(%i1) batch("temp/diffeq.diff_B.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.diff_B.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,30,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[30],convfloat)
(%i173) completearray(array_norms,[30],convfloat)
(%i174) completearray(array_fact_1,[30],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[30],convfloat)
(%i184) completearray(array_x,[30],convfloat)
(%i185) completearray(array_tmp0,[30],convfloat)
(%i186) completearray(array_tmp1,[30],convfloat)
(%i187) completearray(array_tmp2,[30],convfloat)
(%i188) completearray(array_m1,[30],convfloat)
(%i189) completearray(array_y_higher,[3,30],convfloat)
(%i190) completearray(array_y_higher_work,[3,30],convfloat)
(%i191) completearray(array_y_higher_work2,[3,30],convfloat)
(%i192) completearray(array_y_set_initial,[2,30],convfloat)
(%i193) completearray(array_given_rad_poles,[2,3],convfloat)
(%i194) completearray(array_given_ord_poles,[2,3],convfloat)
(%i195) completearray(array_rad_test_poles,[2,4],convfloat)
(%i196) completearray(array_ord_test_poles,[2,4],convfloat)
(%i197) completearray(array_fact_2,[30,30],convfloat)
(%i198) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i199) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i200) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i201) 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))
(%i202) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i203) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i204) 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)
(%i205) 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)
(%i206) 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)
(%i207) 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)
(%i208) 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)
(%i209) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i210) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i211) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i212) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i213) log_revs(file,revs):=printf(file,revs)
(%i214) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i215) 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)
(%i216) logstart(file):=(printf(file,""),0)
(%i217) logend(file):=(printf(file,"
~%"),0)
(%i218) 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)
(%i219) 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)
(%i220) 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)
(%i221) 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)
(%i222) 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)
(%i223) c(in_val):=(ret:in_val,ret)
(%i224) 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)
(%i225) 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)
(%i226) 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)
(%i227) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i228) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i229) 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)
(%i230) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i231) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i232) 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)
(%i233) log10(x):=log(x)/glob_log_10
(%i234) c(x):=x
(%i235) 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
(%i236) 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)
(%i237) exact_soln_y(x):=block(exp(c(x))+c(1.0))
(%o237) exact_soln_y(x) := block(exp(c(x)) + c(1.0))
(%i238) exact_soln_yp(x):=block(exp(c(x)))
(%o238) exact_soln_yp(x) := block(exp(c(x)))
(%i239) exact_soln_ypp(x):=block(exp(c(x)))
(%o239) exact_soln_ypp(x) := block(exp(c(x)))
(%i240) display_poles():=(
block(mode_declare([[rad_given],convfloat]),
if glob_type_given_pole = 1
or glob_type_given_pole = 2
then (rad_given
:sqrt(
array_given_rad_poles[1,2]
*array_given_rad_poles[1,2]
+(array_x[1]
-array_given_rad_poles[1,1])
*(array_x[1]
-array_given_rad_poles[1,1])),
omniout_float(always,
"Radius of convergence (given) for eq 1 ",
4,rad_given,4," "),
omniout_float(always,
"Order of pole (given) ",
4,
array_given_ord_poles[
1,1],4," "),
if rad_given < glob_least_given_sing
then glob_least_given_sing
:rad_given)
elseif glob_type_given_pole = 3
then omniout_str(always,
"NO POLE (given) for Equation 1")
elseif glob_type_given_pole = 5
then omniout_str(always,
"SOME POLE (given) for Equation 1")
else omniout_str(always,
"NO info (given) for Equation 1"),
if array_rad_test_poles[1,1] < glob_large_float
then (omniout_float(always,
"Radius of convergence (ratio test) for eq 1 ",
4,
array_rad_test_poles[1,1],
4," "),
if
array_rad_test_poles[1,1]
< glob_least_ratio_sing
then glob_least_ratio_sing
:array_rad_test_poles[1,1],
omniout_float(always,
"Order of pole (ratio test) ",
4,
array_ord_test_poles[1,1],
4," "))
else omniout_str(always,
"NO POLE (ratio test) for Equation 1"),
if array_rad_test_poles[1,2] > glob__small
and array_rad_test_poles[1,2]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (three term test) for eq 1 ",
4,
array_rad_test_poles[1,2],
4," "),
if
array_rad_test_poles[1,2]
< glob_least_3_sing
then glob_least_3_sing
:array_rad_test_poles[1,2],
omniout_float(always,
"Order of pole (three term test) ",
4,
array_ord_test_poles[1,2],
4," "))
else omniout_str(always,
"NO REAL POLE (three term test) for Equation 1"),
if array_rad_test_poles[1,3] > glob__small
and array_rad_test_poles[1,3]
< glob_large_float
then (omniout_float(always,
"Radius of convergence (six term test) for eq 1 ",
4,
array_rad_test_poles[1,3],
4," "),
if
array_rad_test_poles[1,3]
< glob_least_6_sing
then glob_least_6_sing
:array_rad_test_poles[1,3],
omniout_float(always,
"Order of pole (six term test) ",
4,
array_ord_test_poles[1,3],
4," "))
else omniout_str(always,
"NO COMPLEX POLE (six term test) for Equation 1")),
0)
(%i241) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i242) est_size_answer():=block([min_size],
min_size:glob_estimated_size_answer,
if abs(array_y[1]) < min_size
then (min_size:abs(array_y[1]),
omniout_float(always,"min_size",32,min_size,
32,"")),
if min_size < glob__1
then (min_size:glob__1,
omniout_float(always,"min_size",32,min_size,
32,"")),min_size)
(%i243) test_suggested_h():=block(
[max_estimated_step_error,hn_div_ho,hn_div_ho_2,
hn_div_ho_3,no_terms,est_tmp],
max_estimated_step_error:glob__small,
no_terms:ats_max_terms,hn_div_ho:glob__0_5,
hn_div_ho_2:glob__0_25,hn_div_ho_3:glob__0_125,
omniout_float(always,"hn_div_ho",32,hn_div_ho,32,""),
omniout_float(always,"hn_div_ho_2",32,hn_div_ho_2,32,
""),
omniout_float(always,"hn_div_ho_3",32,hn_div_ho_3,32,
""),
est_tmp:abs(array_y[no_terms]*hn_div_ho_3
+array_y[no_terms-1]*hn_div_ho_2
+array_y[no_terms-2]*hn_div_ho
+array_y[no_terms-3]),
if est_tmp >= max_estimated_step_error
then max_estimated_step_error:est_tmp,
omniout_float(always,"max_estimated_step_error",32,
max_estimated_step_error,32,""),
max_estimated_step_error)
(%i244) track_estimated_error():=block(
[hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,
est_tmp],no_terms:ats_max_terms,
hn_div_ho:glob__0_5,hn_div_ho_2:glob__0_25,
hn_div_ho_3:glob__0_125,
est_tmp:c(abs(array_y[no_terms]))*c(hn_div_ho_3)
+c(abs(array_y[no_terms-1]))
*c(hn_div_ho_2)
+c(abs(array_y[no_terms-2]))
*c(hn_div_ho)
