(%i1) batch("temp/diffeq.mult_c_sin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.mult_c_sin.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([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_g,[40],convfloat)
(%i187) completearray(array_tmp1,[40],convfloat)
(%i188) completearray(array_tmp2,[40],convfloat)
(%i189) completearray(array_tmp3,[40],convfloat)
(%i190) completearray(array_m1,[40],convfloat)
(%i191) completearray(array_y_higher,[2,40],convfloat)
(%i192) completearray(array_y_higher_work,[2,40],convfloat)
(%i193) completearray(array_y_higher_work2,[2,40],convfloat)
(%i194) completearray(array_y_set_initial,[2,40],convfloat)
(%i195) completearray(array_given_rad_poles,[2,3],convfloat)
(%i196) completearray(array_given_ord_poles,[2,3],convfloat)
(%i197) completearray(array_rad_test_poles,[2,4],convfloat)
(%i198) completearray(array_ord_test_poles,[2,4],convfloat)
(%i199) completearray(array_fact_2,[40,40],convfloat)
(%i200) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i201) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i202) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i203) omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (if vallen = 4
then printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel)
else printf(true,"~a = ~g ~s ~%",prelabel,
value,postlabel))
(%i204) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i205) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i206) logitem_time(fd,secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],convfloat]),
secs:secs_in,printf(fd,"
~%"),
if secs >= 0
then (years_int
:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int
:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,
truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if truncate(years_int) > 0.1
then printf(fd,
"~d Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(fd,
"~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(fd,
"~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(fd,
"~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(fd,"~d Seconds~%",
sec_int))
else printf(fd," 0.0 Seconds~%"),
printf(fd," | ~%")),0)
(%i207) omniout_timestr(secs_in):=(
block(mode_declare(
[[days_int,hours_int,minutes_int,sec_int,
years_int],fixnum,[secs,secs_temp],
convfloat]),secs:secs_in,
if secs >= 0
then (
years_int:truncate(secs/glob_sec_in_year),
sec_temp
:mod(truncate(secs),
truncate(glob_sec_in_year)),
days_int:truncate(sec_temp/glob_sec_in_day),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_day)),
hours_int
:truncate(sec_temp/glob_sec_in_hour),
sec_temp
:mod(sec_temp,truncate(glob_sec_in_hour)),
minutes_int
:truncate(sec_temp/glob_sec_in_minute),
sec_int
:mod(sec_temp,
truncate(glob_sec_in_minute)),
if years_int > 0
then printf(true,
"= ~f Years ~f Days ~f Hours ~f Minutes ~f Seconds~%",
years_int,days_int,
hours_int,minutes_int,
sec_int)
elseif days_int > 0.1
then printf(true,
"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",
days_int,hours_int,
minutes_int,sec_int)
elseif hours_int > 0.1
then printf(true,
"= ~d Hours ~d Minutes ~d Seconds~%",
hours_int,minutes_int,
sec_int)
elseif minutes_int > 0.1
then printf(true,
"= ~d Minutes ~d Seconds~%",
minutes_int,sec_int)
else printf(true,"= ~d Seconds~%",
sec_int))
else printf(true,"= 0.0 Seconds~%")),0)
(%i208) zero_ats_ar(arr_a):=(
block(mode_declare([iii],fixnum),iii:1,
while iii <= ats_max_terms do
(arr_a[iii]:glob__0,iii:1+iii)),0)
(%i209) ats(mmm_ats,arr_a,arr_b,jjj_ats):=block(
mode_declare([[iii_ats,lll_ats,ma_ats],fixnum,[ret_ats],
convfloat]),ret_ats:glob__0,
if jjj_ats <= mmm_ats
then (ma_ats:1+mmm_ats,iii_ats:jjj_ats,
while iii_ats <= mmm_ats do
(lll_ats:ma_ats-iii_ats,
if lll_ats <= ats_max_terms
and iii_ats <= ats_max_terms
then ret_ats
:c(arr_a[iii_ats])*c(arr_b[lll_ats])+ret_ats,
iii_ats:1+iii_ats)),ret_ats)
(%i210) att(mmm_att,arr_aa,arr_bb,jjj_att):=block(
mode_declare([[al_att,iii_att,lll_att,ma_att],convfloat,[ret_att],
fixnum]),ret_att:glob__0,
if jjj_att < mmm_att
then (ma_att:2+mmm_att,iii_att:jjj_att,
while iii_att < mmm_att and iii_att <= ats_max_terms do
(lll_att:ma_att-iii_att,al_att:lll_att-1,
if lll_att <= ats_max_terms
and iii_att <= ats_max_terms
then ret_att
:c(arr_aa[iii_att])*c(arr_bb[lll_att])
*c(al_att)
+ret_att,iii_att:1+iii_att),
ret_att:ret_att/c(mmm_att)),ret_att)
(%i211) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i212) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i213) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i214) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i215) log_revs(file,revs):=printf(file,revs)
(%i216) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i217) logitem_h_reason(file):=(printf(file,""),
if glob_h_reason = 1 then printf(file,"Max H")
elseif glob_h_reason = 2
then printf(file,"Display_interval")
elseif glob_h_reason = 3
then printf(file,"Optimal")
elseif glob_h_reason = 4
then printf(file,"Pole Accuracy")
elseif glob_h_reason = 5
then printf(file,"Min H (Pole)")
elseif glob_h_reason = 6 then printf(file,"Pole")
elseif glob_h_reason = 7
then printf(file,"Opt Iter")
else printf(file,"Impossible"),
printf(file," | "),0)
(%i218) logstart(file):=(printf(file,""),0)
(%i219) logend(file):=(printf(file,"
~%"),0)
(%i220) chk_data():=(
block(mode_declare([[errflag],boolean]),errflag:false,
if glob_max_iter < 2
then (omniout_str(always,"Illegal max_iter"),
errflag:true),if errflag then quit()),0)
(%i221) comp_expect_sec(t_end2,t_start2,t2,clock_sec2):=block(
mode_declare([[ms2,rrr,sec_left,sub1,sub2],
convfloat]),ms2:c(clock_sec2),
sub1:c(t_end2-t_start2),sub2:c(t2-t_start2),
if sub1 = glob__0 then sec_left:glob__0
else (if sub2 > glob__0
then (rrr:sub1/sub2,
sec_left:rrr*c(ms2)-c(ms2))
else sec_left:glob__0),sec_left)
(%i222) comp_percent(t_end2,t_start2,t2):=block(
mode_declare([[rrr,sub1,sub2],convfloat]),
sub1:t_end2-t_start2,sub2:t2-t_start2,
if sub2 > glob_small_float then rrr:glob__100*sub2/sub1
else rrr:0.0,rrr)
(%i223) comp_rad_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret:abs(term1*glob_h/term2)
else ret:glob_larger_float,ret)
(%i224) comp_ord_from_ratio(term1,term2,last_no):=(
if abs(term2) > glob__0
then ret
:abs(term2)*c(last_no)
*log(abs(term1*glob_h/term2))
/log(c(last_no))
+glob__1 else ret:glob_larger_float,ret)
(%i225) c(in_val):=(ret:in_val,ret)
(%i226) comp_rad_from_three_terms(term1,term2,term3,last_no):=(
temp:abs(
term1*term3-term1*term3*c(last_no)
+glob__m2*term2*term2
+term2*term2*c(last_no)),
if abs(temp) > glob__0
then ret:abs(term2*glob_h*term1/temp)
else ret:glob_larger_float,ret)
(%i227) comp_ord_from_three_terms(term1,term2,term3,last_no):=(
ret:abs(
(-term1*term3*c(last_no*last_no)
+term2*term2*c(last_no*last_no)
+glob__4*term2*term2
-glob__4*term2*term2*c(last_no)
-glob__3*term1*term3
+glob__4*term1*term3*c(last_no))
/(term1*term3-term1*term3*c(last_no)
-glob__2*term2*term2
+term2*term2*c(last_no))),
ret)
(%i228) comp_rad_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=
(
if term5 # glob__0 and term4 # glob__0
and term3 # glob__0
and term2 # glob__0
and term1 # glob__0
then (rm0:term6/term5,rm1:term5/term4,
rm2:term4/term3,rm3:term3/term2,
rm4:term2/term1,
nr1
:c(last_no-3)*rm2
-glob__2*c(last_no-2)*rm1
+c(last_no-1)*rm0,
nr2
:c(last_no-4)*rm3
-glob__2*c(last_no-3)*rm2
+c(last_no-2)*rm1,
dr1
:(-glob__1)/rm3+glob__2/rm2
+glob__m1/rm1,
dr2
:(-glob__1)/rm4+glob__2/rm3
+glob__m1/rm2,
ds1
:glob__5/rm3-glob__8/rm2
+glob__3/rm1,
ds2
:glob__5/rm4-glob__8/rm3
+glob__3/rm2,
if
abs(nr1*dr2-nr2*dr1) = glob__0
or abs(dr1) = glob__0
then (rad_c:glob_larger_float,
ord_no:glob_larger_float)
else (if
abs(nr1*dr2-nr2*dr1) > glob__0
then (
rcs
:(dr1*dr2-ds2*dr1+ds1*dr2)
/(nr1*dr2-nr2*dr1),
ord_no
:(rcs*nr1-ds1)/(glob__2*dr1)
-c(last_no)/glob__2,
if abs(rcs) # glob__0
then (if rcs > glob__0
then rad_c
:sqrt(rcs)
*abs(glob_h)
else (
rad_c
:glob_larger_float,
ord_no
:glob_larger_float))
else (
rad_c:glob_larger_float,
ord_no:glob_larger_float))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float)))
else (rad_c:glob_larger_float,
ord_no:glob_larger_float),
glob_six_term_ord_save:ord_no,rad_c)
(%i229) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i230) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i231) factorial_1(nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms
then (if array_fact_1[nnn] = 0
then (ret:factorial_2(nnn),
array_fact_1[nnn]:ret)
else ret:array_fact_1[nnn])
else ret:factorial_2(nnn),ret)
(%i232) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i233) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i234) factorial_3(mmm,nnn):=block(mode_declare([[ret],convfloat]),
if nnn <= ats_max_terms and mmm <= ats_max_terms
then (if array_fact_2[mmm,nnn] = 0
then (ret:factorial_1(mmm)/factorial_1(nnn),
array_fact_2[mmm,nnn]:ret)
else ret:array_fact_2[mmm,nnn])
else ret:factorial_2(mmm)/factorial_2(nnn),ret)
(%i235) log10(x):=log(x)/glob_log_10
(%i236) c(x):=x
(%i237) expt(x,y):=if y = 0.0 then 1.0 elseif x <= 0.0 and y < 0.0
then print("expt error x = ",x,"y = ",y) else x^y
(%i238) estimated_needed_step_error(x_start,x_end,estimated_h,
estimated_answer):=block(
[desired_abs_gbl_error,range,
estimated_steps,step_error],
omniout_float(always,
"glob_desired_digits_correct",
32,
glob_desired_digits_correct,
32,""),
desired_abs_gbl_error
:expt(glob__10,
c(-glob_desired_digits_correct))
*c(abs(c(estimated_answer))),
omniout_float(always,"estimated_h",32,
estimated_h,32,""),
omniout_float(always,"estimated_answer",
32,estimated_answer,32,""),
omniout_float(always,
"desired_abs_gbl_error",32,
desired_abs_gbl_error,32,
""),range:x_end-x_start,
omniout_float(always,"range",32,range,32,
""),
estimated_steps:range/estimated_h,
omniout_float(always,"estimated_steps",32,
estimated_steps,32,""),
step_error
:c(
abs(desired_abs_gbl_error)
/sqrt(c(estimated_steps))
/c(ats_max_terms)),
omniout_float(always,"step_error",32,
step_error,32,""),
step_error)
(%i239) exact_soln_y(x):=block(cos(x)*c(-2.0))
(%o239) exact_soln_y(x) := block(cos(x) c(- 2.0))
(%i240) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
omniout_float(always,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(always,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(always,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(always,
"SOME POLE (given) for Equation 1")
else omniout_str(always,
"NO info (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(always,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(always,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(always,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > glob__small
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(always,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(always,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > glob__small
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(always,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(always,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%i241) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i242) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(always,"min_size",32,min_size,
32,"")),
if min_size < glob__1
then (min_size:glob__1,
omniout_float(always,"min_size",32,min_size,
32,"")),min_size)
(%i243) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:glob__small,
no_terms:ats_max_terms,hn_div_ho:glob__0_5,
hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125,
omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(always,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i244) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:ats_max_terms,
hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25,
hn_div_ho_3:glob__0_125,
est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3)
+c(abs(array_y[no_terms-1]))
*c(hn_div_ho_2)
+c(abs(array_y[no_terms-2]))
*c(hn_div_ho)
+c(abs(array_y[no_terms-3])),
if glob_prec*c(abs(array_y[1])) > c(est_tmp)
then est_tmp
:c(glob_prec)*c(abs(array_y[1])),
if c(est_tmp) >= c(array_max_est_error[1])
then array_max_est_error[1]:c(est_tmp))
(%i245) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
-glob_h/glob__10 then ret:true else ret:false,
return(ret))
(%i246) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(19)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i247) prog_report(x_start,x_end):=(
block(mode_declare([[clock_sec],convfloat,[opt_clock_sec],
convfloat,[clock_sec1],convfloat,
[expect_sec],convfloat,[left_sec],
convfloat,[percent_done],convfloat,
[total_clock_sec],convfloat]),
clock_sec1:elapsed_time_seconds(),
total_clock_sec:clock_sec1-glob_orig_start_sec,
glob_clock_sec:clock_sec1-glob_clock_start_sec,
left_sec:-clock_sec1+glob_orig_start_sec
+glob_max_sec,
expect_sec:comp_expect_sec(x_end,x_start,
glob_h+array_x[1],
clock_sec1
-glob_orig_start_sec),
opt_clock_sec:clock_sec1
-glob_optimal_clock_start_sec,
glob_optimal_expect_sec
:comp_expect_sec(x_end,x_start,glob_h+array_x[1],
opt_clock_sec),
glob_total_exp_sec
:c(total_clock_sec)+glob_optimal_expect_sec,
percent_done:comp_percent(x_end,x_start,
glob_h+array_x[1]),
glob_percent_done:percent_done,
omniout_str_noeol(info,
"Total Elapsed Time "),
omniout_timestr(total_clock_sec),
omniout_str_noeol(info,
"Elapsed Time(since restart) "),
omniout_timestr(glob_clock_sec),
if c(percent_done) < glob__100
then (omniout_str_noeol(info,
"Expected Time Remaining "),
omniout_timestr(expect_sec),
omniout_str_noeol(info,
"Optimized Time Remaining "),
omniout_timestr(glob_optimal_expect_sec),
omniout_str_noeol(info,
"Expected Total Time "),
omniout_timestr(glob_total_exp_sec)),
omniout_str_noeol(info,
"Time to Timeout "),
omniout_timestr(left_sec),
omniout_float(info,
"Percent Done ",33,
percent_done,4,"%")),0)
(%i248) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i249) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),array_tmp1[1]:sin(array_x[1]),
array_tmp1_g[1]:cos(array_x[1]),
array_tmp2[1]:array_const_2D0[1]*array_tmp1[1],
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp3[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_tmp1_g[1]*array_x[2]/c(1),
array_tmp1_g[2]:neg(array_tmp1[1])*array_x[2]/c(1),
array_tmp2[2]:array_const_2D0[1]*array_tmp1[2],
array_tmp3[2]:array_tmp2[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp3[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_tmp1_g[2]*array_x[2]/c(2),
array_tmp1_g[3]:neg(array_tmp1[2])*array_x[2]/c(2),
array_tmp2[3]:array_const_2D0[1]*array_tmp1[3],
array_tmp3[3]:array_tmp2[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp3[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_tmp1_g[3]*array_x[2]/c(3),
array_tmp1_g[4]:neg(array_tmp1[3])*array_x[2]/c(3),
array_tmp2[4]:array_const_2D0[1]*array_tmp1[4],
array_tmp3[4]:array_tmp2[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp3[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_tmp1_g[4]*array_x[2]/c(4),
