542677922243879 " "
absolute error = 2.9451441285743840000000000000E-13 " "
relative error = 1.78033093699357740000000000E-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) = -0.15096835546343534 " "
y[1] (numeric) = -0.1509683554631395 " "
absolute error = 2.9584668048698860000000000000E-13 " "
relative error = 1.95966021871810670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999997313 " "
y[1] (closed_form) = -0.13648710479355897 " "
y[1] (numeric) = -0.13648710479326115 " "
absolute error = 2.97817326355698240000000000000E-13 " "
relative error = 2.18201805076132520000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.44999999999973 " "
y[1] (closed_form) = -0.12198310862929795 " "
y[1] (numeric) = -0.12198310862899878 " "
absolute error = 2.99177349560864060000000000000E-13 " "
relative error = 2.45261293077923330000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.459999999999729 " "
y[1] (closed_form) = -0.10745644850155767 " "
y[1] (numeric) = -0.10745644850125675 " "
absolute error = 3.00912073036840870000000000000E-13 " "
relative error = 2.80031656762301130000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999728 " "
y[1] (closed_form) = -9.2907206055217410E-2 " "
y[1] (numeric) = -9.290720605491499E-2 " "
absolute error = 3.02410874120084800000000000000E-13 " "
relative error = 3.25497759496021670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.479999999999727 " "
y[1] (closed_form) = -7.83354630483983300E-2 " "
y[1] (numeric) = -7.83354630480941800E-2 " "
absolute error = 3.04159475383869450000000000000E-13 " "
relative error = 3.88278135530965460000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997258 " "
y[1] (closed_form) = -6.3741301351725400E-2 " "
y[1] (numeric) = -6.37413013514199300E-2 " "
absolute error = 3.054639874378040000000000000E-13 " "
relative error = 4.7922458588074540000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997247 " "
y[1] (closed_form) = -4.91248029475932500E-2 " "
y[1] (numeric) = -4.91248029472860560E-2 " "
absolute error = 3.0719177201987690000000000000E-13 " "
relative error = 6.2532927073029010000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997236 " "
y[1] (closed_form) = -3.4486049929425500E-2 " "
y[1] (numeric) = -3.44860499291166240E-2 " "
absolute error = 3.08877923238526360000000000000E-13 " "
relative error = 8.9566048843121870000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997225 " "
y[1] (closed_form) = -1.98251245009373200E-2 " "
y[1] (numeric) = -1.98251245006271400E-2 " "
absolute error = 3.10178965845508970000000000000E-13 " "
relative error = 1.5645751219915108000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997214 " "
y[1] (closed_form) = -5.142108975396686000E-3 " "
y[1] (numeric) = -5.142108975084732000E-3 " "
absolute error = 3.1195532268490920000000000000E-13 " "
relative error = 6.066680503612694000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999997203 " "
y[1] (closed_form) = 9.562914225119012000E-3 " "
y[1] (numeric) = 9.562914225432697000E-3 " "
absolute error = 3.1368484199045810000000000000E-13 " "
relative error = 3.280222269133175000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.549999999999719 " "
y[1] (closed_form) = 2.42898625704628400E-2 " "
y[1] (numeric) = 2.428986257077823000E-2 " "
absolute error = 3.15393544614295250000000000000E-13 " "
relative error = 1.2984575095860063000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999718 " "
y[1] (closed_form) = 3.90386534231619300E-2 " "
y[1] (numeric) = 3.903865342347874000E-2 " "
absolute error = 3.16816017864596230000000000000E-13 " "
relative error = 8.1154443118324080000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999717 " "
y[1] (closed_form) = 5.38092040391600100E-2 " "
y[1] (numeric) = 5.38092040394786200E-2 " "
absolute error = 3.1861319138570820000000000000E-13 " "
relative error = 5.9211652927226980000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.579999999999716 " "
y[1] (closed_form) = 6.86014315685643500E-2 " "
y[1] (numeric) = 6.86014315688844400E-2 " "
absolute error = 3.20091175787240450000000000000E-13 " "
relative error = 4.6659547544182406000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997148 " "
y[1] (closed_form) = 8.34152530563889700E-2 " "
y[1] (numeric) = 8.34152530567106600E-2 " "
absolute error = 3.2168712138513910000000000000E-13 " "
relative error = 3.8564544204844364000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997137 " "
y[1] (closed_form) = 9.8250585443302900E-2 " "
y[1] (numeric) = 9.82505854436262100E-2 " "
absolute error = 3.2332470034646120000000000000E-13 " "
relative error = 3.2908170357217975000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997125 " "
y[1] (closed_form) = 0.1131073455663767 " "