+c(abs(array_y[no_terms-3])),
if glob_prec*c(abs(array_y[1])) > c(est_tmp)
then est_tmp
:c(glob_prec)*c(abs(array_y[1])),
if c(est_tmp) >= c(array_max_est_error[1])
then array_max_est_error[1]:c(est_tmp))
(%i245) reached_interval():=block(mode_declare([[ret],boolean]),
if glob_check_sign*array_x[1]
>= glob_check_sign*glob_next_display
-glob_h/glob__10 then ret:true else ret:false,
return(ret))
(%i246) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(21)
*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:-10-2+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:-10-2+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:-10-2+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i249) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_y_higher[2,1],
array_tmp2[1]:array_tmp1[1]+array_const_0D0[1],
if not array_y_set_initial[1,3]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp2[1])*expt(glob_h,c(2))
*c(factorial_3(0,2)),
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),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[3,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_y_higher[2,2],
array_tmp2[2]:array_tmp1[2],
if not array_y_set_initial[1,4]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp2[2])*expt(glob_h,c(2))
*c(factorial_3(1,3)),
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),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[3,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_y_higher[2,3],
array_tmp2[3]:array_tmp1[3],
if not array_y_set_initial[1,5]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp2[3])*expt(glob_h,c(2))
*c(factorial_3(2,4)),
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),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[3,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_y_higher[2,4],
array_tmp2[4]:array_tmp1[4],
if not array_y_set_initial[1,6]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp2[4])*expt(glob_h,c(2))
*c(factorial_3(3,5)),
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),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[3,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_y_higher[2,5],
array_tmp2[5]:array_tmp1[5],
if not array_y_set_initial[1,7]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp2[5])*expt(glob_h,c(2))
*c(factorial_3(4,6)),
if 7 <= ats_max_terms
then (array_y[7]:temporary,
array_y_higher[1,7]:temporary),
temporary:c(temporary)*c(6)/c(glob_h),
array_y_higher[2,6]:c(temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[3,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(if kkk <= ats_max_terms
then array_tmp1[kkk]:array_y_higher[2,kkk],
array_tmp2[kkk]:array_tmp1[kkk],order_d:2,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp2[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(exp(c(x))+c(1.0))
(%o250) exact_soln_y(x) := block(exp(c(x)) + c(1.0))
(%i251) exact_soln_yp(x):=block(exp(c(x)))
(%o251) exact_soln_yp(x) := block(exp(c(x)))
(%i252) exact_soln_ypp(x):=block(exp(c(x)))
(%o252) exact_soln_ypp(x) := block(exp(c(x)))
(%i253) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:30,
glob_html_log:true,term:1,
while term <= 30 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 30 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 3 do
(term:1,
while term <= 30 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 3 do
(term:1,
while term <= 30 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 3 do
(term:1,
while term <= 30 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 30 do
(term:1,
while term <= 30 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_m1),
zero_ats_ar(array_const_2),array_const_2[1]:c(2),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
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]:true,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/diff_Bpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(1.0),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,
"array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (c(1.0) + exp(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_yp (x) := (block("),
omniout_str(always," (exp(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_ypp (x) := (block("),
omniout_str(always," (exp(c(x))) "),
omniout_str(always,"));"),omniout_str(always,""),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(1.0),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
array_y_init[1+1]:exact_soln_yp(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:2,
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:2,
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:3,ord:3,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[3,iii]
:array_y_higher[3,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:3,
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:2,
calc_term:2,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: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: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:3,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:3,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 , 2 ) = diff ( y , x , 1 ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:36:56-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"diff_B"),
logitem_str(html_log_file,
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "),
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,
"diff_B diffeq.max"),
logitem_str(html_log_file,
"diff_B maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i254) main():=(glob_iolevel:2,compile(all),main_prog())
(%i255) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp2 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_2 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/diff_Bpostode.ode#################"
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(1.0),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"array_y_init[1 + 1] : exact_soln_yp(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (c(1.0) + exp(c(x))) "
"));"
"exact_soln_yp (x) := (block("
" (exp(c(x))) "
"));"
"exact_soln_ypp (x) := (block("
" (exp(c(x))) "
"));"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1. " "
y[1] (closed_form) = 3.718281828459045 " "
y[1] (numeric) = 3.718281828459045 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.009999999999999 " "
y[1] (closed_form) = 3.7456010150169137 " "
y[1] (numeric) = 3.7456010150169163 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 7.11377225822420700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999978 " "
y[1] (closed_form) = 3.773194763964292 " "
y[1] (numeric) = 3.773194763964298 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 1.64774132448141870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999967 " "
y[1] (closed_form) = 3.80106583469907 " "
y[1] (numeric) = 3.801065834699079 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 2.45348905081241330000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999956 " "
y[1] (closed_form) = 3.829217014351547 " "
y[1] (numeric) = 3.8292170143515594 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 3.24726904461105750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999945 " "
y[1] (closed_form) = 3.857651118063148 " "