array_tmp1_g[5]:neg(array_tmp1[4])*array_x[2]/c(4),
array_tmp2[5]:array_const_2D0[1]*array_tmp1[5],
array_tmp3[5]:array_tmp2[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp3[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp1[kkk]
:array_tmp1_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp1_g[kkk]
:neg(array_tmp1[kkk-1])*array_x[2]/c(kkk-1),
array_tmp2[kkk]
:array_const_2D0[1]*array_tmp1[kkk],
array_tmp3[kkk]:array_tmp2[kkk],order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp3[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i250) exact_soln_y(x):=block(cos(x)*c(-2.0))
(%o250) exact_soln_y(x) := block(cos(x) c(- 2.0))
(%i251) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms: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_g[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[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_g),
zero_ats_ar(array_tmp1),zero_ats_ar(array_tmp2),
zero_ats_ar(array_tmp3),zero_ats_ar(array_m1),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_2D0),array_const_2D0[1]:c(2.0),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,
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/mult_c_sinpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = 2.0 * sin ( x ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.1),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,""),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (cos(x) * c(-2.0)) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:3,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = 2.0 * sin ( x ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T22:01:52-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"mult_c_sin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = 2.0 * sin ( x ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"mult_c_sin diffeq.max"),
logitem_str(html_log_file,
"mult_c_sin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i252) main():=(glob_iolevel:2,compile(all),main_prog())
(%i253) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp1_g in translation.
warning: encountered undefined variable array_const_2D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/mult_c_sinpostode.ode#################"
"diff ( y , x , 1 ) = 2.0 * sin ( x ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
""
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (cos(x) * c(-2.0)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = -1.9900083305560516 " "
y[1] (numeric) = -1.9900083305560516 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = -1.9879121959133936 " "
y[1] (numeric) = -1.9879121959133939 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.116973905494893400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = -1.9856172717077325 " "
y[1] (numeric) = -1.9856172717077325 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (closed_form) = -1.9831237874295762 " "
y[1] (numeric) = -1.9831237874295762 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (closed_form) = -1.9804319924252742 " "
y[1] (numeric) = -1.9804319924252745 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.121192779021466400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (closed_form) = -1.9775421558720845 " "
y[1] (numeric) = -1.9775421558720843 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.122831208759294100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (closed_form) = -1.9744545667512539 " "
y[1] (numeric) = -1.9744545667512534 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.249174112832397000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (closed_form) = -1.9711695338191213 " "
y[1] (numeric) = -1.9711695338191206 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.37938367728556730000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (closed_form) = -1.967687385576243 " "
y[1] (numeric) = -1.9676873855762425 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.256909370387663300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = -1.9640084702345406 " "
y[1] (numeric) = -1.9640084702345402 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.26113693795337720000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = -1.9601331556824833 " "
y[1] (numeric) = -1.9601331556824828 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.265607357146299200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = -1.9560618294482965 " "
y[1] (numeric) = -1.956061829448296 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.270322968141130200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = -1.951794898661211 " "
y[1] (numeric) = -1.951794898661211 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = -1.9473327900107495 " "
y[1] (numeric) = -1.9473327900107498 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.140249915494955500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = -1.942675949704059 " "
y[1] (numeric) = -1.942675949704059 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = -1.9378248434212895 " "
y[1] (numeric) = -1.9378248434212892 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.145844556998271800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = -1.9327799562690264 " "
y[1] (numeric) = -1.9327799562690264 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = -1.927541792731781 " "
y[1] (numeric) = -1.927541792731781 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (closed_form) = -1.9221108766215418 " "
y[1] (numeric) = -1.922110876621542 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.155212259738704300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (closed_form) = -1.9164877510253941 " "
y[1] (numeric) = -1.9164877510253948 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.475805229742204000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (closed_form) = -1.910672978251212 " "
y[1] (numeric) = -1.9106729782512129 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.6485109163633600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (closed_form) = -1.9046671397714268 " "
y[1] (numeric) = -1.9046671397714274 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.497376527717251000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (closed_form) = -1.8984708361648817 " "
y[1] (numeric) = -1.8984708361648825 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.6783885366095096000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (closed_form) = -1.8920846870567738 " "
y[1] (numeric) = -1.892084687056775 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.86772374524187200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (closed_form) = -1.8855093310566924 " "
y[1] (numeric) = -1.8855093310566935 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.88818631835121400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (closed_form) = -1.8787454256947578 " "
y[1] (numeric) = -1.8787454256947587 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.72750808892417100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (closed_form) = -1.8717936473558696 " "
y[1] (numeric) = -1.8717936473558703 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.55879942063104470000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (closed_form) = -1.8646546912120687 " "
y[1] (numeric) = -1.8646546912120696 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.763232698719079000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (closed_form) = -1.8573292711530203 " "
y[1] (numeric) = -1.8573292711530212 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.78201917933888300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (closed_form) = -1.849818119714626 " "
y[1] (numeric) = -1.8498181197146264 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.40071823882108400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (closed_form) = -1.84212198800577 " "
y[1] (numeric) = -1.8421219880057704 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.410748108657132200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (closed_form) = -1.83424164563321 " "
y[1] (numeric) = -1.8342416456332107 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.63165789175577100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (closed_form) = -1.8261778806246163 " "
y[1] (numeric) = -1.8261778806246172 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.863592036260659400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (closed_form) = -1.81793149934977 " "
y[1] (numeric) = -1.817931499349771 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 6.10706742813057800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (closed_form) = -1.8095033264399265 " "
y[1] (numeric) = -1.8095033264399274 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.90840998589129550000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (closed_form) = -1.8008942047053536 " "
y[1] (numeric) = -1.8008942047053542 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.698905871508876000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = -1.7921049950510501 " "
y[1] (numeric) = -1.792104995051051 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 4.956062407910561400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = -1.7831365763906577 " "
y[1] (numeric) = -1.7831365763906584 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.73574197060917770000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (closed_form) = -1.773989845558568 " "
y[1] (numeric) = -1.7739898455585688 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.755003538734188000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (closed_form) = -1.7646657172202427 " "
y[1] (numeric) = -1.7646657172202436 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.033125600123359000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = -1.755165123780745 " "
y[1] (numeric) = -1.755165123780746 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.06036957814503900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = -1.7454890152915021 " "
y[1] (numeric) = -1.7454890152915028 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.816316281221898700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (closed_form) = -1.7356383593552995 " "
y[1] (numeric) = -1.7356383593552998 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.279325291056078500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (closed_form) = -1.7256141410295216 " "
y[1] (numeric) = -1.7256141410295223 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.860270954766693600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = -1.7154173627276479 " "
y[1] (numeric) = -1.7154173627276483 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.588811443204271000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (closed_form) = -1.7050490441190111 " "
y[1] (numeric) = -1.7050490441190116 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.604553877096954500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = -1.6945102220268318 " "
y[1] (numeric) = -1.6945102220268322 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.620752616758370000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (closed_form) = -1.683801950324537 " "
y[1] (numeric) = -1.6838019503245376 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.95612925051371360000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = -1.6729252998303734 " "
y[1] (numeric) = -1.672925299830374 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 3.981850324354809000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = -1.6618813582003265 " "
y[1] (numeric) = -1.6618813582003273 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.344415323738546000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = -1.6506712298193562 " "
y[1] (numeric) = -1.6506712298193569 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.03553295617803500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = -1.6392960356909585 " "
y[1] (numeric) = -1.6392960356909592 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.06353581215317450000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = -1.6277569133250673 " "
y[1] (numeric) = -1.627756913325068 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.092342101710768600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = -1.6160550166243033 " "
y[1] (numeric) = -1.6160550166243037 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.747983238699995000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = -1.6041915157685847 " "
y[1] (numeric) = -1.6041915157685849 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.384152719562585800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = -1.592167597098111 " "
y[1] (numeric) = -1.592167597098111 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = -1.5799844629947295 " "
y[1] (numeric) = -1.5799844629947297 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.405359420460149000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = -1.567643331761698 " "
y[1] (numeric) = -1.5676433317616982 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.416422986187172700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = -1.5551454375018552 " "
y[1] (numeric) = -1.5551454375018556 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 2.85561208065167100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = -1.5424920299942126 " "
y[1] (numeric) = -1.5424920299942129 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.43951865298042690000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = -1.529684374568976 " "
y[1] (numeric) = -1.529684374568977 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.80628549566239800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = -1.5167237519810157 " "
y[1] (numeric) = -1.5167237519810166 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 5.85590104025246700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = -1.5036114582817892 " "
y[1] (numeric) = -1.5036114582817903 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.38370952489171400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = -1.49034880468974 " "
y[1] (numeric) = -1.4903488046897413 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 8.93930082245101500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = -1.476937117459175 " "
y[1] (numeric) = -1.4769371174591768 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.20273017612027880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = -1.463377737747641 " "
y[1] (numeric) = -1.4633777377476425 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.06214013947454210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = -1.4496720214818095 " "
y[1] (numeric) = -1.4496720214818113 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.2253508470036649000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = -1.435821339221886 " "