y[1] (numeric) = 0.11310734556670193 " "
absolute error = 3.2523983506393960000000000000E-13 " "
relative error = 2.8754970195377240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997114 " "
y[1] (closed_form) = 0.12798545015983254 " "
y[1] (numeric) = 0.12798545016015922 " "
absolute error = 3.2668312499595230000000000000E-13 " "
relative error = 2.5525020585385250000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997103 " "
y[1] (closed_form) = 0.14288481585579071 " "
y[1] (numeric) = 0.14288481585611926 " "
absolute error = 3.28542748562199450000000000000E-13 " "
relative error = 2.29935382982743000000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999997092 " "
y[1] (closed_form) = 0.15780535918502347 " "
y[1] (numeric) = 0.15780535918535335 " "
absolute error = 3.29875016191749640000000000000E-13 " "
relative error = 2.09039171987168120000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999708 " "
y[1] (closed_form) = 0.17274699657770265 " "
y[1] (numeric) = 0.17274699657803422 " "
absolute error = 3.315681063043030000000000000E-13 " "
relative error = 1.91938564995636080000000000E-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) = 0.18770964436415483 " "
y[1] (numeric) = 0.18770964436448806 " "
absolute error = 3.33233440841240740000000000000E-13 " "
relative error = 1.77526009369433970000000000E-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) = 0.20269321877561297 " "
y[1] (numeric) = 0.20269321877594773 " "
absolute error = 3.34759997500100300000000000000E-13 " "
relative error = 1.65155992648520180000000000E-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) = 0.2176976359449696 " "
y[1] (numeric) = 0.21769763594530628 " "
absolute error = 3.3667513221757870000000000000E-13 " "
relative error = 1.54652635870921760000000000E-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) = 0.23272281190753397 " "
y[1] (numeric) = 0.2327228119078722 " "
absolute error = 3.38229444452053940000000000000E-13 " "
relative error = 1.45335750148309540000000000E-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) = 0.24776866260178498 " "
y[1] (numeric) = 0.2477686626021249 " "
absolute error = 3.3992253456460730000000000000E-13 " "
relative error = 1.3719351389926680000000000E-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) = 0.26283510387012976 " "
y[1] (numeric) = 0.2628351038704713 " "
absolute error = 3.4156011352592940000000000000E-13 " "
relative error = 1.2995224324932590000000000E-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) = 0.27792205145965987 " "
y[1] (numeric) = 0.2779220514600031 " "
absolute error = 3.43225448062867140000000000000E-13 " "
relative error = 1.2349701877207321000000000E-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) = 0.2930294210229103 " "
y[1] (numeric) = 0.29302942102325524 " "
absolute error = 3.44946293751036140000000000000E-13 " "
relative error = 1.17717290143390340000000000E-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) = 0.3081571281186184 " "
y[1] (numeric) = 0.30815712811896506 " "
absolute error = 3.46667139439205130000000000000E-13 " "
relative error = 1.12496875070098370000000000E-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) = 0.3233050882124837 " "
y[1] (numeric) = 0.32330508821283205 " "
absolute error = 3.48332473976142860000000000000E-13 " "
relative error = 1.07741104818990840000000000E-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) = 0.33847321667792896 " "
y[1] (numeric) = 0.33847321667827884 " "
absolute error = 3.4988678621061810000000000000E-13 " "
relative error = 1.03372074648833910000000000E-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) = 0.35366142879686113 " "
y[1] (numeric) = 0.35366142879721285 " "
absolute error = 3.5171865420124960000000000000E-13 " "
relative error = 9.94506682274567500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.779999999999694 " "
y[1] (closed_form) = 0.36886963976043496 " "
y[1] (numeric) = 0.3688696397607885 " "
absolute error = 3.5355052219188110000000000000E-13 " "
relative error = 9.58470104564574600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996927 " "
y[1] (closed_form) = 0.3840977646698156 " "
y[1] (numeric) = 0.38409776467017076 " "
absolute error = 3.5516034557758760000000000000E-13 " "
relative error = 9.24661318669470300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996916 " "
y[1] (closed_form) = 0.39934571853694245 " "
y[1] (numeric) = 0.3993457185372993 " "
absolute error = 3.5682568011452530000000000000E-13 " "
relative error = 8.93525743613340600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996905 " "
y[1] (closed_form) = 0.4146134162852948 " "
y[1] (numeric) = 0.414613416285653 " "
absolute error = 3.58213458895306760000000000000E-13 " "
relative error = 8.63969772383874500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996894 " "