y[1] (numeric) = 3.857651118063164 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 4.14428652703801860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0599999999999934 " "
y[1] (closed_form) = 3.886370989267939 " "
y[1] (numeric) = 3.8863709892679577 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 4.7992708017862170000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0699999999999923 " "
y[1] (closed_form) = 3.915379499976974 " "
y[1] (numeric) = 3.9153794999769955 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 5.4442441844854030000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999912 " "
y[1] (closed_form) = 3.944679551065498 " "
y[1] (numeric) = 3.944679551065523 " "
absolute error = 2.486899575160350700000000000000E-14 " "
relative error = 6.3044400513816490000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.08999999999999 " "
y[1] (closed_form) = 3.974274072563036 " "
y[1] (numeric) = 3.974274072563064 " "
absolute error = 2.797762022055394500000000000000E-14 " "
relative error = 7.0396806334272240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.099999999999989 " "
y[1] (closed_form) = 4.0041660239464 " "
y[1] (numeric) = 4.004166023946432 " "
absolute error = 3.19744231092045100000000000000E-14 " "
relative error = 7.9852890509498310000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999879 " "
y[1] (closed_form) = 4.034358394435639 " "
y[1] (numeric) = 4.034358394435674 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 8.5859893895595470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999868 " "
y[1] (closed_form) = 4.0648542032929615 " "
y[1] (numeric) = 4.064854203293000 " "
absolute error = 3.90798504668055100000000000000E-14 " "
relative error = 9.6140841743220950000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999857 " "
y[1] (closed_form) = 4.095656500124667 " "
y[1] (numeric) = 4.09565650012471 " "
absolute error = 4.26325641456060100000000000000E-14 " "
relative error = 1.040921379620296000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999846 " "
y[1] (closed_form) = 4.126768365186107 " "
y[1] (numeric) = 4.1267683651861535 " "
absolute error = 4.61852778244065100000000000000E-14 " "
relative error = 1.1191633195124502000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999835 " "
y[1] (closed_form) = 4.158192909689715 " "
y[1] (numeric) = 4.158192909689767 " "
absolute error = 5.151434834260726000000000000000E-14 " "
relative error = 1.2388638396877857000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999824 " "
y[1] (closed_form) = 4.189933276116129 " "
y[1] (numeric) = 4.189933276116184 " "
absolute error = 5.506706202140776000000000000000E-14 " "
relative error = 1.314270619422664000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999813 " "
y[1] (closed_form) = 4.221992638528440 " "
y[1] (numeric) = 4.2219926385285 " "
absolute error = 6.03961325396085200000000000000E-14 " "
relative error = 1.4305125022827936000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999802 " "
y[1] (closed_form) = 4.254374202889606 " "
y[1] (numeric) = 4.254374202889670 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.5240085038610685000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.189999999999979 " "
y[1] (closed_form) = 4.28708120738305 " "
y[1] (numeric) = 4.2870812073831175 " "
absolute error = 6.75015598972095200000000000000E-14 " "
relative error = 1.5745342024536618000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.199999999999978 " "
y[1] (closed_form) = 4.320116922736474 " "
y[1] (numeric) = 4.320116922736548 " "
absolute error = 7.3718808835110390000000000000E-14 " "
relative error = 1.7064077235301997000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999769 " "
y[1] (closed_form) = 4.353484652548946 " "
y[1] (numeric) = 4.353484652549024 " "
absolute error = 7.7271522513910900000000000000E-14 " "
relative error = 1.7749349930214814000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999758 " "
y[1] (closed_form) = 4.387187733621253 " "
y[1] (numeric) = 4.387187733621335 " "
absolute error = 8.26005930321116500000000000000E-14 " "
relative error = 1.8827685990982618000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999747 " "
y[1] (closed_form) = 4.421229536289587 " "
y[1] (numeric) = 4.421229536289673 " "
absolute error = 8.61533067109121500000000000000E-14 " "
relative error = 1.9486277743275526000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999736 " "
y[1] (closed_form) = 4.4556134647625845 " "
y[1] (numeric) = 4.455613464762675 " "
absolute error = 9.05941988094127700000000000000E-14 " "
relative error = 2.0332598311294503000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999725 " "
y[1] (closed_form) = 4.4903429574617455 " "
y[1] (numeric) = 4.4903429574618405 " "
absolute error = 9.5035090907913400000000000000E-14 " "
relative error = 2.1164327938468613000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999714 " "
y[1] (closed_form) = 4.525421487365281 " "
y[1] (numeric) = 4.5254214873653815 " "
absolute error = 1.00364161426114150000000000000E-13 " "
relative error = 2.2177859389744176000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999703 " "
y[1] (closed_form) = 4.560852562355414 " "
y[1] (numeric) = 4.560852562355520 " "
absolute error = 1.04805053524614780000000000000E-13 " "
relative error = 2.2979268040729883000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999692 " "
y[1] (closed_form) = 4.596639725569170 " "
y[1] (numeric) = 4.596639725569280 " "
absolute error = 1.10134124042815530000000000000E-13 " "
relative error = 2.3959703308959754000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.289999999999968 " "
y[1] (closed_form) = 4.632786555752693 " "
y[1] (numeric) = 4.632786555752810 " "
absolute error = 1.1635137298071640000000000000E-13 " "
relative error = 2.511477090094704000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.299999999999967 " "
y[1] (closed_form) = 4.669296667619123 " "
y[1] (numeric) = 4.6692966676192444 " "
absolute error = 1.21680443498917160000000000000E-13 " "
relative error = 2.605969424533526000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999659 " "
y[1] (closed_form) = 4.706173712210072 " "
y[1] (numeric) = 4.706173712210197 " "
absolute error = 1.25233157177717660000000000000E-13 " "
relative error = 2.6610398348195860000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999648 " "
y[1] (closed_form) = 4.743421377260730 " "
y[1] (numeric) = 4.74342137726086 " "
absolute error = 1.29674049276218280000000000000E-13 " "
relative error = 2.733766177676239000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999637 " "
y[1] (closed_form) = 4.781043387568643 " "
y[1] (numeric) = 4.781043387568778 " "
absolute error = 1.35003119794419040000000000000E-13 " "
relative error = 2.823716683798464000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999626 " "
y[1] (closed_form) = 4.819043505366192 " "
y[1] (numeric) = 4.8190435053663325 " "
absolute error = 1.40332190312619800000000000000E-13 " "
relative error = 2.912034102957453000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999615 " "
y[1] (closed_form) = 4.857425530696826 " "
y[1] (numeric) = 4.85742553069697 " "
absolute error = 1.4388490399142030000000000000E-13 " "
relative error = 2.9621638681258206000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3599999999999604 " "