y[1] (numeric) = -1.4358213392218877 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.23717122101201740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = -1.421827076024554 " "
y[1] (numeric) = -1.4218270760245555 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.0931795157686090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = -1.4076906313044713 " "
y[1] (numeric) = -1.4076906313044728 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.10415754705625720000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = -1.3934134186943299 " "
y[1] (numeric) = -1.3934134186943314 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.11547098199445820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = -1.3789968659034932 " "
y[1] (numeric) = -1.3789968659034946 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.66113602207000500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = -1.3644424145752263 " "
y[1] (numeric) = -1.3644424145752276 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.76419096415252600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = -1.3497515201425332 " "
y[1] (numeric) = -1.3497515201425347 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.15155435002665120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = -1.3349256516826153 " "
y[1] (numeric) = -1.3349256516826167 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.98008861295700500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = -1.3199662917699633 " "
y[1] (numeric) = -1.3199662917699646 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.009319433274110000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = -1.3048749363281027 " "
y[1] (numeric) = -1.3048749363281038 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.5082715110561200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = -1.2896530944800013 " "
y[1] (numeric) = -1.2896530944800024 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.60869507759222300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = -1.2743022883971593 " "
y[1] (numeric) = -1.2743022883971604 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.71239920648353600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = -1.2588240531473927 " "
y[1] (numeric) = -1.2588240531473935 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.05562002473216500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = -1.243219936541328 " "
y[1] (numeric) = -1.2432199365413288 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.14417774035270200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = -1.227491498977622 " "
y[1] (numeric) = -1.2274914989776233 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.08535792765964900000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = -1.2116403132869245 " "
y[1] (numeric) = -1.2116403132869258 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.09955703432813880000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = -1.1956679645745953 " "
y[1] (numeric) = -1.1956679645745965 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.28537903095999500000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = -1.1795760500621952 " "
y[1] (numeric) = -1.1795760500621961 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.52964100664212700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = -1.1633661789277658 " "
y[1] (numeric) = -1.1633661789277667 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.63455596172417900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = -1.147039972144912 " "
y[1] (numeric) = -1.1470399721449132 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.67902646451884700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = -1.1305990623207074 " "
y[1] (numeric) = -1.1305990623207083 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.85582130129330800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = -1.1140450935324333 " "
y[1] (numeric) = -1.1140450935324346 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.19588303676811740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (closed_form) = -1.097379721163174 " "
y[1] (numeric) = -1.0973797211631753 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.21404433110723350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (closed_form) = -1.0806046117362784 " "
y[1] (numeric) = -1.08060461173628 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.43837275687524940000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0099999999999996 " "
y[1] (closed_form) = -1.0637214427487116 " "
y[1] (numeric) = -1.0637214427487116 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999985 " "
y[1] (closed_form) = -1.0467319025033017 " "
y[1] (numeric) = -1.0467319025032997 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.9091817489712730000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999974 " "
y[1] (closed_form) = -1.0296376899399151 " "
y[1] (numeric) = -1.0296376899399113 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.6661034464907843000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = -1.0124405144655633 " "
y[1] (numeric) = -1.0124405144655573 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 5.9215373617683920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = -0.9951420957834624 " "
y[1] (numeric) = -0.9951420957834546 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 7.8094989703532210000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = -0.9777441637210655 " "
y[1] (numeric) = -0.9777441637210558 " "
absolute error = 9.769962616701378000000000000000E-15 " "
relative error = 9.9923507387854770000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = -0.9602484580570806 " "
y[1] (numeric) = -0.9602484580570687 " "
absolute error = 1.187938636348917500000000000000E-14 " "
relative error = 1.2371159009747684000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = -0.9426567283474944 " "
y[1] (numeric) = -0.9426567283474804 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.4839771137898500000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = -0.9249707337506181 " "
y[1] (numeric) = -0.9249707337506022 " "
absolute error = 1.58761892521397390000000000000E-14 " "
relative error = 1.7163990894894762000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = -0.9071922428511732 " "
y[1] (numeric) = -0.9071922428511554 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.9580820420349046000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = -0.8893230334834342 " "
y[1] (numeric) = -0.8893230334834143 " "
absolute error = 1.987299214079030200000000000000E-14 " "
relative error = 2.2346201990236075000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = -0.871364892553447 " "
y[1] (numeric) = -0.8713648925534251 " "
absolute error = 2.187139358511558400000000000000E-14 " "
relative error = 2.510015467919951000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = -0.8533196158603393 " "
y[1] (numeric) = -0.8533196158603154 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.8102972070699783000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = -0.835189007916743 " "
y[1] (numeric) = -0.835189007916717 " "
absolute error = 2.597921877622866300000000000000E-14 " "
relative error = 3.1105795849768225000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = -0.8169748817683435 " "
y[1] (numeric) = -0.8169748817683156 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 3.4245386051522586000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = -0.7986790588125774 " "
y[1] (numeric) = -0.7986790588125475 " "
absolute error = 2.98649993624167100000000000000E-14 " "
relative error = 3.73929916314796000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = -0.7803033686164936 " "
y[1] (numeric) = -0.7803033686164618 " "
absolute error = 3.18634008067419900000000000000E-14 " "
relative error = 4.0834631873032884000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = -0.761849648733799 " "
y[1] (numeric) = -0.761849648733765 " "
absolute error = 3.39728245535297900000000000000E-14 " "
relative error = 4.459255787541929000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = -0.7433197445211035 " "
y[1] (numeric) = -0.7433197445210676 " "
absolute error = 3.586020369539255600000000000000E-14 " "
relative error = 4.824330842778313000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = -0.724715508953387 " "
y[1] (numeric) = -0.7247155089533491 " "
absolute error = 3.78586051397178400000000000000E-14 " "
relative error = 5.2239264472747560000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = -0.7060388024387028 " "
y[1] (numeric) = -0.7060388024386629 " "
absolute error = 3.98570065840431200000000000000E-14 " "
relative error = 5.645158091364737000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = -0.6872914926321383 " "
y[1] (numeric) = -0.6872914926320965 " "
absolute error = 4.174438572590588600000000000000E-14 " "
relative error = 6.0737527196846730000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = -0.6684754542490516 " "
y[1] (numeric) = -0.6684754542490079 " "
absolute error = 4.37427871702311700000000000000E-14 " "
relative error = 6.543663928449056000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = -0.6495925688776012 " "
y[1] (numeric) = -0.6495925688775553 " "
absolute error = 4.585221091701896500000000000000E-14 " "
relative error = 7.058610752928521000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = -0.6306447247905883 " "
y[1] (numeric) = -0.6306447247905403 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 7.605174954842109000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = -0.6116338167566319 " "
y[1] (numeric) = -0.6116338167565818 " "
absolute error = 5.00710584105945600000000000000E-14 " "
relative error = 8.186443757493833000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = -0.592561745850693 " "
y[1] (numeric) = -0.5925617458506407 " "
absolute error = 5.22915044598448700000000000000E-14 " "
relative error = 8.824650734882351000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = -0.5734304192639689 " "
y[1] (numeric) = -0.5734304192639145 " "
absolute error = 5.44009282066326700000000000000E-14 " "
relative error = 9.486927511878321000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = -0.5542417501131753 " "
y[1] (numeric) = -0.5542417501131188 " "
absolute error = 5.65103519534204700000000000000E-14 " "
relative error = 1.019597530173090200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = -0.5349976572492372 " "
y[1] (numeric) = -0.5349976572491786 " "
absolute error = 5.86197757002082700000000000000E-14 " "
relative error = 1.095701540107853300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = -0.515700065065404 " "
y[1] (numeric) = -0.5157000650653433 " "
absolute error = 6.07291994469960600000000000000E-14 " "
relative error = 1.177606976630767900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = -0.4963509033048129 " "
y[1] (numeric) = -0.49635090330474996 " "
absolute error = 6.29496454962463800000000000000E-14 " "
relative error = 1.268248835191270200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = -0.4769521068675157 " "
y[1] (numeric) = -0.4769521068674506 " "
absolute error = 6.51145803942654300000000000000E-14 " "
relative error = 1.365222617883360700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = -0.45750561561699055 " "
y[1] (numeric) = -0.4575056156169232 " "
absolute error = 6.73350264435157400000000000000E-14 " "
relative error = 1.4717857911472400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = -0.4380133741861571 " "
y[1] (numeric) = -0.4380133741860876 " "
absolute error = 6.9499961341534800000000000000E-14 " "
relative error = 1.586708658626416500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = -0.41847733178291496 " "
y[1] (numeric) = -0.41847733178284335 " "
absolute error = 7.1609385088322600000000000000E-14 " "
relative error = 1.7111891051119100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = -0.3988994419952245 " "
y[1] (numeric) = -0.39889944199515076 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 1.84805495004911400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = -0.3792816625957496 " "
y[1] (numeric) = -0.3792816625956737 " "
absolute error = 7.58837437331294500000000000000E-14 " "
relative error = 2.000722713926951800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = -0.35962595534608216 " "
y[1] (numeric) = -0.3596259553460041 " "
absolute error = 7.8048678631148500000000000000E-14 " "
relative error = 2.170273793392893400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = -0.3399342858005674 " "
y[1] (numeric) = -0.3399342858004872 " "
absolute error = 8.02136135291675600000000000000E-14 " "
relative error = 2.359679999334555700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = -0.32020862310975023 " "
y[1] (numeric) = -0.3202086231096678 " "
absolute error = 8.24340595784178700000000000000E-14 " "
relative error = 2.57438599803615900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = -0.3004509398234617 " "
y[1] (numeric) = -0.3004509398233771 " "
absolute error = 8.45989944764369300000000000000E-14 " "
relative error = 2.815734060480737000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = -0.2806632116935658 " "
y[1] (numeric) = -0.28066321169347896 " "
absolute error = 8.68194405256872400000000000000E-14 " "
relative error = 3.093367313863657000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = -0.26084741747638573 " "
y[1] (numeric) = -0.2608474174762967 " "
absolute error = 8.90398865749375500000000000000E-14 " "
relative error = 3.413485455841181500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = -0.24100553873483022 " "
y[1] (numeric) = -0.24100553873473896 " "
absolute error = 9.12603326241878700000000000000E-14 " "
relative error = 3.786648767628463000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = -0.2211395596402385 " "
y[1] (numeric) = -0.22113955964014503 " "
absolute error = 9.34530230978225500000000000000E-14 " "
relative error = 4.22597491149285400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = -0.20125146677396508 " "
y[1] (numeric) = -0.20125146677386946 " "
absolute error = 9.56179579958416100000000000000E-14 " "
relative error = 4.7511682537566100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = -0.18134324892872328 " "
y[1] (numeric) = -0.1813432489286254 " "
absolute error = 9.78661596207075500000000000000E-14 " "
relative error = 5.39673575933194500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = -0.16141689690970748 " "
y[1] (numeric) = -0.16141689690960748 " "
absolute error = 1.00003338943110980000000000000E-13 " "
relative error = 6.19534515020755800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = -0.14147440333551434 " "