y[1] (closed_form) = 0.4299007727506561 " "
y[1] (numeric) = 0.42990077275101624 " "
absolute error = 3.6015634918840080000000000000E-13 " "
relative error = 8.37766228899739000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8299999999996883 " "
y[1] (closed_form) = 0.4452077026818828 " "
y[1] (numeric) = 0.4452077026822446 " "
absolute error = 3.61766172574107260000000000000E-13 " "
relative error = 8.1257842214963290000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999687 " "
y[1] (closed_form) = 0.4605341207416691 " "
y[1] (numeric) = 0.4605341207420327 " "
absolute error = 3.63598040564738770000000000000E-13 " "
relative error = 7.89513793199906200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999686 " "
y[1] (closed_form) = 0.4758799415073167 " "
y[1] (numeric) = 0.47587994150768215 " "
absolute error = 3.6542990855537030000000000000E-13 " "
relative error = 7.67903575422608500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999685 " "
y[1] (closed_form) = 0.49124507947150287 " "
y[1] (numeric) = 0.49124507947187007 " "
absolute error = 3.67206265394770500000000000000E-13 " "
relative error = 7.47501157242781500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999684 " "
y[1] (closed_form) = 0.5066294490430503 " "
y[1] (numeric) = 0.506629449043419 " "
absolute error = 3.6870506647801450000000000000E-13 " "
relative error = 7.27760826328680600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.879999999999683 " "
y[1] (closed_form) = 0.5220329645476969 " "
y[1] (numeric) = 0.5220329645480671 " "
absolute error = 3.7025937871248970000000000000E-13 " "
relative error = 7.09264364240469300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996817 " "
y[1] (closed_form) = 0.537455540228867 " "
y[1] (numeric) = 0.5374555402292394 " "
absolute error = 3.7236880245927750000000000000E-13 " "
relative error = 6.9283647592638100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996806 " "
y[1] (closed_form) = 0.5528970902484446 " "
y[1] (numeric) = 0.5528970902488186 " "
absolute error = 3.74034136996215240000000000000E-13 " "
relative error = 6.76498653353633700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996795 " "
y[1] (closed_form) = 0.5683575286875436 " "
y[1] (numeric) = 0.5683575286879192 " "
absolute error = 3.75588449230690460000000000000E-13 " "
relative error = 6.60831308240084000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996784 " "
y[1] (closed_form) = 0.5838367695472826 " "
y[1] (numeric) = 0.5838367695476598 " "
absolute error = 3.7725378376762820000000000000E-13 " "
relative error = 6.46163111754947300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9299999999996773 " "
y[1] (closed_form) = 0.5993347267495585 " "
y[1] (numeric) = 0.5993347267499373 " "
absolute error = 3.7880809600210340000000000000E-13 " "
relative error = 6.32047633976654900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999676 " "
y[1] (closed_form) = 0.6148513141378206 " "
y[1] (numeric) = 0.6148513141382015 " "
absolute error = 3.8091751974889120000000000000E-13 " "
relative error = 6.1952786143595610000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999675 " "
y[1] (closed_form) = 0.6303864454778477 " "
y[1] (numeric) = 0.6303864454782303 " "
absolute error = 3.82582854285828940000000000000E-13 " "
relative error = 6.06902094786987600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999674 " "
y[1] (closed_form) = 0.6459400344585224 " "
y[1] (numeric) = 0.6459400344589066 " "
absolute error = 3.84137166520304160000000000000E-13 " "
relative error = 5.94694779744249800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999673 " "
y[1] (closed_form) = 0.6615119946926086 " "
y[1] (numeric) = 0.6615119946929943 " "
absolute error = 3.8569147875477940000000000000E-13 " "
relative error = 5.83045329259679700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.979999999999672 " "
y[1] (closed_form) = 0.6771022397175286 " "
y[1] (numeric) = 0.6771022397179163 " "
absolute error = 3.87689880199104660000000000000E-13 " "
relative error = 5.72572142666135500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996707 " "
y[1] (closed_form) = 0.6927106829961427 " "
y[1] (numeric) = 0.692710682996532 " "
absolute error = 3.8935521473604240000000000000E-13 " "
relative error = 5.62074794417759100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996696 " "
y[1] (closed_form) = 0.7083372379175261 " "
y[1] (numeric) = 0.708337237917917 " "
absolute error = 3.9090952697051760000000000000E-13 " "
relative error = 5.51869231271492800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999673 " "
y[1] (closed_form) = 0.7239818177977563 " "
y[1] (numeric) = 0.723981817798142 " "
absolute error = 3.8569147875477940000000000000E-13 " "