y[1] (closed_form) = 4.89619330179506 " "
y[1] (numeric) = 4.89619330179521 " "
absolute error = 1.50102152929321160000000000000E-13 " "
relative error = 3.065690908777849000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3699999999999593 " "
y[1] (closed_form) = 4.935350695470312 " "
y[1] (numeric) = 4.935350695470470 " "
absolute error = 1.57207580286922170000000000000E-13 " "
relative error = 3.1853375775546816000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999581 " "
y[1] (closed_form) = 4.974901627494582 " "
y[1] (numeric) = 4.974901627494743 " "
absolute error = 1.6164847238542280000000000000E-13 " "
relative error = 3.2492797745395990000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.389999999999957 " "
y[1] (closed_form) = 5.01485005299403 " "
y[1] (numeric) = 5.0148500529941975 " "
absolute error = 1.67865721323323670000000000000E-13 " "
relative error = 3.3473726940868814000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.399999999999956 " "
y[1] (closed_form) = 5.055199966844496 " "
y[1] (numeric) = 5.055199966844671 " "
absolute error = 1.74971148680924670000000000000E-13 " "
relative error = 3.4612112246499980000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999548 " "
y[1] (closed_form) = 5.095955404070992 " "
y[1] (numeric) = 5.095955404071173 " "
absolute error = 1.81188397618825550000000000000E-13 " "
relative error = 3.5555334231159100000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999537 " "
y[1] (closed_form) = 5.137120440251201 " "
y[1] (numeric) = 5.137120440251388 " "
absolute error = 1.8651746813702630000000000000E-13 " "
relative error = 3.6307785715046564000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999526 " "
y[1] (closed_form) = 5.178699191923048 " "
y[1] (numeric) = 5.178699191923242 " "
absolute error = 1.9362289549462730000000000000E-13 " "
relative error = 3.738832635743953000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999515 " "
y[1] (closed_form) = 5.220695816996348 " "
y[1] (numeric) = 5.220695816996547 " "
absolute error = 1.98951966012828050000000000000E-13 " "
relative error = 3.810832367691788000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4499999999999504 " "
y[1] (closed_form) = 5.263114515168606 " "
y[1] (numeric) = 5.263114515168812 " "
absolute error = 2.06057393370429050000000000000E-13 " "
relative error = 3.915122742941646000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4599999999999493 " "
y[1] (closed_form) = 5.305959528344988 " "
y[1] (numeric) = 5.3059595283452 " "
absolute error = 2.12274642308329930000000000000E-13 " "
relative error = 4.0006834046572853000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4699999999999482 " "
y[1] (closed_form) = 5.349235141062516 " "
y[1] (numeric) = 5.349235141062734 " "
absolute error = 2.1849189124623080000000000000E-13 " "
relative error = 4.084544528039421000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999471 " "
y[1] (closed_form) = 5.392945680918524 " "
y[1] (numeric) = 5.39294568091875 " "
absolute error = 2.2559731860383180000000000000E-13 " "
relative error = 4.183192858812703000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.489999999999946 " "
y[1] (closed_form) = 5.437095519003425 " "
y[1] (numeric) = 5.437095519003657 " "
absolute error = 2.3181456754173269000000000000E-13 " "
relative error = 4.2635735703282696000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.499999999999945 " "
y[1] (closed_form) = 5.481689070337818 " "
y[1] (numeric) = 5.481689070338060 " "
absolute error = 2.41584530158434060000000000000E-13 " "
relative error = 4.407118445766680700000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999438 " "
y[1] (closed_form) = 5.526730794313998 " "
y[1] (numeric) = 5.526730794314247 " "
absolute error = 2.48689957516035070000000000000E-13 " "
relative error = 4.4997660782010923000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999427 " "
y[1] (closed_form) = 5.572225195141898 " "
y[1] (numeric) = 5.572225195142154 " "
absolute error = 2.5668356329333620000000000000E-13 " "
relative error = 4.606482227551102000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999416 " "
y[1] (closed_form) = 5.618176822299511 " "
y[1] (numeric) = 5.618176822299775 " "
absolute error = 2.6378899065093720000000000000E-13 " "
relative error = 4.695277471579628000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999405 " "
y[1] (closed_form) = 5.664590270987849 " "
y[1] (numeric) = 5.664590270988121 " "
absolute error = 2.72670774847938450000000000000E-13 " "
relative error = 4.813601016201783400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5499999999999394 " "
y[1] (closed_form) = 5.711470182590456 " "
y[1] (numeric) = 5.7114701825907375 " "
absolute error = 2.8155255904493970000000000000E-13 " "
relative error = 4.929598685521643400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5599999999999383 " "
y[1] (closed_form) = 5.75882124513756 " "
y[1] (numeric) = 5.758821245137850 " "
absolute error = 2.90434343241940950000000000000E-13 " "
relative error = 5.043294988313244000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5699999999999372 " "
y[1] (closed_form) = 5.806648193774876 " "
y[1] (numeric) = 5.8066481937751755 " "
absolute error = 2.9931612743894220000000000000E-13 " "
relative error = 5.154714345529484000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999361 " "
y[1] (closed_form) = 5.854955811237123 " "
y[1] (numeric) = 5.854955811237431 " "
absolute error = 3.08197911635943460000000000000E-13 " "
relative error = 5.263881087615292000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.589999999999935 " "
y[1] (closed_form) = 5.903748928326303 " "
y[1] (numeric) = 5.903748928326620 " "
absolute error = 3.1619151741324460000000000000E-13 " "
relative error = 5.35577513969389000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.599999999999934 " "
y[1] (closed_form) = 5.953032424394787 " "
y[1] (numeric) = 5.953032424395112 " "
absolute error = 3.25073301610245840000000000000E-13 " "
relative error = 5.460633815433893000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999328 " "
y[1] (closed_form) = 6.002811227833251 " "
y[1] (numeric) = 6.002811227833585 " "
absolute error = 3.3395508580724710000000000000E-13 " "
relative error = 5.5633114741106060000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999317 " "
y[1] (closed_form) = 6.053090316563522 " "
y[1] (numeric) = 6.053090316563867 " "
absolute error = 3.4461322684364860000000000000E-13 " "
relative error = 5.6931783406677040000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999306 " "
y[1] (closed_form) = 6.103874718536372 " "
y[1] (numeric) = 6.103874718536726 " "
absolute error = 3.54383189460349970000000000000E-13 " "
relative error = 5.805872594077853000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999295 " "
y[1] (closed_form) = 6.155169512234318 " "
y[1] (numeric) = 6.155169512234684 " "
absolute error = 3.6592950891645160000000000000E-13 " "
relative error = 5.9450760566238200000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6499999999999284 " "
y[1] (closed_form) = 6.206979827179476 " "
y[1] (numeric) = 6.206979827179852 " "
absolute error = 3.7658764995285310000000000000E-13 " "