y[1] (numeric) = -0.14147440333541217 " "
absolute error = 1.02168273841130030000000000000E-13 " "
relative error = 7.22167907637909100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = -0.12151776243888261 " "
y[1] (numeric) = -0.12151776243877825 " "
absolute error = 1.04360964314764710000000000000E-13 " "
relative error = 8.58812425609409100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = -0.10154896986727145 " "
y[1] (numeric) = -0.1015489698671649 " "
absolute error = 1.0655365478839940000000000000E-13 " "
relative error = 1.04928346321650800000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = -8.15700224832974300E-2 " "
y[1] (numeric) = -8.15700224831886800E-2 " "
absolute error = 1.0876022304984190000000000000E-13 " "
relative error = 1.3333357002826868000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = -6.15829181650498700E-2 " "
y[1] (numeric) = -6.15829181649389000E-2 " "
absolute error = 1.10959852417380490000000000000E-13 " "
relative error = 1.80179594802562460000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = -4.15896556063047400E-2 " "
y[1] (numeric) = -4.15896556061915700E-2 " "
absolute error = 1.13166420678822990000000000000E-13 " "
relative error = 2.7210232695859987000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = -2.1592234116656900E-2 " "
y[1] (numeric) = -2.159223411654153700E-2 " "
absolute error = 1.15366050046361580000000000000E-13 " "
relative error = 5.3429417920846240000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = -1.5926534215908716000E-3 " "
y[1] (numeric) = -1.5926534214733000000E-3 " "
absolute error = 1.1757153410563159000000000000E-13 " "
relative error = 7.38211669354853000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = 1.84070865374901100E-2 " "
y[1] (numeric) = 1.840708653760988700E-2 " "
absolute error = 1.19775717122294620000000000000E-13 " "
relative error = 6.5070437343978820000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = 3.84049858032565300E-2 " "
y[1] (numeric) = 3.84049858033785100E-2 " "
absolute error = 1.21978815936785170000000000000E-13 " "
relative error = 3.17611928205535350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = 5.83990446024466800E-2 " "
y[1] (numeric) = 5.83990446025708700E-2 " "
absolute error = 1.24192323092131570000000000000E-13 " "
relative error = 2.1266156653345047000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = 7.83872635458422900E-2 " "
y[1] (numeric) = 7.83872635459686900E-2 " "
absolute error = 1.26398891353574070000000000000E-13 " "
relative error = 1.61249271419780770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = 9.83676438282058200E-2 " "
y[1] (numeric) = 9.83676438283344200E-2 " "
absolute error = 1.28605459615016570000000000000E-13 " "
relative error = 1.30739595470660640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = 0.1183381874281593 " "
y[1] (numeric) = 0.11833818742829011 " "
absolute error = 1.30812027876459070000000000000E-13 " "
relative error = 1.10540841227496730000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = 0.13829689730798478 " "
y[1] (numeric) = 0.1382968973081178 " "
absolute error = 1.33032473925709380000000000000E-13 " "
relative error = 9.61933901014773900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = 0.1582417776133265 " "
y[1] (numeric) = 0.15824177761346175 " "
absolute error = 1.3525291997495970000000000000E-13 " "
relative error = 8.54723209097527400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = 0.1781708338727746 " "
y[1] (numeric) = 0.17817083387291202 " "
absolute error = 1.37417854872978750000000000000E-13 " "
relative error = 7.71270201109929700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = 0.19808207319731064 " "
y[1] (numeric) = 0.19808207319745022 " "
absolute error = 1.3958278977099780000000000000E-13 " "
relative error = 7.04671490549064500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = 0.2179735044795948 " "
y[1] (numeric) = 0.2179735044797365 " "
absolute error = 1.41719969093401230000000000000E-13 " "
relative error = 6.50170622488056100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = 0.23784313859307496 " "
y[1] (numeric) = 0.2378431385932189 " "
absolute error = 1.43940415142651550000000000000E-13 " "
relative error = 6.05190530170890300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = 0.2576889885908978 " "
y[1] (numeric) = 0.2576889885910439 " "
absolute error = 1.4610535004067060000000000000E-13 " "
relative error = 5.66983288031079700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = 0.2775090699046016 " "
y[1] (numeric) = 0.27750906990474994 " "
absolute error = 1.48325796089920900000000000000E-13 " "
relative error = 5.34489903846783700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = 0.2973014005425718 " "
y[1] (numeric) = 0.2973014005427223 " "
absolute error = 1.50490730987939970000000000000E-13 " "
relative error = 5.06189108807748700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = 0.3170640012882381 " "
y[1] (numeric) = 0.31706400128839074 " "
absolute error = 1.52655665885959020000000000000E-13 " "
relative error = 4.81466408251064900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = 0.33679489589799466 " "
y[1] (numeric) = 0.3367948958981495 " "
absolute error = 1.54820600783978080000000000000E-13 " "
relative error = 4.596880851509957000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 0.3564921112988229 " "
y[1] (numeric) = 0.35649211129897984 " "
absolute error = 1.56930024530765880000000000000E-13 " "
relative error = 4.402061632135871000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 0.3761536777855971 " "
y[1] (numeric) = 0.3761536777857562 " "
absolute error = 1.59094959428784930000000000000E-13 " "
relative error = 4.229520241975862600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 0.39577762921805304 " "
y[1] (numeric) = 0.3957776292182143 " "
absolute error = 1.612598943268040000000000000E-13 " "
relative error = 4.07450756237559100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 0.4153620032174008 " "
y[1] (numeric) = 0.4153620032175643 " "
absolute error = 1.6348034037605430000000000000E-13 " "
relative error = 3.93585207866229860000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 0.4349048413625607 " "
y[1] (numeric) = 0.4349048413627263 " "
absolute error = 1.6558976412284210000000000000E-13 " "
relative error = 3.807494154446473500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 0.4544041893860038 " "
y[1] (numeric) = 0.4544041893861716 " "
absolute error = 1.6781021017209240000000000000E-13 " "
relative error = 3.692972338103649400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 0.4738580973691772 " "
y[1] (numeric) = 0.47385809736934714 " "
absolute error = 1.6991963391888020000000000000E-13 " "
relative error = 3.585875916487670000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 0.49326461993749415 " "
y[1] (numeric) = 0.4932646199376662 " "
absolute error = 1.720290576656680000000000000E-13 " "
relative error = 3.48756125439256700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 0.5126218164548698 " "
y[1] (numeric) = 0.512621816455044 " "
absolute error = 1.74193992563687060000000000000E-13 " "
relative error = 3.39809947552286330000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 0.5319277512177835 " "
y[1] (numeric) = 0.5319277512179598 " "
absolute error = 1.76303416310474860000000000000E-13 " "
relative error = 3.31442410941805100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 0.551180493648847 " "
y[1] (numeric) = 0.5511804936490252 " "
absolute error = 1.78190795452337620000000000000E-13 " "
relative error = 3.23289371640683700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 0.5703781184898612 " "
y[1] (numeric) = 0.5703781184900415 " "
absolute error = 1.80300219199125420000000000000E-13 " "
relative error = 3.16106479814636130000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 0.58951870599434 " "
y[1] (numeric) = 0.5895187059945224 " "
absolute error = 1.82409642945913220000000000000E-13 " "
relative error = 3.094212975621244400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 0.6086003421194832 " "
y[1] (numeric) = 0.6086003421196676 " "
absolute error = 1.8440804439023850000000000000E-13 " "
relative error = 3.03003517461110200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 0.6276211187175799 " "
y[1] (numeric) = 0.6276211187177662 " "
absolute error = 1.86295423532101270000000000000E-13 " "
relative error = 2.968278440227748400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 0.6465791337268205 " "
y[1] (numeric) = 0.6465791337270087 " "
absolute error = 1.88182802673964030000000000000E-13 " "
relative error = 2.91043729774105640000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 0.6654724913615027 " "
y[1] (numeric) = 0.665472491361693 " "
absolute error = 1.90292226420751830000000000000E-13 " "
relative error = 2.859505522631437500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 0.6842993023016073 " "
y[1] (numeric) = 0.6842993023017998 " "
absolute error = 1.92512672470002140000000000000E-13 " "
relative error = 2.813281729536990500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 0.7030576838817293 " "
y[1] (numeric) = 0.7030576838819238 " "
absolute error = 1.94511073914327430000000000000E-13 " "
relative error = 2.76664459223873200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 0.7217457602793426 " "
y[1] (numeric) = 0.7217457602795392 " "
absolute error = 1.96620497661115220000000000000E-13 " "
relative error = 2.724234882724018700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 0.7403616627023807 " "
y[1] (numeric) = 0.7403616627025793 " "
absolute error = 1.9861889910544050000000000000E-13 " "
relative error = 2.68272803835446100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 0.7589035295761146 " "
y[1] (numeric) = 0.7589035295763153 " "
absolute error = 2.0072832285222830000000000000E-13 " "
relative error = 2.64497811684108300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = 0.7773695067293085 " "
y[1] (numeric) = 0.7773695067295112 " "
absolute error = 2.02726724296553580000000000000E-13 " "
relative error = 2.607855370472436000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = 0.7957577475796351 " "
y[1] (numeric) = 0.7957577475798399 " "
absolute error = 2.04725125740878870000000000000E-13 " "
relative error = 2.572706660583170000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = 0.8140664133183331 " "
y[1] (numeric) = 0.8140664133185398 " "
absolute error = 2.06723527185204150000000000000E-13 " "
relative error = 2.539393884861908500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = 0.8322936730940858 " "
y[1] (numeric) = 0.8322936730942944 " "
absolute error = 2.08610906327066910000000000000E-13 " "
relative error = 2.50645791348560100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 0.850437704196105 " "
y[1] (numeric) = 0.8504377041963154 " "
absolute error = 2.10387263166467160000000000000E-13 " "
relative error = 2.473870362619215700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 0.8684966922364001 " "
y[1] (numeric) = 0.8684966922366123 " "
absolute error = 2.12163620005867410000000000000E-13 " "
relative error = 2.442883454852786000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 0.8864688313312163 " "
y[1] (numeric) = 0.8864688313314306 " "
absolute error = 2.1427304375265520000000000000E-13 " "
relative error = 2.417152596678214500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 0.9043523242816212 " "
y[1] (numeric) = 0.9043523242818374 " "
absolute error = 2.1627144519698050000000000000E-13 " "
relative error = 2.391451200932969400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 0.9221453827532221 " "
y[1] (numeric) = 0.9221453827534404 " "
absolute error = 2.18269846641305780000000000000E-13 " "
relative error = 2.366978686046488400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 0.9398462274549998 " "
y[1] (numeric) = 0.93984622745522 " "
absolute error = 2.20157225783168540000000000000E-13 " "
relative error = 2.342481348032114700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 0.9574530883172345 " "
y[1] (numeric) = 0.9574530883174567 " "
absolute error = 2.22155627227493820000000000000E-13 " "
relative error = 2.32027688811304600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 0.9749642046685125 " "
y[1] (numeric) = 0.9749642046687367 " "
absolute error = 2.2415402867181910000000000000E-13 " "
relative error = 2.299100085915783700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 0.9923778254117911 " "
y[1] (numeric) = 0.992377825412017 " "
absolute error = 2.25930385511219360000000000000E-13 " "
relative error = 2.276656931723244300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 1.0096922091995073 " "
y[1] (numeric) = 1.0096922091997353 " "
absolute error = 2.28039809258007150000000000000E-13 " "
relative error = 2.258508159024016400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 1.0269056246077108 " "
y[1] (numeric) = 1.0269056246079409 " "
absolute error = 2.30038210702332440000000000000E-13 " "
relative error = 2.240110533917949500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 1.0440163503092057 " "
y[1] (numeric) = 1.0440163503094375 " "
absolute error = 2.3181456754173269000000000000E-13 " "
relative error = 2.220411274910362200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 1.0610226752456802 " "
y[1] (numeric) = 1.061022675245914 " "
absolute error = 2.33812968986057970000000000000E-13 " "
relative error = 2.20365666484854800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = 1.0779228987988128 " "
y[1] (numeric) = 1.0779228987990481 " "
absolute error = 2.3536728122053320000000000000E-13 " "
relative error = 2.18352612680197800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 1.0947153309603317 " "
y[1] (numeric) = 1.0947153309605686 " "
absolute error = 2.3692159345500840000000000000E-13 " "
relative error = 2.16423015878630800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 1.1113982925010142 " "
y[1] (numeric) = 1.1113982925012527 " "
absolute error = 2.3847590568948362000000000000E-13 " "
relative error = 2.145728559226358600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 1.127970115138609 " "
y[1] (numeric) = 1.1279701151388488 " "
absolute error = 2.3980817331903380000000000000E-13 " "
relative error = 2.12601530927586100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 1.1444291417046617 " "
y[1] (numeric) = 1.1444291417049033 " "
absolute error = 2.41584530158434060000000000000E-13 " "
relative error = 2.110961014140085900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 1.1607737263102318 " "
y[1] (numeric) = 1.1607737263104754 " "
absolute error = 2.43582931602759340000000000000E-13 " "
relative error = 2.098453178958830700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 1.1770022345104791 " "