relative error = 5.3273641585087700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999676 " "
y[1] (closed_form) = 0.7396443358806727 " "
y[1] (numeric) = 0.739644335881053 " "
absolute error = 3.80362408236578630000000000000E-13 " "
relative error = 5.14250417105800400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.02999999999968 " "
y[1] (closed_form) = 0.7553247053386776 " "
y[1] (numeric) = 0.7553247053390529 " "
absolute error = 3.75366404625765400000000000000E-13 " "
relative error = 4.969603165005123700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999683 " "
y[1] (closed_form) = 0.7710228392735115 " "
y[1] (numeric) = 0.7710228392738812 " "
absolute error = 3.69704267200177130000000000000E-13 " "
relative error = 4.794984640773123000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999686 " "
y[1] (closed_form) = 0.7867386507170334 " "
y[1] (numeric) = 0.786738650717398 " "
absolute error = 3.6459724128690140000000000000E-13 " "
relative error = 4.63428663323719460000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.05999999999969 " "
y[1] (closed_form) = 0.8024720526320062 " "
y[1] (numeric) = 0.8024720526323654 " "
absolute error = 3.59268170768700660000000000000E-13 " "
relative error = 4.47701785489409640000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999693 " "
y[1] (closed_form) = 0.8182229579128777 " "
y[1] (numeric) = 0.8182229579132315 " "
absolute error = 3.5382807794803740000000000000E-13 " "
relative error = 4.32434796073898600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999696 " "
y[1] (closed_form) = 0.8339912793865658 " "
y[1] (numeric) = 0.8339912793869144 " "
absolute error = 3.48610029732299150000000000000E-13 " "
relative error = 4.18002008352792200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997 " "
y[1] (closed_form) = 0.8497769298132427 " "
y[1] (numeric) = 0.8497769298135861 " "
absolute error = 3.4339198151656090000000000000E-13 " "
relative error = 4.04096615793075200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999703 " "
y[1] (closed_form) = 0.8655798218871203 " "
y[1] (numeric) = 0.8655798218874583 " "
absolute error = 3.37951888695897650000000000000E-13 " "
relative error = 3.904341115058591600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999706 " "
y[1] (closed_form) = 0.881399868237235 " "
y[1] (numeric) = 0.8813998682375678 " "
absolute error = 3.3273384048015940000000000000E-13 " "
relative error = 3.7750611552236100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.11999999999971 " "
y[1] (closed_form) = 0.8972369814282354 " "
y[1] (numeric) = 0.8972369814285629 " "
absolute error = 3.2751579226442120000000000000E-13 " "
relative error = 3.650270765066734000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999713 " "
y[1] (closed_form) = 0.9130910739611685 " "
y[1] (numeric) = 0.9130910739614908 " "
absolute error = 3.22297744048682940000000000000E-13 " "
relative error = 3.529743672232956700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999716 " "
y[1] (closed_form) = 0.9289620582742673 " "
y[1] (numeric) = 0.9289620582745842 " "
absolute error = 3.1696867353048220000000000000E-13 " "
relative error = 3.41207340716707900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.14999999999972 " "
y[1] (closed_form) = 0.9448498467437383 " "
y[1] (numeric) = 0.9448498467440501 " "
absolute error = 3.11861647617206470000000000000E-13 " "
relative error = 3.30064770282795460000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999723 " "
y[1] (closed_form) = 0.9607543516845515 " "
y[1] (numeric) = 0.960754351684858 " "
absolute error = 3.0653257709900570000000000000E-13 " "
relative error = 3.190540605530880500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999726 " "
y[1] (closed_form) = 0.9766754853512278 " "
y[1] (numeric) = 0.976675485351529 " "
absolute error = 3.01203506580804970000000000000E-13 " "
relative error = 3.083967101646740700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.17999999999973 " "
y[1] (closed_form) = 0.9926131599386304 " "
y[1] (numeric) = 0.9926131599389263 " "
absolute error = 2.9587443606260420000000000000E-13 " "
relative error = 2.98076277853194100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999733 " "
y[1] (closed_form) = 1.0085672875827534 " "
y[1] (numeric) = 1.0085672875830445 " "
absolute error = 2.91100477056716040000000000000E-13 " "
relative error = 2.886277203719352000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999736 " "
y[1] (closed_form) = 1.0245377803615145 " "
y[1] (numeric) = 1.0245377803618 " "
absolute error = 2.85549361933590260000000000000E-13 " "
relative error = 2.78710426698791300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20999999999974 " "
y[1] (closed_form) = 1.0405245502955447 " "