relative error = 6.067164070742258000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6599999999999273 " "
y[1] (closed_form) = 6.259310844446516 " "
y[1] (numeric) = 6.259310844446902 " "
absolute error = 3.85469434149854350000000000000E-13 " "
relative error = 6.158336656053064000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999262 " "
y[1] (closed_form) = 6.312167797180775 " "
y[1] (numeric) = 6.312167797181173 " "
absolute error = 3.9790393202565610000000000000E-13 " "
relative error = 6.30376036903476000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.679999999999925 " "
y[1] (closed_form) = 6.365555971121573 " "
y[1] (numeric) = 6.365555971121980 " "
absolute error = 4.0767389464235750000000000000E-13 " "
relative error = 6.404372163120384000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.689999999999924 " "
y[1] (closed_form) = 6.419480705130795 " "
y[1] (numeric) = 6.419480705131212 " "
absolute error = 4.17443857259058860000000000000E-13 " "
relative error = 6.5027667569031760000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.699999999999923 " "
y[1] (closed_form) = 6.473947391726778 " "
y[1] (numeric) = 6.473947391727207 " "
absolute error = 4.2899017671516050000000000000E-13 " "
relative error = 6.626408136454398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999218 " "
y[1] (closed_form) = 6.528961477623572 " "
y[1] (numeric) = 6.52896147762401 " "
absolute error = 4.38760139331861860000000000000E-13 " "
relative error = 6.720213326967935000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999207 " "
y[1] (closed_form) = 6.5845284642756114 " "
y[1] (numeric) = 6.584528464276060 " "
absolute error = 4.49418280368263370000000000000E-13 " "
relative error = 6.8253677208107510000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999196 " "
y[1] (closed_form) = 6.6406539084278675 " "
y[1] (numeric) = 6.640653908428330 " "
absolute error = 4.6185277824406510000000000000E-13 " "
relative error = 6.9549292074672480000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999185 " "
y[1] (closed_form) = 6.697343422671526 " "
y[1] (numeric) = 6.697343422672 " "
absolute error = 4.7339909770016675000000000000E-13 " "
relative error = 7.068460848187041000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7499999999999174 " "
y[1] (closed_form) = 6.7546026760052555 " "
y[1] (numeric) = 6.7546026760057405 " "
absolute error = 4.8494541715626840000000000000E-13 " "
relative error = 7.1794810208299380000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7599999999999163 " "
y[1] (closed_form) = 6.812437394402102 " "
y[1] (numeric) = 6.8124373944025995 " "
absolute error = 4.9737991503207013000000000000E-13 " "
relative error = 7.301056673794547000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999152 " "
y[1] (closed_form) = 6.870853361382103 " "
y[1] (numeric) = 6.870853361382612 " "
absolute error = 5.0892623448817180000000000000E-13 " "
relative error = 7.407030942453398000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.779999999999914 " "
y[1] (closed_form) = 6.929856418590637 " "
y[1] (numeric) = 6.929856418591157 " "
absolute error = 5.2047255394427340000000000000E-13 " "
relative error = 7.510582074226075000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.789999999999913 " "
y[1] (closed_form) = 6.989452466382592 " "
y[1] (numeric) = 6.989452466383125 " "
absolute error = 5.3290705182007510000000000000E-13 " "
relative error = 7.62444632656444000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.799999999999912 " "
y[1] (closed_form) = 7.049647464412413 " "
y[1] (numeric) = 7.049647464412958 " "
absolute error = 5.4534154969587690000000000000E-13 " "
relative error = 7.735727955884826000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999108 " "
y[1] (closed_form) = 7.110447432230065 " "
y[1] (numeric) = 7.110447432230624 " "
absolute error = 5.5955240441107890000000000000E-13 " "
relative error = 7.869440140640843000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999097 " "
y[1] (closed_form) = 7.171858449882996 " "
y[1] (numeric) = 7.17185844988357 " "
absolute error = 5.7376325912628090000000000000E-13 " "
relative error = 8.000203338308237000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999086 " "
y[1] (closed_form) = 7.233886658524147 " "
y[1] (numeric) = 7.233886658524736 " "
absolute error = 5.888622922611830000000000000E-13 " "
relative error = 8.140330641858887000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999075 " "
y[1] (closed_form) = 7.2965382610260745 " "
y[1] (numeric) = 7.296538261026676 " "
absolute error = 6.0129679013698480000000000000E-13 " "
relative error = 8.240850230975525000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8499999999999064 " "
y[1] (closed_form) = 7.359819522601236 " "
y[1] (numeric) = 7.359819522601850 " "
absolute error = 6.1461946643248670000000000000E-13 " "
relative error = 8.35101274623725000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8599999999999053 " "
y[1] (closed_form) = 7.423736771428525 " "
y[1] (numeric) = 7.423736771429154 " "
absolute error = 6.2883032114768870000000000000E-13 " "
relative error = 8.470536341857455000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999042 " "
y[1] (closed_form) = 7.48829639928609 " "
y[1] (numeric) = 7.488296399286730 " "
absolute error = 6.4126481902349040000000000000E-13 " "
relative error = 8.563560853235277000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.879999999999903 " "
y[1] (closed_form) = 7.553504862190513 " "
y[1] (numeric) = 7.5535048621911685 " "
absolute error = 6.5547567373869240000000000000E-13 " "
relative error = 8.677768608049915000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.889999999999902 " "
y[1] (closed_form) = 7.619368681042428 " "
y[1] (numeric) = 7.619368681043098 " "
absolute error = 6.6968652845389440000000000000E-13 " "
relative error = 8.789265311706543000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999009 " "
y[1] (closed_form) = 7.685894442278607 " "
y[1] (numeric) = 7.68589444227929 " "
absolute error = 6.8300920474939630000000000000E-13 " "
relative error = 8.886528560583603000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999998998 " "
y[1] (closed_form) = 7.75308879853061 " "
y[1] (numeric) = 7.753088798531308 " "
absolute error = 6.9810823788429840000000000000E-13 " "
relative error = 9.00425954126317000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998987 " "
y[1] (closed_form) = 7.8209584692900584 " "
y[1] (numeric) = 7.820958469290772 " "
absolute error = 7.1320727101920060000000000000E-13 " "
relative error = 9.119179878268057000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998976 " "
y[1] (closed_form) = 7.889510241580587 " "
y[1] (numeric) = 7.889510241581315 " "
absolute error = 7.2830630415410270000000000000E-13 " "
relative error = 9.231324655815308000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998965 " "
y[1] (closed_form) = 7.958750970636552 " "
y[1] (numeric) = 7.958750970637295 " "
absolute error = 7.4340533728900480000000000000E-13 " "
relative error = 9.340728715243948000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9499999999998954 " "
y[1] (closed_form) = 8.028687580588558 " "