y[1] (numeric) = 1.1770022345107245 " "
absolute error = 2.4535928844215960000000000000E-13 " "
relative error = 2.084611917021599300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 1.1931130434681074 " "
y[1] (numeric) = 1.1931130434683546 " "
absolute error = 2.47135645281559850000000000000E-13 " "
relative error = 2.071351466942251400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 1.2091045421156463 " "
y[1] (numeric) = 1.2091045421158952 " "
absolute error = 2.4891200212096010000000000000E-13 " "
relative error = 2.05864748208970500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 1.2249751313165576 " "
y[1] (numeric) = 1.224975131316808 " "
absolute error = 2.5046631435543530000000000000E-13 " "
relative error = 2.044664482994389000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 1.2407232240251465 " "
y[1] (numeric) = 1.2407232240253987 " "
absolute error = 2.52242671194835570000000000000E-13 " "
relative error = 2.033029335716885200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 1.2563472454452653 " "
y[1] (numeric) = 1.2563472454455198 " "
absolute error = 2.5446311724408590000000000000E-13 " "
relative error = 2.02542026630464700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 1.2718456331877923 " "
y[1] (numeric) = 1.271845633188048 " "
absolute error = 2.55795384873636070000000000000E-13 " "
relative error = 2.011214082895443600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 1.2872168374268682 " "
y[1] (numeric) = 1.287216837427126 " "
absolute error = 2.57793786317961350000000000000E-13 " "
relative error = 2.002722298391374500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 1.3024593210548787 " "
y[1] (numeric) = 1.3024593210551378 " "
absolute error = 2.59126053947511540000000000000E-13 " "
relative error = 1.989513605212959400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = 1.317571559836163 " "
y[1] (numeric) = 1.3175715598364233 " "
absolute error = 2.6023627697213670000000000000E-13 " "
relative error = 1.975120630294239500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = 1.3325520425594362 " "
y[1] (numeric) = 1.3325520425596982 " "
absolute error = 2.62012633811536940000000000000E-13 " "
relative error = 1.966246911514904800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = 1.3473992711889098 " "
y[1] (numeric) = 1.3473992711891736 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 1.957764088874537300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = 1.3621117610140936 " "
y[1] (numeric) = 1.362111761014359 " "
absolute error = 2.6534330288541240000000000000E-13 " "
relative error = 1.94802886576549400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = 1.3766880407982653 " "
y[1] (numeric) = 1.376688040798532 " "
absolute error = 2.6667557051496260000000000000E-13 " "
relative error = 1.937080606586312500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = 1.3911266529255935 " "
y[1] (numeric) = 1.391126652925862 " "
absolute error = 2.68451927354362850000000000000E-13 " "
relative error = 1.929744691396703400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = 1.4054261535468975 " "
y[1] (numeric) = 1.4054261535471677 " "
absolute error = 2.7022828419376310000000000000E-13 " "
relative error = 1.922749790245353600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = 1.4195851127240313 " "
y[1] (numeric) = 1.419585112724303 " "
absolute error = 2.7178259642823830000000000000E-13 " "
relative error = 1.914521320294185800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = 1.4336021145728766 " "
y[1] (numeric) = 1.43360211457315 " "
absolute error = 2.73336908662713540000000000000E-13 " "
relative error = 1.906644151010831700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = 1.4474757574049288 " "
y[1] (numeric) = 1.4474757574052037 " "
absolute error = 2.74891220897188760000000000000E-13 " "
relative error = 1.899107598112873800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = 1.4612046538674666 " "
y[1] (numeric) = 1.4612046538677428 " "
absolute error = 2.76223488526738950000000000000E-13 " "
relative error = 1.890381937914309400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = 1.474787431082284 " "
y[1] (numeric) = 1.4747874310825617 " "
absolute error = 2.77777800761214170000000000000E-13 " "
relative error = 1.883510768445896300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = 1.4882227307829785 " "
y[1] (numeric) = 1.4882227307832578 " "
absolute error = 2.7933211299568940000000000000E-13 " "
relative error = 1.876950991393124300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = 1.5015092094507765 " "
y[1] (numeric) = 1.5015092094510571 " "
absolute error = 2.80664380625239600000000000000E-13 " "
relative error = 1.86921517935878200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = 1.5146455384488828 " "
y[1] (numeric) = 1.5146455384491648 " "
absolute error = 2.81996648254789760000000000000E-13 " "
relative error = 1.861799616454003200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = 1.5276304041553446 " "
y[1] (numeric) = 1.5276304041556283 " "
absolute error = 2.83773005094190000000000000E-13 " "
relative error = 1.85760249548773180000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = 1.540462508094412 " "
y[1] (numeric) = 1.5404625080946974 " "
absolute error = 2.85327317328665230000000000000E-13 " "
relative error = 1.852218511190004700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = 1.5531405670663847 " "
y[1] (numeric) = 1.5531405670666711 " "
absolute error = 2.8643754035329040000000000000E-13 " "
relative error = 1.844247368377748600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = 1.5656633132759301 " "
y[1] (numeric) = 1.5656633132762174 " "
absolute error = 2.8732571877299050000000000000E-13 " "
relative error = 1.835169262360768500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = 1.578029494458863 " "
y[1] (numeric) = 1.5780294944591515 " "
absolute error = 2.88435941797615670000000000000E-13 " "
relative error = 1.82782351540600300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = 1.5902378740073704 " "
y[1] (numeric) = 1.5902378740076597 " "
absolute error = 2.8932412021731580000000000000E-13 " "
relative error = 1.819376364670678400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = 1.6022872310936707 " "
y[1] (numeric) = 1.602287231093961 " "
absolute error = 2.90434343241940950000000000000E-13 " "
relative error = 1.812623464793510500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = 1.6141763607920967 " "
y[1] (numeric) = 1.6141763607923885 " "
absolute error = 2.91766610871491140000000000000E-13 " "
relative error = 1.807526227978692400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = 1.625904074199586 " "
y[1] (numeric) = 1.6259040741998794 " "
absolute error = 2.93320923105966360000000000000E-13 " "
relative error = 1.804048146262041000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = 1.6374691985545708 " "
y[1] (numeric) = 1.6374691985548655 " "
absolute error = 2.94653190735516550000000000000E-13 " "
relative error = 1.79944264597839900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = 1.6488705773542536 " "
y[1] (numeric) = 1.6488705773545493 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 1.79373334585615600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = 1.660107070470255 " "
y[1] (numeric) = 1.660107070470552 " "
absolute error = 2.9709568138969190000000000000E-13 " "
relative error = 1.78961758957832900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = 1.6711775542626275 " "
y[1] (numeric) = 1.6711775542629255 " "
absolute error = 2.979838598093920000000000000E-13 " "
relative error = 1.783077202355504400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = 1.682080921692217 " "
y[1] (numeric) = 1.682080921692516 " "
absolute error = 2.99094082834017170000000000000E-13 " "
relative error = 1.77811946486570200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = 1.6928160824313667 " "
y[1] (numeric) = 1.692816082431667 " "
absolute error = 3.00204305858642330000000000000E-13 " "
relative error = 1.773401782829610600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = 1.7033819629729487 " "
y[1] (numeric) = 1.7033819629732498 " "
absolute error = 3.01092484278342450000000000000E-13 " "
relative error = 1.767615783325774700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = 1.7137775067377137 " "
y[1] (numeric) = 1.713777506738016 " "
absolute error = 3.02424751907892640000000000000E-13 " "
relative error = 1.76466752958835200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = 1.7240016741799482 " "
y[1] (numeric) = 1.7240016741802513 " "
absolute error = 3.03090885722667740000000000000E-13 " "
relative error = 1.75806607535249800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = 1.7340534428914278 " "
y[1] (numeric) = 1.734053442891732 " "
absolute error = 3.0420110874729290000000000000E-13 " "
relative error = 1.754277585816825500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = 1.7439318077036583 " "
y[1] (numeric) = 1.7439318077039636 " "
absolute error = 3.05311331771918050000000000000E-13 " "
relative error = 1.750706824792307700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = 1.75363578078839 " "
y[1] (numeric) = 1.7536357807886962 " "
absolute error = 3.06199510191618200000000000000E-13 " "
relative error = 1.746083842187336200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = 1.763164391756401 " "
y[1] (numeric) = 1.7631643917567086 " "
absolute error = 3.07531777821168360000000000000E-13 " "
relative error = 1.744203655989310400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = 1.7725166877545355 " "
y[1] (numeric) = 1.7725166877548442 " "
absolute error = 3.0864200084579350000000000000E-13 " "
relative error = 1.741264288105452100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = 1.7816917335609868 " "
y[1] (numeric) = 1.7816917335612963 " "
absolute error = 3.09530179265493640000000000000E-13 " "
relative error = 1.737282457088408200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = 1.79068861167882 " "
y[1] (numeric) = 1.7906886116791303 " "
absolute error = 3.10196313080268740000000000000E-13 " "
relative error = 1.732273892050115400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = 1.799506422427721 " "
y[1] (numeric) = 1.7995064224280322 " "
absolute error = 3.11084491499968860000000000000E-13 " "
relative error = 1.72872120723127800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = 1.808144284033963 " "
y[1] (numeric) = 1.8081442840342754 " "
absolute error = 3.12416759129519050000000000000E-13 " "
relative error = 1.727830914204028200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = 1.8166013327185835 " "
y[1] (numeric) = 1.816601332718897 " "
absolute error = 3.1352698215414420000000000000E-13 " "
relative error = 1.725898668614011500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = 1.8248767227837617 " "
y[1] (numeric) = 1.824876722784076 " "
absolute error = 3.14415160573844330000000000000E-13 " "
relative error = 1.722939180758572800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = 1.832969626697387 " "
y[1] (numeric) = 1.8329696266977022 " "
absolute error = 3.15303338993544460000000000000E-13 " "
relative error = 1.720177652706949300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = 1.840879235175812 " "
y[1] (numeric) = 1.840879235176128 " "
absolute error = 3.15969472808319550000000000000E-13 " "
relative error = 1.716405219694615600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = 1.8486047572647806 " "
y[1] (numeric) = 1.8486047572650974 " "
absolute error = 3.1685765122801970000000000000E-13 " "
relative error = 1.714036761956873600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = 1.8561454204185217 " "
y[1] (numeric) = 1.8561454204188388 " "
absolute error = 3.1707969583294470000000000000E-13 " "
relative error = 1.708269688058438300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = 1.8635004705770035 " "
y[1] (numeric) = 1.8635004705773215 " "
absolute error = 3.17967874252644830000000000000E-13 " "
relative error = 1.706293501252463300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = 1.8706691722413396 " "
y[1] (numeric) = 1.8706691722416582 " "
absolute error = 3.18634008067419900000000000000E-13 " "
relative error = 1.703315651936729600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = 1.8776508085473373 " "
y[1] (numeric) = 1.8776508085476566 " "
absolute error = 3.193001418821950000000000000E-13 " "
relative error = 1.700529941076874600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = 1.884444681337184 " "
y[1] (numeric) = 1.884444681337504 " "
absolute error = 3.1996627569697010000000000000E-13 " "
relative error = 1.69793403258685800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = 1.8910501112292626 " "
y[1] (numeric) = 1.8910501112295832 " "
absolute error = 3.2063240951174520000000000000E-13 " "
relative error = 1.695525716678764300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = 1.8974664376860881 " "
y[1] (numeric) = 1.8974664376864097 " "
absolute error = 3.21520587931445330000000000000E-13 " "
relative error = 1.694473122399632600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = 1.9036930190803616 " "
y[1] (numeric) = 1.903693019080684 " "
absolute error = 3.22408766351145460000000000000E-13 " "
relative error = 1.693596410344011500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = 1.9097292327591329 " "
y[1] (numeric) = 1.9097292327594562 " "
absolute error = 3.2329694477084560000000000000E-13 " "
relative error = 1.69289415077839900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = 1.915574475106064 " "
y[1] (numeric) = 1.9155744751063877 " "
absolute error = 3.23741033980695650000000000000E-13 " "
relative error = 1.6900467102056700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = 1.9212281616017912 " "
y[1] (numeric) = 1.921228161602115 " "
absolute error = 3.23741033980695650000000000000E-13 " "
relative error = 1.68507333200228600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = 1.9266897268823764 " "
y[1] (numeric) = 1.9266897268827008 " "
absolute error = 3.24407167795470740000000000000E-13 " "
relative error = 1.683754074509972400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = 1.931958624795843 " "
y[1] (numeric) = 1.9319586247961675 " "
absolute error = 3.24629212400395800000000000000E-13 " "
relative error = 1.680311411610590500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = 1.93703432845679 " "
y[1] (numeric) = 1.937034328457115 " "
absolute error = 3.25073301610245840000000000000E-13 " "
relative error = 1.678201035648281500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = 1.9419163302990814 " "
y[1] (numeric) = 1.941916330299407 " "
absolute error = 3.2551739082009590000000000000E-13 " "