y[1] (numeric) = 1.040524550295825 " "
absolute error = 2.8022029141538950000000000000E-13 " "
relative error = 2.69306756227709700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999743 " "
y[1] (closed_form) = 1.0565275093489803 " "
y[1] (numeric) = 1.0565275093492548 " "
absolute error = 2.7444713168733870000000000000E-13 " "
relative error = 2.59763356144365600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999746 " "
y[1] (closed_form) = 1.0725465694302563 " "
y[1] (numeric) = 1.0725465694305252 " "
absolute error = 2.6889601656421290000000000000E-13 " "
relative error = 2.507080104755285400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.23999999999975 " "
y[1] (closed_form) = 1.0885816423928976 " "
y[1] (numeric) = 1.088581642393161 " "
absolute error = 2.63344901441087130000000000000E-13 " "
relative error = 2.419156186229705600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999753 " "
y[1] (closed_form) = 1.1046326400363133 " "
y[1] (numeric) = 1.1046326400365716 " "
absolute error = 2.5823787552781140000000000000E-13 " "
relative error = 2.337771546559788000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999756 " "
y[1] (closed_form) = 1.1206994741065919 " "
y[1] (numeric) = 1.1206994741068448 " "
absolute error = 2.52908805009610660000000000000E-13 " "
relative error = 2.25670494948011400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.26999999999976 " "
y[1] (closed_form) = 1.1367820562972923 " "
y[1] (numeric) = 1.1367820562975397 " "
absolute error = 2.4735768988648488000000000000E-13 " "
relative error = 2.17594646674996120000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999763 " "
y[1] (closed_form) = 1.1528802982502413 " "
y[1] (numeric) = 1.1528802982504829 " "
absolute error = 2.41584530158434060000000000000E-13 " "
relative error = 2.095486673899221400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2899999999997664 " "
y[1] (closed_form) = 1.1689941115563274 " "
y[1] (numeric) = 1.1689941115565636 " "
absolute error = 2.3625545964023330000000000000E-13 " "
relative error = 2.021014967523636400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.29999999999977 " "
y[1] (closed_form) = 1.1851234077562975 " "
y[1] (numeric) = 1.1851234077565285 " "
absolute error = 2.30926389122032560000000000000E-13 " "
relative error = 1.948542975446140600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999773 " "
y[1] (closed_form) = 1.201268098341552 " "
y[1] (numeric) = 1.2012680983417774 " "
absolute error = 2.25375273998906780000000000000E-13 " "
relative error = 1.876144670037068500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3199999999997765 " "
y[1] (closed_form) = 1.2174280947549418 " "
y[1] (numeric) = 1.2174280947551621 " "
absolute error = 2.20268248085631060000000000000E-13 " "
relative error = 1.809291645515781000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.32999999999978 " "
y[1] (closed_form) = 1.233603308391566 " "
y[1] (numeric) = 1.2336033083917812 " "
absolute error = 2.15161222172355340000000000000E-13 " "
relative error = 1.744168653802439500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999783 " "
y[1] (closed_form) = 1.2497936505995684 " "
y[1] (numeric) = 1.2497936505997782 " "
absolute error = 2.09832151654154600000000000000E-13 " "
relative error = 1.678934370913878500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3499999999997865 " "
y[1] (closed_form) = 1.2659990326809356 " "
y[1] (numeric) = 1.26599903268114 " "
absolute error = 2.0428103653102880000000000000E-13 " "
relative error = 1.613595518303313500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.35999999999979 " "
y[1] (closed_form) = 1.2822193658922951 " "
y[1] (numeric) = 1.2822193658924939 " "
absolute error = 1.98729921407903020000000000000E-13 " "
relative error = 1.549890188014802500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999793 " "
y[1] (closed_form) = 1.2984545614457148 " "
y[1] (numeric) = 1.2984545614459082 " "
absolute error = 1.93400850889702270000000000000E-13 " "
relative error = 1.489469532721787700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3799999999997965 " "
y[1] (closed_form) = 1.3147045305095015 " "
y[1] (numeric) = 1.3147045305096896 " "
absolute error = 1.88071780371501520000000000000E-13 " "
relative error = 1.430525080023996300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3899999999998 " "
y[1] (closed_form) = 1.3309691842090001 " "
y[1] (numeric) = 1.3309691842091826 " "
absolute error = 1.82520665248375740000000000000E-13 " "
relative error = 1.37133652239175200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999803 " "
y[1] (closed_form) = 1.347248433627394 " "
y[1] (numeric) = 1.3472484336275712 " "
absolute error = 1.77191594730174980000000000000E-13 " "