y[1] (numeric) = 8.028687580589317 " "
absolute error = 7.5850437042390700000000000000E-13 " "
relative error = 9.447426653613832000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9599999999998943 " "
y[1] (closed_form) = 8.099327065155883 " "
y[1] (numeric) = 8.099327065156656 " "
absolute error = 7.727152251391090000000000000E-13 " "
relative error = 9.540486745663197000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998932 " "
y[1] (closed_form) = 8.170676488345848 " "
y[1] (numeric) = 8.17067648834664 " "
absolute error = 7.9225515037251170000000000000E-13 " "
relative error = 9.696322593392798000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.979999999999892 " "
y[1] (closed_form) = 8.24274298516023 " "
y[1] (numeric) = 8.242742985161039 " "
absolute error = 8.082423619271140000000000000E-13 " "
relative error = 9.805502408387936000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.989999999999891 " "
y[1] (closed_form) = 8.31553376230877 " "
y[1] (numeric) = 8.315533762309595 " "
absolute error = 8.2600593032111650000000000000E-13 " "
relative error = 9.933288156018258000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998899 " "
y[1] (closed_form) = 8.389056098929837 " "
y[1] (numeric) = 8.38905609893068 " "
absolute error = 8.437694987151190000000000000E-13 " "
relative error = 1.00579789759989300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998888 " "
y[1] (closed_form) = 8.463317347318364 " "
y[1] (numeric) = 8.463317347319224 " "
absolute error = 8.5975671026972120000000000000E-13 " "
relative error = 1.015862545367199900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998877 " "
y[1] (closed_form) = 8.538324933661075 " "
y[1] (numeric) = 8.53832493366195 " "
absolute error = 8.7574392182432350000000000000E-13 " "
relative error = 1.025662443896733600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998866 " "
y[1] (closed_form) = 8.614086358779112 " "
y[1] (numeric) = 8.614086358780005 " "
absolute error = 8.935074902183260000000000000E-13 " "
relative error = 1.03726321400028810000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998855 " "
y[1] (closed_form) = 8.690609198878118 " "
y[1] (numeric) = 8.690609198879029 " "
absolute error = 9.1127105861232850000000000000E-13 " "
relative error = 1.048569827222199200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998844 " "
y[1] (closed_form) = 8.767901106305874 " "
y[1] (numeric) = 8.767901106306802 " "
absolute error = 9.2725827016693070000000000000E-13 " "
relative error = 1.057560137739289200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0599999999998833 " "
y[1] (closed_form) = 8.845969810317532 " "
y[1] (numeric) = 8.84596981031848 " "
absolute error = 9.4679819540033350000000000000E-13 " "
relative error = 1.07031587909788200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999882 " "
y[1] (closed_form) = 8.924823117848554 " "
y[1] (numeric) = 8.92482311784952 " "
absolute error = 9.6633812063373630000000000000E-13 " "
relative error = 1.082753246617491300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999881 " "
y[1] (closed_form) = 9.004468914295401 " "
y[1] (numeric) = 9.004468914296387 " "
absolute error = 9.858780458671390000000000000E-13 " "
relative error = 1.09487639443340100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.08999999999988 " "
y[1] (closed_form) = 9.084915164304089 " "
y[1] (numeric) = 9.084915164305094 " "
absolute error = 1.0054179711005418000000000000E-12 " "
relative error = 1.106689443893731200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.099999999999879 " "
y[1] (closed_form) = 9.16616991256666 " "
y[1] (numeric) = 9.166169912567685 " "
absolute error = 1.0249578963339445000000000000E-12 " "
relative error = 1.118196483493880100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998778 " "
y[1] (closed_form) = 9.248241284625653 " "
y[1] (numeric) = 9.2482412846267 " "
absolute error = 1.0462741784067475000000000000E-12 " "
relative error = 1.13132231978644610000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998766 " "
y[1] (closed_form) = 9.331137487686664 " "
y[1] (numeric) = 9.33113748768773 " "
absolute error = 1.0658141036401503000000000000E-12 " "
relative error = 1.142212409844560600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998755 " "
y[1] (closed_form) = 9.414866811439081 " "
y[1] (numeric) = 9.414866811440172 " "
absolute error = 1.0906830993917538000000000000E-12 " "
relative error = 1.158468963221627000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998744 " "
y[1] (closed_form) = 9.499437628885056 " "
y[1] (numeric) = 9.499437628886167 " "
absolute error = 1.1102230246251565000000000000E-12 " "
relative error = 1.168725000361377000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998733 " "
y[1] (closed_form) = 9.584858397176806 " "
y[1] (numeric) = 9.584858397177937 " "
absolute error = 1.1315393066979595000000000000E-12 " "
relative error = 1.180548798750382700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1599999999998722 " "
y[1] (closed_form) = 9.671137658462348 " "
y[1] (numeric) = 9.6711376584635 " "
absolute error = 1.1528555887707626000000000000E-12 " "
relative error = 1.192057883450766300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999871 " "
y[1] (closed_form) = 9.758284040739706 " "
y[1] (numeric) = 9.758284040740879 " "
absolute error = 1.1723955140041653000000000000E-12 " "
relative error = 1.201436142983284500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.17999999999987 " "
y[1] (closed_form) = 9.846306258719732 " "
y[1] (numeric) = 9.846306258720928 " "
absolute error = 1.1954881529163686000000000000E-12 " "
relative error = 1.214148861008323100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.189999999999869 " "
y[1] (closed_form) = 9.935213114697579 " "
y[1] (numeric) = 9.935213114698797 " "
absolute error = 1.2185807918285718000000000000E-12 " "
relative error = 1.226527078745672800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.199999999999868 " "
y[1] (closed_form) = 10.025013499432928 " "
y[1] (numeric) = 10.02501349943417 " "
absolute error = 1.241673430740775100000000000E-12 " "
relative error = 1.238575320433245400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998667 " "
y[1] (closed_form) = 10.115716393039092 " "
y[1] (numeric) = 10.115716393040357 " "
absolute error = 1.2647660696529783000000000000E-12 " "
relative error = 1.250298071348954800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998656 " "
y[1] (closed_form) = 10.207330865881014 " "
y[1] (numeric) = 10.207330865882303 " "
absolute error = 1.2896350654045818000000000000E-12 " "
relative error = 1.263440053378999700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998645 " "
y[1] (closed_form) = 10.299866079482326 " "
y[1] (numeric) = 10.299866079483639 " "
absolute error = 1.312727704316785000000000000E-12 " "
relative error = 1.274509487974588600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998634 " "
y[1] (closed_form) = 10.3933312874415 " "
y[1] (numeric) = 10.393331287442837 " "
absolute error = 1.3375967000683886000000000000E-12 " "
relative error = 1.286975910875310400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2499999999998623 " "
y[1] (closed_form) = 10.487735836357219 " "