relative error = 1.67626887802092800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = 1.946604142126601 " "
y[1] (numeric) = 1.9466041421269271 " "
absolute error = 3.261835246348710000000000000E-13 " "
relative error = 1.675654117732053300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = 1.9510972951620729 " "
y[1] (numeric) = 1.9510972951623995 " "
absolute error = 3.26627613844721050000000000000E-13 " "
relative error = 1.674071378473152600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = 1.9553953400939375 " "
y[1] (numeric) = 1.9553953400942647 " "
absolute error = 3.27293747659496150000000000000E-13 " "
relative error = 1.673798341177252200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = 1.9594978471212834 " "
y[1] (numeric) = 1.9594978471216113 " "
absolute error = 3.27959881474271240000000000000E-13 " "
relative error = 1.673693502425022700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = 1.9634044059968265 " "
y[1] (numeric) = 1.9634044059971554 " "
absolute error = 3.28848059893971370000000000000E-13 " "
relative error = 1.674887042575491400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = 1.967114626067935 " "
y[1] (numeric) = 1.9671146260682641 " "
absolute error = 3.2907010449889640000000000000E-13 " "
relative error = 1.672856782914956800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = 1.9706281363156937 " "
y[1] (numeric) = 1.970628136316023 " "
absolute error = 3.29292149103821430000000000000E-13 " "
relative error = 1.671000951602514600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = 1.9739445853920052 " "
y[1] (numeric) = 1.973944585392335 " "
absolute error = 3.2973623831367150000000000000E-13 " "
relative error = 1.67044323712962380000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = 1.977063641654726 " "
y[1] (numeric) = 1.9770636416550562 " "
absolute error = 3.30180327523521560000000000000E-13 " "
relative error = 1.67005411746469300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = 1.979984993200829 " "
y[1] (numeric) = 1.9799849932011593 " "
absolute error = 3.30180327523521560000000000000E-13 " "
relative error = 1.667590050719296200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = 1.9827083478975938 " "
y[1] (numeric) = 1.9827083478979242 " "
absolute error = 3.3040237212844660000000000000E-13 " "
relative error = 1.66641943318993800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = 1.9852334334118205 " "
y[1] (numeric) = 1.9852334334121513 " "
absolute error = 3.30846461338296650000000000000E-13 " "
relative error = 1.66653682015471700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = 1.9875599972370617 " "
y[1] (numeric) = 1.9875599972373927 " "
absolute error = 3.3106850594322170000000000000E-13 " "
relative error = 1.665703205958286600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = 1.9896878067188735 " "
y[1] (numeric) = 1.9896878067192052 " "
absolute error = 3.31734639757996800000000000000E-13 " "
relative error = 1.667269803020249300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = 1.9916166490780813 " "
y[1] (numeric) = 1.991616649078413 " "
absolute error = 3.31734639757996800000000000000E-13 " "
relative error = 1.665655084333406400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = 1.9933463314320563 " "
y[1] (numeric) = 1.993346331432388 " "
absolute error = 3.31734639757996800000000000000E-13 " "
relative error = 1.664209748838138800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = 1.9948766808140046 " "
y[1] (numeric) = 1.9948766808143368 " "
absolute error = 3.32178728967846840000000000000E-13 " "
relative error = 1.665159215918560500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = 1.9962075441902631 " "
y[1] (numeric) = 1.9962075441905953 " "
absolute error = 3.32178728967846840000000000000E-13 " "
relative error = 1.664049061103969600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = 1.9973387884756035 " "
y[1] (numeric) = 1.9973387884759357 " "
absolute error = 3.32178728967846840000000000000E-13 " "
relative error = 1.663106584043111400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = 1.9982703005465399 " "
y[1] (numeric) = 1.9982703005468725 " "
absolute error = 3.3262281817769690000000000000E-13 " "
relative error = 1.664553679683486200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = 1.9990019872526412 " "
y[1] (numeric) = 1.999001987252974 " "
absolute error = 3.32844862782621930000000000000E-13 " "
relative error = 1.665055187063982600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = 1.9995337754258466 " "
y[1] (numeric) = 1.9995337754261802 " "
absolute error = 3.335109965973970000000000000E-13 " "
relative error = 1.66794380118119420000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = 1.9998656118877822 " "
y[1] (numeric) = 1.999865611888116 " "
absolute error = 3.33733041202322060000000000000E-13 " "
relative error = 1.668777337929688300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = 1.9999974634550783 " "
y[1] (numeric) = 1.9999974634554119 " "
absolute error = 3.335109965973970000000000000E-13 " "
relative error = 1.667557097903729000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = 1.999929316942688 " "
y[1] (numeric) = 1.9999293169430212 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.666503656749100400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = 1.9996611791652055 " "
y[1] (numeric) = 1.9996611791655388 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.666727120899598700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = 1.9991930769361852 " "
y[1] (numeric) = 1.9991930769365185 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.667117377693434000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = 1.9985250570654602 " "
y[1] (numeric) = 1.9985250570657935 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.667674622413079800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 1.9976571863544605 " "
y[1] (numeric) = 1.9976571863547938 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.668399134091137500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 1.9965895515895344 " "
y[1] (numeric) = 1.996589551589868 " "
absolute error = 3.335109965973970000000000000E-13 " "
relative error = 1.670403395289135300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 1.9953222595332682 " "
y[1] (numeric) = 1.9953222595336022 " "
absolute error = 3.3395508580724710000000000000E-13 " "
relative error = 1.673689972693250500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 1.993855436913812 " "
y[1] (numeric) = 1.9938554369141457 " "
absolute error = 3.33733041202322060000000000000E-13 " "
relative error = 1.673807614251565400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 1.992189230412205 " "
y[1] (numeric) = 1.9921892304125386 " "
absolute error = 3.335109965973970000000000000E-13 " "
relative error = 1.67409296017723200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 1.990323806647709 " "
y[1] (numeric) = 1.9903238066480426 " "
absolute error = 3.33733041202322060000000000000E-13 " "
relative error = 1.676777618233018800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 1.9882593521611458 " "
y[1] (numeric) = 1.988259352161479 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.676285096459887700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 1.985996073396244 " "
y[1] (numeric) = 1.9859960733965774 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.678195422725664900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 1.9835341966789937 " "
y[1] (numeric) = 1.983534196679327 " "
absolute error = 3.332889519924720000000000000E-13 " "
relative error = 1.680278326184108700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 1.9808739681950152 " "
y[1] (numeric) = 1.9808739681953482 " "
absolute error = 3.33066907387546960000000000000E-13 " "
relative error = 1.681413925041579700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 1.97801565396494 " "
y[1] (numeric) = 1.9780156539652727 " "
absolute error = 3.3262281817769690000000000000E-13 " "
relative error = 1.681598512685949200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 1.9749595398178095 " "
y[1] (numeric) = 1.9749595398181419 " "
absolute error = 3.32400773572771870000000000000E-13 " "
relative error = 1.683076371293337500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 1.9717059313624912 " "
y[1] (numeric) = 1.9717059313628231 " "
absolute error = 3.3195668436292180000000000000E-13 " "
relative error = 1.683601388435914400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 1.9682551539571194 " "
y[1] (numeric) = 1.9682551539574513 " "
absolute error = 3.3195668436292180000000000000E-13 " "
relative error = 1.686553106163764500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 1.9646075526765592 " "
y[1] (numeric) = 1.964607552676891 " "
absolute error = 3.31734639757996800000000000000E-13 " "
relative error = 1.688554232147001800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 1.960763492277899 " "
y[1] (numeric) = 1.9607634922782302 " "
absolute error = 3.3129055054814670000000000000E-13 " "
relative error = 1.689599749550992300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 1.9567233571639748 " "
y[1] (numeric) = 1.956723357164306 " "
absolute error = 3.3106850594322170000000000000E-13 " "
relative error = 1.691953564775063300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 1.952487551344932 " "
y[1] (numeric) = 1.9524875513452626 " "
absolute error = 3.3062441673337160000000000000E-13 " "
relative error = 1.693349678494121800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 1.9480564983978221 " "
y[1] (numeric) = 1.9480564983981523 " "
absolute error = 3.30180327523521560000000000000E-13 " "
relative error = 1.694921722214310400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 1.9434306414242475 " "
y[1] (numeric) = 1.9434306414245772 " "
absolute error = 3.2973623831367150000000000000E-13 " "
relative error = 1.696670986272108800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 1.9386104430060507 " "
y[1] (numeric) = 1.9386104430063802 " "
absolute error = 3.29514193708746460000000000000E-13 " "
relative error = 1.69974424153928900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 1.9335963851590567 " "
y[1] (numeric) = 1.9335963851593858 " "
absolute error = 3.2907010449889640000000000000E-13 " "
relative error = 1.70185519079684900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 1.9283889692848717 " "
y[1] (numeric) = 1.9283889692852 " "
absolute error = 3.2840397068412130000000000000E-13 " "
relative error = 1.702996521525983500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 1.9229887161207437 " "
y[1] (numeric) = 1.9229887161210717 " "
absolute error = 3.27959881474271240000000000000E-13 " "
relative error = 1.705469609493427700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 1.917396165687489 " "
y[1] (numeric) = 1.917396165687816 " "
absolute error = 3.2707170305457110000000000000E-13 " "
relative error = 1.70581181347725490000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 1.9116118772354902 " "
y[1] (numeric) = 1.9116118772358168 " "
absolute error = 3.26627613844721050000000000000E-13 " "
relative error = 1.708650263865691700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 1.9056364291887726 " "
y[1] (numeric) = 1.9056364291890988 " "
absolute error = 3.261835246348710000000000000E-13 " "
relative error = 1.711677629786532700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 1.8994704190871614 " "
y[1] (numeric) = 1.8994704190874867 " "
absolute error = 3.25295346215170870000000000000E-13 " "
relative error = 1.712558105387604600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 1.893114463526528 " "
y[1] (numeric) = 1.8931144635268524 " "
absolute error = 3.24407167795470740000000000000E-13 " "
relative error = 1.713616234230016500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 1.8865691980971324 " "
y[1] (numeric) = 1.886569198097456 " "
absolute error = 3.2351898937577060000000000000E-13 " "
relative error = 1.714853553752942200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 1.8798352773200626 " "
y[1] (numeric) = 1.8798352773203857 " "
absolute error = 3.23074900165920550000000000000E-13 " "
relative error = 1.718634095570882600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 1.8729133745817852 " "
y[1] (numeric) = 1.8729133745821074 " "
absolute error = 3.22186721746220430000000000000E-13 " "
relative error = 1.720243584774248400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 1.8658041820668056 " "
y[1] (numeric) = 1.8658041820671267 " "
absolute error = 3.21076498721595270000000000000E-13 " "
relative error = 1.720847781388985300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 1.8585084106884509 " "
y[1] (numeric) = 1.858508410688771 " "
absolute error = 3.20188320301895150000000000000E-13 " "
relative error = 1.722824166199426500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 1.8510267900177793 " "
y[1] (numeric) = 1.8510267900180983 " "
absolute error = 3.19078097277270000000000000E-13 " "
relative error = 1.72378973118052610000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 1.843360068210623 " "
y[1] (numeric) = 1.8433600682109414 " "
absolute error = 3.1841196346249490000000000000E-13 " "
relative error = 1.72734545438852920000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 1.8355090119327742 " "
y[1] (numeric) = 1.8355090119330915 " "
absolute error = 3.17301740437869740000000000000E-13 " "
relative error = 1.7286852768091499000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 1.8274744062833177 " "
y[1] (numeric) = 1.8274744062836343 " "
absolute error = 3.16635606623094650000000000000E-13 " "
relative error = 1.73264044374258600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 1.8192570547161233 " "
y[1] (numeric) = 1.819257054716439 " "
absolute error = 3.1574742820339450000000000000E-13 " "
relative error = 1.73558446501483400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 1.8108577789594997 " "
y[1] (numeric) = 1.810857778959815 " "
absolute error = 3.15303338993544460000000000000E-13 " "
relative error = 1.74118223229388300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 1.8022774189340236 " "
y[1] (numeric) = 1.8022774189343378 " "
absolute error = 3.1419311596891930000000000000E-13 " "
relative error = 1.743311616003890300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 1.7935168326685467 " "
y[1] (numeric) = 1.7935168326688602 " "
absolute error = 3.1352698215414420000000000000E-13 " "
relative error = 1.748112849811685700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 1.7845768962143953 " "
y[1] (numeric) = 1.7845768962147077 " "
absolute error = 3.12416759129519050000000000000E-13 " "
relative error = 1.75064890614826100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 1.7754585035577652 " "