relative error = 1.315210990842246900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4099999999998065 " "
y[1] (closed_form) = 1.3635421898065052 " "
y[1] (numeric) = 1.363542189806677 " "
absolute error = 1.71862524211974230000000000000E-13 " "
relative error = 1.26041222264169600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999981 " "
y[1] (closed_form) = 1.379850363747595 " "
y[1] (numeric) = 1.3798503637477613 " "
absolute error = 1.66311409088848450000000000000E-13 " "
relative error = 1.20528582995880900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999813 " "
y[1] (closed_form) = 1.3961728664121644 " "
y[1] (numeric) = 1.396172866412325 " "
absolute error = 1.60538249360797640000000000000E-13 " "
relative error = 1.149845074509599600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4399999999998165 " "
y[1] (closed_form) = 1.4125096087227564 " "
y[1] (numeric) = 1.4125096087229114 " "
absolute error = 1.54987134237671850000000000000E-13 " "
relative error = 1.097246583531682900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.44999999999982 " "
y[1] (closed_form) = 1.428860501563757 " "
y[1] (numeric) = 1.4288605015639064 " "
absolute error = 1.49436019114546070000000000000E-13 " "
relative error = 1.04584050683045700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999823 " "
y[1] (closed_form) = 1.445225455782197 " "
y[1] (numeric) = 1.4452254557823414 " "
absolute error = 1.44328993201270350000000000000E-13 " "
relative error = 9.986607461405071000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999827 " "
y[1] (closed_form) = 1.4616043821885567 " "
y[1] (numeric) = 1.461604382188695 " "
absolute error = 1.3833378886829450000000000000E-13 " "
relative error = 9.46451656508844000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.47999999999983 " "
y[1] (closed_form) = 1.4779971915575638 " "
y[1] (numeric) = 1.477997191557697 " "
absolute error = 1.33226762955018780000000000000E-13 " "
relative error = 9.014006502584752000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999833 " "
y[1] (closed_form) = 1.4944037946290023 " "
y[1] (numeric) = 1.4944037946291295 " "
absolute error = 1.27231558622042940000000000000E-13 " "
relative error = 8.513867475398721000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.499999999999837 " "
y[1] (closed_form) = 1.5108241021085103 " "
y[1] (numeric) = 1.5108241021086322 " "
absolute error = 1.2190248810384219000000000000E-13 " "
relative error = 8.068608909118854000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50999999999984 " "
y[1] (closed_form) = 1.527258024668388 " "
y[1] (numeric) = 1.5272580246685046 " "
absolute error = 1.16573417585641440000000000000E-13 " "
relative error = 7.632856773560112000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999843 " "
y[1] (closed_form) = 1.5437054729483997 " "
y[1] (numeric) = 1.5437054729485105 " "
absolute error = 1.10800257857590620000000000000E-13 " "
relative error = 7.177551663787763000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999847 " "
y[1] (closed_form) = 1.5601663575565774 " "
y[1] (numeric) = 1.5601663575566826 " "
absolute error = 1.05249142734464840000000000000E-13 " "
relative error = 6.746020526894235000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.53999999999985 " "
y[1] (closed_form) = 1.5766405890700268 " "
y[1] (numeric) = 1.576640589070127 " "
absolute error = 1.00142116821189120000000000000E-13 " "
relative error = 6.351613520254318000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999853 " "
y[1] (closed_form) = 1.5931280780357318 " "
y[1] (numeric) = 1.5931280780358263 " "
absolute error = 9.45910016980633400000000000000E-14 " "
relative error = 5.937438615399370000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999857 " "
y[1] (closed_form) = 1.6096287349713583 " "
y[1] (numeric) = 1.6096287349714475 " "
absolute error = 8.92619311798625900000000000000E-14 " "
relative error = 5.545498116461677000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.56999999999986 " "
y[1] (closed_form) = 1.6261424703660616 " "
y[1] (numeric) = 1.6261424703661451 " "
absolute error = 8.34887714518117700000000000000E-14 " "
relative error = 5.134160934436304000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999863 " "
y[1] (closed_form) = 1.6426691946812895 " "
y[1] (numeric) = 1.6426691946813674 " "
absolute error = 7.79376563286859900000000000000E-14 " "
relative error = 4.74457404942128000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999867 " "
y[1] (closed_form) = 1.659208818351591 " "
y[1] (numeric) = 1.659208818351663 " "
absolute error = 7.19424519957101400000000000000E-14 " "
relative error = 4.3359492307414527000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.59999999999987 " "
y[1] (closed_form) = 1.67576125178542 " "