y[1] (numeric) = 10.487735836358581 " "
absolute error = 1.3624656958199920000000000000E-12 " "
relative error = 1.29910375039845320000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2599999999998612 " "
y[1] (closed_form) = 10.583089166763049 " "
y[1] (numeric) = 10.583089166764438 " "
absolute error = 1.3891110484109960000000000000E-12 " "
relative error = 1.312576154771140600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.26999999999986 " "
y[1] (closed_form) = 10.679400814071487 " "
y[1] (numeric) = 10.679400814072903 " "
absolute error = 1.4157564010019996000000000000E-12 " "
relative error = 1.325688983539749000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.279999999999859 " "
y[1] (closed_form) = 10.776680409527527 " "
y[1] (numeric) = 10.77668040952897 " "
absolute error = 1.4424017535930034000000000000E-12 " "
relative error = 1.338447182972777300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999858 " "
y[1] (closed_form) = 10.87493768117178 " "
y[1] (numeric) = 10.874937681173249 " "
absolute error = 1.4690471061840070000000000000E-12 " "
relative error = 1.350855654766121600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.299999999999857 " "
y[1] (closed_form) = 10.974182454813294 " "
y[1] (numeric) = 10.974182454814786 " "
absolute error = 1.4921397450962104000000000000E-12 " "
relative error = 1.359681918211370400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998557 " "
y[1] (closed_form) = 11.074424655012132 " "
y[1] (numeric) = 11.074424655013653 " "
absolute error = 1.5205614545266144000000000000E-12 " "
relative error = 1.373038782505445200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998546 " "
y[1] (closed_form) = 11.175674306071855 " "
y[1] (numeric) = 11.175674306073406 " "
absolute error = 1.5507595207964187000000000000E-12 " "
relative error = 1.38762053932967200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998535 " "
y[1] (closed_form) = 11.277941533041941 " "
y[1] (numeric) = 11.277941533043519 " "
absolute error = 1.5774048733874224000000000000E-12 " "
relative error = 1.398663815347832600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998524 " "
y[1] (closed_form) = 11.381236562730313 " "
y[1] (numeric) = 11.381236562731916 " "
absolute error = 1.602273869139026000000000000E-12 " "
relative error = 1.407820547712653000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3499999999998513 " "
y[1] (closed_form) = 11.485569724726016 " "
y[1] (numeric) = 11.485569724727647 " "
absolute error = 1.63069557856943000000000000E-12 " "
relative error = 1.419777701631017300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.35999999999985 " "
y[1] (closed_form) = 11.590951452432193 " "
y[1] (numeric) = 11.590951452433853 " "
absolute error = 1.659117287999834000000000000E-12 " "
relative error = 1.43139007596455120000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.369999999999849 " "
y[1] (closed_form) = 11.697392284109439 " "
y[1] (numeric) = 11.697392284111128 " "
absolute error = 1.6893153542696382000000000000E-12 " "
relative error = 1.444181158705366300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999848 " "
y[1] (closed_form) = 11.804902863929616 " "
y[1] (numeric) = 11.80490286393134 " "
absolute error = 1.723066134218243000000000000E-12 " "
relative error = 1.459619070211195800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999847 " "
y[1] (closed_form) = 11.913493943040303 " "
y[1] (numeric) = 11.913493943042054 " "
absolute error = 1.751487843648647000000000000E-12 " "
relative error = 1.470171430835235000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.399999999999846 " "
y[1] (closed_form) = 12.023176380639901 " "
y[1] (numeric) = 12.023176380641685 " "
absolute error = 1.7834622667578515000000000000E-12 " "
relative error = 1.483353658214345600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998447 " "
y[1] (closed_form) = 12.133961145063576 " "
y[1] (numeric) = 12.133961145065385 " "
absolute error = 1.808331262509455000000000000E-12 " "
relative error = 1.490305796178631500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998436 " "
y[1] (closed_form) = 12.245859314880088 " "
y[1] (numeric) = 12.245859314881926 " "
absolute error = 1.8385293287792592000000000000E-12 " "
relative error = 1.501347746617700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998425 " "
y[1] (closed_form) = 12.358882079999667 " "
y[1] (numeric) = 12.35888208000154 " "
absolute error = 1.8740564655672642000000000000E-12 " "
relative error = 1.516364063866296500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998414 " "
y[1] (closed_form) = 12.473040742793014 " "
y[1] (numeric) = 12.473040742794922 " "
absolute error = 1.907807245515869000000000000E-12 " "
relative error = 1.529544627374210800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4499999999998403 " "
y[1] (closed_form) = 12.588346719221539 " "
y[1] (numeric) = 12.58834671922348 " "
absolute error = 1.9415580254644738000000000000E-12 " "
relative error = 1.54234552699430200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.459999999999839 " "
y[1] (closed_form) = 12.704811539978973 " "
y[1] (numeric) = 12.704811539980945 " "
absolute error = 1.971756091734278000000000000E-12 " "
relative error = 1.55197586798484800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999838 " "
y[1] (closed_form) = 12.822446851644447 " "
y[1] (numeric) = 12.822446851646452 " "
absolute error = 2.0055068716828828000000000000E-12 " "
relative error = 1.5640594146238798000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999837 " "
y[1] (closed_form) = 12.941264417847156 " "
y[1] (numeric) = 12.9412644178492 " "
absolute error = 2.042810365310288000000000000E-12 " "
relative error = 1.578524554751443400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999836 " "
y[1] (closed_form) = 13.061276120442738 " "
y[1] (numeric) = 13.061276120444816 " "
absolute error = 2.078337502098293000000000000E-12 " "
relative error = 1.591220859993459400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.499999999999835 " "
y[1] (closed_form) = 13.18249396070146 " "
y[1] (numeric) = 13.182493960703573 " "
absolute error = 2.112088282046897800000000000E-12 " "
relative error = 1.602191731202970400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998337 " "
y[1] (closed_form) = 13.304930060508365 " "
y[1] (numeric) = 13.304930060510515 " "
absolute error = 2.149391775674303000000000000E-12 " "
relative error = 1.6154852117968800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998326 " "
y[1] (closed_form) = 13.428596663575464 " "
y[1] (numeric) = 13.428596663577649 " "
absolute error = 2.184918912462308000000000000E-12 " "
relative error = 1.627064217654860500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998315 " "
y[1] (closed_form) = 13.553506136666115 " "
y[1] (numeric) = 13.55350613666834 " "
absolute error = 2.2239987629291136000000000000E-12 " "
relative error = 1.640902907707814400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998304 " "
y[1] (closed_form) = 13.679670970831726 " "
y[1] (numeric) = 13.679670970833987 " "
absolute error = 2.261302256556518800000000000E-12 " "
relative error = 1.653038484169792600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5499999999998293 " "