y[1] (numeric) = 1.7754585035580766 " "
absolute error = 3.1130653610489390000000000000E-13 " "
relative error = 1.753386719436585100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 1.766162566530323 " "
y[1] (numeric) = 1.7661625665306333 " "
absolute error = 3.10196313080268740000000000000E-13 " "
relative error = 1.75632933773281300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 1.756690014718025 " "
y[1] (numeric) = 1.7566900147183344 " "
absolute error = 3.0930813466056860000000000000E-13 " "
relative error = 1.760743967741042700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 1.747041795368159 " "
y[1] (numeric) = 1.7470417953684672 " "
absolute error = 3.08197911635943460000000000000E-13 " "
relative error = 1.7641129848928203000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 1.7372188732946192 " "
y[1] (numeric) = 1.7372188732949265 " "
absolute error = 3.07309733216243330000000000000E-13 " "
relative error = 1.76897533143554500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 1.7272222307814278 " "
y[1] (numeric) = 1.7272222307817342 " "
absolute error = 3.0642155479654320000000000000E-13 " "
relative error = 1.77407139241087900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 1.7170528674845051 " "
y[1] (numeric) = 1.7170528674848107 " "
absolute error = 3.0553337637684310000000000000E-13 " "
relative error = 1.77940576066508480000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 1.7067118003317068 " "
y[1] (numeric) = 1.7067118003320112 " "
absolute error = 3.0442315335221790000000000000E-13 " "
relative error = 1.783682243792138500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 1.6962000634211305 " "
y[1] (numeric) = 1.6962000634214338 " "
absolute error = 3.03312930327592770000000000000E-13 " "
relative error = 1.788190773415191400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 1.6855187079177074 " "
y[1] (numeric) = 1.6855187079180096 " "
absolute error = 3.0220270730296760000000000000E-13 " "
relative error = 1.792935942409736300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 1.6746688019480866 " "
y[1] (numeric) = 1.674668801948388 " "
absolute error = 3.0131452888326750000000000000E-13 " "
relative error = 1.799248475476215300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 1.6636514304938241 " "
y[1] (numeric) = 1.6636514304941241 " "
absolute error = 2.9998226125371730000000000000E-13 " "
relative error = 1.80315573175489700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 1.6524676952828836 " "
y[1] (numeric) = 1.6524676952831827 " "
absolute error = 2.99094082834017170000000000000E-13 " "
relative error = 1.809984447428581700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 1.6411187146794666 " "
y[1] (numeric) = 1.6411187146797646 " "
absolute error = 2.979838598093920000000000000E-13 " "
relative error = 1.815736163045294200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 1.629605623572176 " "
y[1] (numeric) = 1.629605623572473 " "
absolute error = 2.96873636784766860000000000000E-13 " "
relative error = 1.82175142556273900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 1.6179295732605288 " "
y[1] (numeric) = 1.617929573260824 " "
absolute error = 2.95319324550291640000000000000E-13 " "
relative error = 1.82529159137100200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 1.6060917313398253 " "
y[1] (numeric) = 1.6060917313401195 " "
absolute error = 2.9420910152566650000000000000E-13 " "
relative error = 1.83183248991782620000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 1.5940932815843933 " "
y[1] (numeric) = 1.594093281584686 " "
absolute error = 2.92654789291191260000000000000E-13 " "
relative error = 1.83586991220687700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 1.5819354238292096 " "
y[1] (numeric) = 1.581935423829501 " "
absolute error = 2.9132252166164110000000000000E-13 " "
relative error = 1.841557608947589600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 1.5696193738499182 " "
y[1] (numeric) = 1.5696193738502082 " "
absolute error = 2.8999025403209090000000000000E-13 " "
relative error = 1.847519588910341600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 1.5571463632412534 " "
y[1] (numeric) = 1.5571463632415423 " "
absolute error = 2.88880031007465730000000000000E-13 " "
relative error = 1.855188682495793600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 1.5445176392938824 " "
y[1] (numeric) = 1.5445176392941697 " "
absolute error = 2.8732571877299050000000000000E-13 " "
relative error = 1.860294188056985400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 1.5317344648696756 " "
y[1] (numeric) = 1.531734464869962 " "
absolute error = 2.8643754035329040000000000000E-13 " "
relative error = 1.870020861466098200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 1.518798118275423 " "
y[1] (numeric) = 1.5187981182757078 " "
absolute error = 2.84661183513890140000000000000E-13 " "
relative error = 1.87425293782375400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 1.505709893135004 " "
y[1] (numeric) = 1.5057098931352872 " "
absolute error = 2.83328915884339950000000000000E-13 " "
relative error = 1.88169658163318100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 1.4924710982600253 " "
y[1] (numeric) = 1.4924710982603073 " "
absolute error = 2.81996648254789760000000000000E-13 " "
relative error = 1.88946136768444800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 1.4790830575189426 " "
y[1] (numeric) = 1.479083057519223 " "
absolute error = 2.80442336020314540000000000000E-13 " "
relative error = 1.89605536074990120000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 1.465547109704673 " "
y[1] (numeric) = 1.4655471097049515 " "
absolute error = 2.78443934575989260000000000000E-13 " "
relative error = 1.899931655094317400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 1.4518646084007183 " "
y[1] (numeric) = 1.4518646084009954 " "
absolute error = 2.77111666946439100000000000000E-13 " "
relative error = 1.908660527593462600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 1.4380369218458067 " "
y[1] (numeric) = 1.4380369218460818 " "
absolute error = 2.7511326550211380000000000000E-13 " "
relative error = 1.913116842292125800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 1.4240654327970705 " "
y[1] (numeric) = 1.424065432797344 " "
absolute error = 2.73558953267638570000000000000E-13 " "
relative error = 1.920971796431637500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 1.409951538391772 " "
y[1] (numeric) = 1.409951538392044 " "
absolute error = 2.72004641033163350000000000000E-13 " "
relative error = 1.92917723500921900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 1.39569665000759 " "
y[1] (numeric) = 1.3956966500078605 " "
absolute error = 2.70450328798688130000000000000E-13 " "
relative error = 1.937744342921632600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 1.381302193121484 " "
y[1] (numeric) = 1.3813021931217528 " "
absolute error = 2.6889601656421290000000000000E-13 " "
relative error = 1.946684931821894300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 1.3667696071671471 " "
y[1] (numeric) = 1.3667696071674145 " "
absolute error = 2.6734170432973770000000000000E-13 " "
relative error = 1.956011480851165300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 1.3521003453910645 " "
y[1] (numeric) = 1.35210034539133 " "
absolute error = 2.65565347490337440000000000000E-13 " "
relative error = 1.964094960818375300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 1.3372958747071892 " "
y[1] (numeric) = 1.3372958747074533 " "
absolute error = 2.64011035255862200000000000000E-13 " "
relative error = 1.97421558122782230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 1.3223576755502529 " "
y[1] (numeric) = 1.322357675550515 " "
absolute error = 2.622346784164620000000000000E-13 " "
relative error = 1.983084329338824200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 1.3072872417277226 " "
y[1] (numeric) = 1.307287241727983 " "
absolute error = 2.6045832157706170000000000000E-13 " "
relative error = 1.992357251439535700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 1.292086080270415 " "
y[1] (numeric) = 1.2920860802706804 " "
absolute error = 2.6534330288541240000000000000E-13 " "
relative error = 2.05360391182203500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 1.2767557112818153 " "
y[1] (numeric) = 1.2767557112820855 " "
absolute error = 2.7022828419376310000000000000E-13 " "
relative error = 2.116523010674171400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 1.261297667786047 " "
y[1] (numeric) = 1.2612976677863221 " "
absolute error = 2.7511326550211380000000000000E-13 " "
relative error = 2.18119221598989800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 1.2457134955745777 " "
y[1] (numeric) = 1.2457134955748579 " "
absolute error = 2.8022029141538950000000000000E-13 " "
relative error = 2.24947624322027300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 1.230004753051642 " "
y[1] (numeric) = 1.2300047530519276 " "
absolute error = 2.85549361933590260000000000000E-13 " "
relative error = 2.32153055689534700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 1.2141730110784015 " "
y[1] (numeric) = 1.2141730110786924 " "
absolute error = 2.908784324517910000000000000E-13 " "
relative error = 2.395691798431916000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 1.1982198528158607 " "
y[1] (numeric) = 1.1982198528161565 " "
absolute error = 2.9576341376014170000000000000E-13 " "
relative error = 2.468356813360142700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 1.1821468735665515 " "
y[1] (numeric) = 1.1821468735668528 " "
absolute error = 3.0131452888326750000000000000E-13 " "
relative error = 2.548875572239157600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 1.1659556806150044 " "
y[1] (numeric) = 1.1659556806153113 " "
absolute error = 3.06865644006393270000000000000E-13 " "
relative error = 2.631880860553219600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 1.1496478930670224 " "
y[1] (numeric) = 1.1496478930673348 " "
absolute error = 3.12416759129519050000000000000E-13 " "
relative error = 2.717499514534453000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 1.1332251416877703 " "
y[1] (numeric) = 1.133225141688088 " "
absolute error = 3.1774582964771980000000000000E-13 " "
relative error = 2.80390734337648600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 1.1166890687387006 " "
y[1] (numeric) = 1.1166890687390236 " "
absolute error = 3.23074900165920550000000000000E-13 " "
relative error = 2.893150020093179000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 1.1000413278133279 " "
y[1] (numeric) = 1.1000413278136567 " "
absolute error = 3.28848059893971370000000000000E-13 " "
relative error = 2.98941550266714600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 1.083283583671872 " "
y[1] (numeric) = 1.0832835836722063 " "
absolute error = 3.34399175017097150000000000000E-13 " "
relative error = 3.08690337467891600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 1.066417512074782 " "
y[1] (numeric) = 1.066417512075122 " "
absolute error = 3.39950290140222930000000000000E-13 " "
relative error = 3.1877785791310603000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 1.049444799615163 " "
y[1] (numeric) = 1.0494447996155083 " "
absolute error = 3.4527936065842370000000000000E-13 " "
relative error = 3.29011455185674800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 1.0323671435501165 " "
y[1] (numeric) = 1.0323671435504678 " "
absolute error = 3.51274564991399530000000000000E-13 " "
relative error = 3.402612793191309700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = 1.0151862516310182 " "
y[1] (numeric) = 1.015186251631375 " "
absolute error = 3.5682568011452530000000000000E-13 " "
relative error = 3.51487896473422700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 0.9979038419327425 " "
y[1] (numeric) = 0.9979038419331049 " "
absolute error = 3.6237679523765110000000000000E-13 " "
relative error = 3.631379898646335000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 0.9805216426818572 " "
y[1] (numeric) = 0.9805216426822253 " "
absolute error = 3.6814995496570190000000000000E-13 " "
relative error = 3.75463364540085830000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 0.9630413920838021 " "
y[1] (numeric) = 0.9630413920841764 " "
absolute error = 3.74256181601140270000000000000E-13 " "
relative error = 3.88618998806827100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 0.9454648381490706 " "
y[1] (numeric) = 0.9454648381494506 " "
absolute error = 3.8002934132919110000000000000E-13 " "
relative error = 4.019497351939303500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 0.9277937385184087 " "
y[1] (numeric) = 0.9277937385187947 " "
absolute error = 3.8591352335970440000000000000E-13 " "
relative error = 4.159475402107893300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 0.9100298602870539 " "
y[1] (numeric) = 0.9100298602874455 " "
absolute error = 3.9157566078529270000000000000E-13 " "
relative error = 4.30288804657219300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 0.892174979828026 " "
y[1] (numeric) = 0.8921749798284235 " "
absolute error = 3.97570865118268560000000000000E-13 " "
relative error = 4.45619832552246200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 0.8742308826144919 " "
y[1] (numeric) = 0.8742308826148955 " "
absolute error = 4.0356606945124440000000000000E-13 " "
relative error = 4.61624128679064550000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 0.8561993630412196 " "
y[1] (numeric) = 0.8561993630416291 " "
absolute error = 4.09561273784220250000000000000E-13 " "
relative error = 4.7834802437770900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 0.8380822242451401 " "
y[1] (numeric) = 0.8380822242455558 " "
absolute error = 4.1566750041965860000000000000E-13 " "
relative error = 4.95974605348598050000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 0.8198812779250357 " "
y[1] (numeric) = 0.8198812779254574 " "
absolute error = 4.21662704752634450000000000000E-13 " "
relative error = 5.14297272185288800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 0.8015983441603708 " "
y[1] (numeric) = 0.8015983441607987 " "
absolute error = 4.27879953690535330000000000000E-13 " "
relative error = 5.33783479978012700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 0.7832352512292862 " "
y[1] (numeric) = 0.7832352512297203 " "
absolute error = 4.3409720262843620000000000000E-13 " "
relative error = 5.54236038210897100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 0.7647938354257725 " "
y[1] (numeric) = 0.7647938354262128 " "
absolute error = 4.4031445156633710000000000000E-13 " "
relative error = 5.75729603418164600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 0.7462759408760422 " "