y[1] (numeric) = 1.6757612517854865 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 3.97511169365784960000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999873 " "
y[1] (closed_form) = 1.6923264053659424 " "
y[1] (numeric) = 1.6923264053660036 " "
absolute error = 6.12843109593086400000000000000E-14 " "
relative error = 3.621305604225725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999877 " "
y[1] (closed_form) = 1.708904189451844 " "
y[1] (numeric) = 1.7089041894518995 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 3.248347775954826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.62999999999988 " "
y[1] (closed_form) = 1.7254945143781346 " "
y[1] (numeric) = 1.7254945143781848 " "
absolute error = 5.018208071305708000000000000000E-14 " "
relative error = 2.9082723992978105000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999883 " "
y[1] (closed_form) = 1.742097290456958 " "
y[1] (numeric) = 1.7420972904570025 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 2.5491642302800230000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999887 " "
y[1] (closed_form) = 1.7587124279783959 " "
y[1] (numeric) = 1.7587124279784347 " "
absolute error = 3.88578058618804800000000000000E-14 " "
relative error = 2.209446254186464000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.65999999999989 " "
y[1] (closed_form) = 1.7753398372112783 " "
y[1] (numeric) = 1.7753398372113118 " "
absolute error = 3.35287353436797300000000000000E-14 " "
relative error = 1.8885812530600904000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999893 " "
y[1] (closed_form) = 1.7919794284039894 " "
y[1] (numeric) = 1.7919794284040171 " "
absolute error = 2.775557561562891400000000000000E-14 " "
relative error = 1.5488780270401412000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999897 " "
y[1] (closed_form) = 1.8086311117852756 " "
y[1] (numeric) = 1.8086311117852976 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.215417325530774000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6899999999999 " "
y[1] (closed_form) = 1.825294797565054 " "
y[1] (numeric) = 1.8252947975650702 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 8.8803497282468890000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999903 " "
y[1] (closed_form) = 1.8419703959352196 " "
y[1] (numeric) = 1.8419703959352307 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 6.027366276217839000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999907 " "
y[1] (closed_form) = 1.8586578170704549 " "
y[1] (numeric) = 1.8586578170704606 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.1060906827649680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.71999999999991 " "
y[1] (closed_form) = 1.8753569711290372 " "
y[1] (numeric) = 1.8753569711290372 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999913 " "
y[1] (closed_form) = 1.8920677682536466 " "
y[1] (numeric) = 1.892067768253641 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 2.93388810711013140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999917 " "
y[1] (closed_form) = 1.9087901185721772 " "
y[1] (numeric) = 1.9087901185721656 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 6.0490251619379520000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.74999999999992 " "
y[1] (closed_form) = 1.925523932198543 " "
y[1] (numeric) = 1.9255239321985258 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 8.8793674767291730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999923 " "
y[1] (closed_form) = 1.9422691192334889 " "
y[1] (numeric) = 1.9422691192334662 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 1.1660871028671548000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999927 " "
y[1] (closed_form) = 1.959025589765399 " "
y[1] (numeric) = 1.959025589765371 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 1.4281395999479707000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.77999999999993 " "
y[1] (closed_form) = 1.9757932538711063 " "
y[1] (numeric) = 1.9757932538710723 " "
absolute error = 3.39728245535297900000000000000E-14 " "
relative error = 1.7194524015591190000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999933 " "
y[1] (closed_form) = 1.9925720216167007 " "
y[1] (numeric) = 1.9925720216166614 " "
absolute error = 3.93018950717305400000000000000E-14 " "
relative error = 1.9724203012668223000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999937 " "
y[1] (closed_form) = 2.0093618030583404 " "
y[1] (numeric) = 2.009361803058296 " "
absolute error = 4.44089209850062600000000000000E-14 " "
relative error = 2.2101007851056914000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.80999999999994 " "
y[1] (closed_form) = 2.02616250824306 " "
y[1] (numeric) = 2.02616250824301 " "
absolute error = 4.97379915032070130000000000000E-14 " "
relative error = 2.4547878712026985000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999943 " "
y[1] (closed_form) = 2.04297404720958 " "
y[1] (numeric) = 2.042974047209525 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 2.695436199819658000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999947 " "
y[1] (closed_form) = 2.059796329989117 " "
y[1] (numeric) = 2.0597963299890565 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 2.9321409918196920000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.83999999999995 " "
y[1] (closed_form) = 2.076629266606194 " "
y[1] (numeric) = 2.0766292666061275 " "
absolute error = 6.66133814775093900000000000000E-14 " "
relative error = 3.2077647439870044000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8499999999999535 " "
y[1] (closed_form) = 2.0934727670794486 " "
y[1] (numeric) = 2.0934727670793762 " "
absolute error = 7.23865412055602100000000000000E-14 " "
relative error = 3.4577254762451415000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999957 " "
y[1] (closed_form) = 2.110326741422444 " "
y[1] (numeric) = 2.110326741422366 " "
absolute error = 7.81597009336110200000000000000E-14 " "
relative error = 3.703677700682894000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.86999999999996 " "
y[1] (closed_form) = 2.1271910996444787 " "
y[1] (numeric) = 2.127191099644395 " "
absolute error = 8.39328606616618300000000000000E-14 " "
relative error = 3.945713230733698400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8799999999999635 " "
y[1] (closed_form) = 2.144065751751396 " "
y[1] (numeric) = 2.144065751751306 " "
absolute error = 9.01501095995627100000000000000E-14 " "
relative error = 4.204633627766449000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999967 " "
y[1] (closed_form) = 2.160950607746395 " "
y[1] (numeric) = 2.1609506077462997 " "
absolute error = 9.54791801177634600000000000000E-14 " "
relative error = 4.4183878972290100000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999997 " "
y[1] (closed_form) = 2.177845577630839 " "
y[1] (numeric) = 2.177845577630737 " "
absolute error = 1.0214051826551440000000000000E-13 " "
relative error = 4.689979827524207000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9099999999999735 " "
y[1] (closed_form) = 2.1947505714050664 " "
y[1] (numeric) = 2.194750571404959 " "
absolute error = 1.07469588783715150000000000000E-13 " "
relative error = 4.896665260458903000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999977 " "
y[1] (closed_form) = 2.2116654990692006 " "
y[1] (numeric) = 2.211665499069088 " "
absolute error = 1.1279865930191590000000000000E-13 " "
relative error = 5.100168147009041000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.92999999999998 " "
y[1] (closed_form) = 2.2285902706239598 " "
y[1] (numeric) = 2.228590270623842 " "
absolute error = 1.1768364061026660000000000000E-13 " "
relative error = 5.280631534719820000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9399999999999835 " "
y[1] (closed_form) = 2.245524796071469 " "
y[1] (numeric) = 2.2455247960713445 " "
absolute error = 1.24344978758017530000000000000E-13 " "
relative error = 5.537457389718353000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999987 " "
y[1] (closed_form) = 2.2624689854160644 " "
y[1] (numeric) = 2.2624689854159343 " "
absolute error = 1.30118138486068350000000000000E-13 " "
relative error = 5.751156781587431000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.95999999999999 " "
y[1] (closed_form) = 2.2794227486651115 " "
y[1] (numeric) = 2.279422748664975 " "
absolute error = 1.36335387423969220000000000000E-13 " "
relative error = 5.981136562044523000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999935 " "
y[1] (closed_form) = 2.2963859958298074 " "
y[1] (numeric) = 2.2963859958296657 " "
absolute error = 1.41664457942169970000000000000E-13 " "
relative error = 6.16901767383314000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999997 " "
y[1] (closed_form) = 2.3133586369259955 " "
y[1] (numeric) = 2.313358636925848 " "
absolute error = 1.4743761767022080000000000000E-13 " "
relative error = 6.373314336861177000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.99 " "
y[1] (closed_form) = 2.3303405819749727 " "
y[1] (numeric) = 2.33034058197482 " "
absolute error = 1.52766688188421540000000000000E-13 " "
relative error = 6.555551981116476000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) + ( 0.1 * x + 0.2 ) ; "
Iterations = 4000
"Total Elapsed Time "= 1 Minutes 19 Seconds
"Elapsed Time(since restart) "= 1 Minutes 19 Seconds
"Time to Timeout "= 1 Minutes 40 Seconds
Percent Done = 100.02500000000009 "%"
(%o257) temp/diffeq.add_full_lin.max