y[1] (numeric) = 0.7462759408764889 " "
absolute error = 4.4664272280670050000000000000E-13 " "
relative error = 5.98495406782634900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 0.7276834193541188 " "
y[1] (numeric) = 0.7276834193545717 " "
absolute error = 4.52859971744601350000000000000E-13 " "
relative error = 6.22331029813147700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 0.7090181300966609 " "
y[1] (numeric) = 0.7090181300971199 " "
absolute error = 4.5896619838003970000000000000E-13 " "
relative error = 6.47326463030597800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 0.6902819396170397 " "
y[1] (numeric) = 0.690281939617505 " "
absolute error = 4.6529446962040310000000000000E-13 " "
relative error = 6.74064382849916400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 0.6714767215186896 " "
y[1] (numeric) = 0.6714767215191614 " "
absolute error = 4.717337631632290000000000000E-13 " "
relative error = 7.02531819861604800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = 0.6526043563077499 " "
y[1] (numeric) = 0.652604356308228 " "
absolute error = 4.7806203440359240000000000000E-13 " "
relative error = 7.32544963549326500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 0.6336667312050144 " "
y[1] (numeric) = 0.633666731205499 " "
absolute error = 4.8461235024888083000000000000E-13 " "
relative error = 7.64774804142417600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 0.6146657399572123 " "
y[1] (numeric) = 0.614665739957703 " "
absolute error = 4.9071857688431920000000000000E-13 " "
relative error = 7.98350298356434700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 0.5956032826476341 " "
y[1] (numeric) = 0.5956032826481312 " "
absolute error = 4.9715787042714510000000000000E-13 " "
relative error = 8.34713113428673800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 0.5764812655061256 " "
y[1] (numeric) = 0.5764812655066291 " "
absolute error = 5.035971639699710000000000000E-13 " "
relative error = 8.73570736991486700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 0.5573016007184658 " "
y[1] (numeric) = 0.5573016007189757 " "
absolute error = 5.0992543521033440000000000000E-13 " "
relative error = 9.14990078178396200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 0.5380662062351506 " "
y[1] (numeric) = 0.5380662062356669 " "
absolute error = 5.1636472875316030000000000000E-13 " "
relative error = 9.59667644556539700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 0.5187770055795988 " "
y[1] (numeric) = 0.5187770055801217 " "
absolute error = 5.2291504459844870000000000000E-13 " "
relative error = 1.00797652743730750000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 0.4994359276558018 " "
y[1] (numeric) = 0.49943592765633116 " "
absolute error = 5.2935433814127460000000000000E-13 " "
relative error = 1.05990440180365190000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 0.4800449065554344 " "
y[1] (numeric) = 0.48004490655597015 " "
absolute error = 5.3573812053286930000000000000E-13 " "
relative error = 1.11601667514204440000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 0.4606058813644475 " "
y[1] (numeric) = 0.46060588136498976 " "
absolute error = 5.4223292522692650000000000000E-13 " "
relative error = 1.177216677348270000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 0.4411207959691611 " "
y[1] (numeric) = 0.4411207959697098 " "
absolute error = 5.4872772992098360000000000000E-13 " "
relative error = 1.24393983447415020000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 0.4215915988618772 " "
y[1] (numeric) = 0.42159159886243236 " "
absolute error = 5.5516702346380950000000000000E-13 " "
relative error = 1.31683606827681270000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 0.4020202429460322 " "
y[1] (numeric) = 0.40202024294659383 " "
absolute error = 5.6160631700663540000000000000E-13 " "
relative error = 1.39696029456413770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 0.3824086853409084 " "
y[1] (numeric) = 0.38240868534147654 " "
absolute error = 5.6815663285192390000000000000E-13 " "
relative error = 1.48573150828262580000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 0.36275888718592325 " "
y[1] (numeric) = 0.36275888718649796 " "
absolute error = 5.7470694869721230000000000000E-13 " "
relative error = 1.58426704072079730000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 0.34307281344451757 " "
y[1] (numeric) = 0.3430728134450988 " "
absolute error = 5.8125726454250070000000000000E-13 " "
relative error = 1.69426792728507140000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = 0.32335243270766045 " "
y[1] (numeric) = 0.32335243270824826 " "
absolute error = 5.8780758038778910000000000000E-13 " "
relative error = 1.8178542077622770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = 0.30359971699699206 " "
y[1] (numeric) = 0.3035997169975865 " "
absolute error = 5.9441340738430880000000000000E-13 " "
relative error = 1.95788524858933940000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = 0.2838166415676229 " "
y[1] (numeric) = 0.283816641568224 " "
absolute error = 6.011302566832910000000000000E-13 " "
relative error = 2.1180232891314238000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = 0.2640051847106099 " "
y[1] (numeric) = 0.2640051847112177 " "
absolute error = 6.0779159483104200000000000000E-13 " "
relative error = 2.30219567656322570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = 0.24416732755512952 " "
y[1] (numeric) = 0.24416732755574388 " "
absolute error = 6.143696662519460000000000000E-13 " "
relative error = 2.5161829488150090000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = 0.2243050538703657 " "
y[1] (numeric) = 0.22430505387098665 " "
absolute error = 6.2094773767285000000000000000E-13 " "
relative error = 2.76831808716944460000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = 0.20442034986713506 " "
y[1] (numeric) = 0.20442034986776264 " "
absolute error = 6.2758132024498540000000000000E-13 " "
relative error = 3.07005305808784550000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = 0.1845152039992674 " "
y[1] (numeric) = 0.18451520399990162 " "
absolute error = 6.3421490281712070000000000000E-13 " "
relative error = 3.43719590077595340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = 0.16459160676476198 " "
y[1] (numeric) = 0.16459160676540283 " "
absolute error = 6.408484853892560000000000000E-13 " "
relative error = 3.89356722366269300000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = 0.14465155050673928 " "
y[1] (numeric) = 0.1446515505073868 " "
absolute error = 6.4750982353700690000000000000E-13 " "
relative error = 4.4763420873725070000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = 0.12469702921420847 " "
y[1] (numeric) = 0.12469702921486261 " "
absolute error = 6.5414340610914220000000000000E-13 " "
relative error = 5.2458619923128570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = 0.10473003832267007 " "
y[1] (numeric) = 0.10473003832333089 " "
absolute error = 6.608186220447010000000000000E-13 " "
relative error = 6.3097334120010430000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = 8.47525745145741300E-2 " "
y[1] (numeric) = 8.47525745152416100E-2 " "
absolute error = 6.6747996019245190000000000000E-13 " "
relative error = 7.8756304928255770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = 6.47666355196536300E-2 " "
y[1] (numeric) = 6.4766635520327800E-2 " "
absolute error = 6.7416905391581850000000000000E-13 " "
relative error = 1.0409202956223347000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = 4.477421991515318500E-2 " "
y[1] (numeric) = 4.47742199158340300E-2 " "
absolute error = 6.8084426985137720000000000000E-13 " "
relative error = 1.5206167101103538000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = 2.47773269259729500E-2 " "
y[1] (numeric) = 2.477732692666047600E-2 " "
absolute error = 6.8752642468083990000000000000E-13 " "
relative error = 2.7748208139439656000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = 4.777956224747818600E-3 " "
y[1] (numeric) = 4.7779562254420227000E-3 " "
absolute error = 6.9420424270161260000000000000E-13 " "
relative error = 1.452931358194377300000000E-8 "%"
Desired digits = 8
Estimated correct digits = 10
Correct digits = 11
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = -1.522189226811817600E-2 " "
y[1] (numeric) = -1.522189226741728600E-2 " "
absolute error = 7.0088726489281330000000000000E-13 " "
relative error = 4.604468699077590700000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = -3.52202185844422200E-2 " "
y[1] (numeric) = -3.522021858373465000E-2 " "
absolute error = 7.075659502753240000000000000E-13 " "
relative error = 2.0089766012635596000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = -5.5215022908257900E-2 " "
y[1] (numeric) = -5.521502290754368000E-2 " "
absolute error = 7.1422728842307490000000000000E-13 " "
relative error = 1.293537973550774000000000E-9 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 12
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = -7.52043057757951200E-2 " "
y[1] (numeric) = -7.52043057750742200E-2 " "
absolute error = 7.2089556546472980000000000000E-13 " "
relative error = 9.585828338259239000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = -9.5186068275424810E-2 " "
y[1] (numeric) = -9.51860682746972200E-2 " "
absolute error = 7.2758465918809630000000000000E-13 " "
relative error = 7.6438146082764990000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = -0.1151583122475484 " "
y[1] (numeric) = -0.11515831224681415 " "
absolute error = 7.3424599733584730000000000000E-13 " "
relative error = 6.3759704619279770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = -0.13511904048441217 " "
y[1] (numeric) = -0.13511904048367127 " "
absolute error = 7.4090733548359820000000000000E-13 " "
relative error = 5.4833673539079930000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = -0.1550662569298263 " "
y[1] (numeric) = -0.15506625692907874 " "
absolute error = 7.4756867363134920000000000000E-13 " "
relative error = 4.8209629124513775000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = -0.17499796687876892 " "
y[1] (numeric) = -0.17499796687801467 " "
absolute error = 7.5425776735471570000000000000E-13 " "
relative error = 4.310094458852960000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = -0.19491217717685477 " "
y[1] (numeric) = -0.1949121771760939 " "
absolute error = 7.6086359435123540000000000000E-13 " "
relative error = 3.90362267443588760000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = -0.21480689641964923 " "
y[1] (numeric) = -0.21480689641888176 " "
absolute error = 7.6746942134775510000000000000E-13 " "
relative error = 3.57283417869609770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = -0.23468013515180683 " "
y[1] (numeric) = -0.23468013515103273 " "
absolute error = 7.7410300391989040000000000000E-13 " "
relative error = 3.2985450746359450000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = -0.2545299060660154 " "
y[1] (numeric) = -0.2545299060652347 " "
absolute error = 7.8070883091641010000000000000E-13 " "
relative error = 3.0672577654349340000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = -0.27435422420172484 " "
y[1] (numeric) = -0.2743542242009375 " "
absolute error = 7.8731465791292980000000000000E-13 " "
relative error = 2.8697012419026570000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = -0.2941511071436419 " "
y[1] (numeric) = -0.294151107142848 " "
absolute error = 7.9392048490944940000000000000E-13 " "
relative error = 2.69902259630713100000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = -0.31391857521996963 " "
y[1] (numeric) = -0.3139185752191692 " "
absolute error = 8.0041528960350660000000000000E-13 " "
relative error = 2.5497544675164190000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = -0.33365465170037334 " "
y[1] (numeric) = -0.3336546516995663 " "
absolute error = 8.0702111660002630000000000000E-13 " "
relative error = 2.4187318009423192000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = -0.35335736299365156 " "
y[1] (numeric) = -0.353357362992838 " "
absolute error = 8.1357143244531470000000000000E-13 " "
relative error = 2.30240407487966060000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = -0.3730247388450939 " "
y[1] (numeric) = -0.3730247388442738 " "
absolute error = 8.2012174829060310000000000000E-13 " "
relative error = 2.19857200578639220000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = -0.39265481253350465 " "
y[1] (numeric) = -0.392654812532678 " "
absolute error = 8.2667206413589160000000000000E-13 " "
relative error = 2.105340461261640000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = -0.4122456210678732 " "
y[1] (numeric) = -0.41224562106704 " "
absolute error = 8.33222379981180000000000000E-13 " "
relative error = 2.02117945564301380000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = -0.4317952053836719 " "
y[1] (numeric) = -0.43179520538283206 " "
absolute error = 8.3982820697769970000000000000E-13 " "
relative error = 1.9449688104606670000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = -0.4513016105387603 " "
y[1] (numeric) = -0.45130161053791396 " "
absolute error = 8.4632301167175680000000000000E-13 " "
relative error = 1.8752935773072538000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = -0.47076288590887816 " "
y[1] (numeric) = -0.47076288590802545 " "
absolute error = 8.5270679406335150000000000000E-13 " "
relative error = 1.81132969396487880000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = -0.49017708538270627 " "
y[1] (numeric) = -0.49017708538184707 " "
absolute error = 8.5920159875740860000000000000E-13 " "
relative error = 1.75283917665507770000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = -0.5095422675564756 " "
y[1] (numeric) = -0.5095422675556099 " "
absolute error = 8.6564089230023460000000000000E-13 " "
relative error = 1.69885983443815200000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = -0.5288564959281064 " "
y[1] (numeric) = -0.5288564959272343 " "
absolute error = 8.7208018584306050000000000000E-13 " "
relative error = 1.64899210382699470000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = -0.5481178390908567 " "
y[1] (numeric) = -0.5481178390899781 " "
absolute error = 8.7851947938588640000000000000E-13 " "
relative error = 1.60279307975645350000000000E-10 "%"
Desired digits = 8
Estimated correct digits = 12
Correct digits = 13
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = 2.0 * sin ( x ) ; "
Iterations = 4900
"Total Elapsed Time "= 1 Minutes 36 Seconds
"Elapsed Time(since restart) "= 1 Minutes 36 Seconds
"Time to Timeout "= 1 Minutes 23 Seconds
Percent Done = 100.0204081632654 "%"
(%o253) temp/diffeq.mult_c_sin.max