y[1] (closed_form) = 13.807103782660846 " "
y[1] (numeric) = 13.807103782663146 " "
absolute error = 2.3003821070233244000000000000E-12 " "
relative error = 1.666085910002484700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999828 " "
y[1] (closed_form) = 13.935817315540854 " "
y[1] (numeric) = 13.935817315543193 " "
absolute error = 2.33946195749013000000000000E-12 " "
relative error = 1.67874040289063200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999827 " "
y[1] (closed_form) = 14.0658244409323 " "
y[1] (numeric) = 14.065824440934684 " "
absolute error = 2.383870878475136000000000000E-12 " "
relative error = 1.694796411320153300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999826 " "
y[1] (closed_form) = 14.197138159656062 " "
y[1] (numeric) = 14.197138159658484 " "
absolute error = 2.4229507289419416000000000000E-12 " "
relative error = 1.706647284610661200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.589999999999825 " "
y[1] (closed_form) = 14.32977160319344 " "
y[1] (numeric) = 14.329771603195905 " "
absolute error = 2.4655832930875476000000000000E-12 " "
relative error = 1.720601947722658600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.599999999999824 " "
y[1] (closed_form) = 14.463738034999318 " "
y[1] (numeric) = 14.463738035001825 " "
absolute error = 2.5064395003937534000000000000E-12 " "
relative error = 1.73291267743419900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998227 " "
y[1] (closed_form) = 14.599050851828515 " "
y[1] (numeric) = 14.599050851831064 " "
absolute error = 2.5490720645393594000000000000E-12 " "
relative error = 1.746053281415956600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998216 " "
y[1] (closed_form) = 14.735723585075474 " "
y[1] (numeric) = 14.735723585078064 " "
absolute error = 2.589928271845565000000000000E-12 " "
relative error = 1.7575847272737100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998205 " "
y[1] (closed_form) = 14.873769902127416 " "
y[1] (numeric) = 14.873769902130045 " "
absolute error = 2.6290081223123707000000000000E-12 " "
relative error = 1.767546586784524700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998194 " "
y[1] (closed_form) = 15.013203607731082 " "
y[1] (numeric) = 15.013203607733754 " "
absolute error = 2.6716406864579767000000000000E-12 " "
relative error = 1.779527378874825300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6499999999998183 " "
y[1] (closed_form) = 15.15403864537323 " "
y[1] (numeric) = 15.154038645375946 " "
absolute error = 2.716049607442983000000000000E-12 " "
relative error = 1.792294233242064700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999817 " "
y[1] (closed_form) = 15.296289098674988 " "
y[1] (numeric) = 15.296289098677748 " "
absolute error = 2.7604585284279890000000000000E-12 " "
relative error = 1.804658967034761800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999816 " "
y[1] (closed_form) = 15.439969192800225 " "
y[1] (numeric) = 15.43996919280303 " "
absolute error = 2.8048674494129955000000000000E-12 " "
relative error = 1.816627620423573200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999815 " "
y[1] (closed_form) = 15.58509329587809 " "
y[1] (numeric) = 15.58509329588094 " "
absolute error = 2.8492763703980020000000000000E-12 " "
relative error = 1.828206168744316900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.689999999999814 " "
y[1] (closed_form) = 15.731675920439828 " "
y[1] (numeric) = 15.731675920442724 " "
absolute error = 2.8954616482224080000000000000E-12 " "
relative error = 1.840529682193870500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998128 " "
y[1] (closed_form) = 15.879731724870048 " "
y[1] (numeric) = 15.879731724872991 " "
absolute error = 2.943423282886215000000000000E-12 " "
relative error = 1.853572424196796300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998117 " "
y[1] (closed_form) = 16.029275514872573 " "
y[1] (numeric) = 16.02927551487556 " "
absolute error = 2.9878322038712213000000000000E-12 " "
relative error = 1.863984558191040500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998106 " "
y[1] (closed_form) = 16.18032224495102 " "
y[1] (numeric) = 16.18032224495406 " "
absolute error = 3.0375701953744283000000000000E-12 " "
relative error = 1.8773236709313900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998095 " "
y[1] (closed_form) = 16.332887019904277 " "
y[1] (numeric) = 16.33288701990736 " "
absolute error = 3.083755473198835000000000000E-12 " "
relative error = 1.888065146988880400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998084 " "
y[1] (closed_form) = 16.486985096336966 " "
y[1] (numeric) = 16.4869850963401 " "
absolute error = 3.133493464702042000000000000E-12 " "
relative error = 1.90058609648299700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7499999999998073 " "
y[1] (closed_form) = 16.642631884185157 " "
y[1] (numeric) = 16.642631884188336 " "
absolute error = 3.1796787425264483000000000000E-12 " "
relative error = 1.910562442679497600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999806 " "
y[1] (closed_form) = 16.799842948257336 " "
y[1] (numeric) = 16.799842948260565 " "
absolute error = 3.2294167340296553000000000000E-12 " "
relative error = 1.92228983567054500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999805 " "
y[1] (closed_form) = 16.95863400979092 " "
y[1] (numeric) = 16.9586340097942 " "
absolute error = 3.2791547255328624000000000000E-12 " "
relative error = 1.933619608536672800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999804 " "
y[1] (closed_form) = 17.119020948024385 " "
y[1] (numeric) = 17.119020948027714 " "
absolute error = 3.3288927170360694000000000000E-12 " "
relative error = 1.944557885140177400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.789999999999803 " "
y[1] (closed_form) = 17.281019801785217 " "
y[1] (numeric) = 17.281019801788595 " "
absolute error = 3.3786307085392764000000000000E-12 " "
relative error = 1.955110721064185500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998018 " "
y[1] (closed_form) = 17.44464677109379 " "
y[1] (numeric) = 17.444646771097215 " "
absolute error = 3.424815986363683000000000000E-12 " "
relative error = 1.96324754023606100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998007 " "
y[1] (closed_form) = 17.60991821878339 " "
y[1] (numeric) = 17.609918218786863 " "
absolute error = 3.47455397786689000000000000E-12 " "
relative error = 1.973066504170815600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999997996 " "
y[1] (closed_form) = 17.77685067213651 " "
y[1] (numeric) = 17.77685067214004 " "
absolute error = 3.5278446830488974000000000000E-12 " "
relative error = 1.984516126120388400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997985 " "
y[1] (closed_form) = 17.9454608245376 " "
y[1] (numeric) = 17.94546082454119 " "
absolute error = 3.588240815588506000000000000E-12 " "
relative error = 1.999525590717709500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997974 " "
y[1] (closed_form) = 18.11576553714241 " "
y[1] (numeric) = 18.115765537146057 " "
absolute error = 3.6486369481281145000000000000E-12 " "
relative error = 2.014067217113946200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8499999999997963 " "
y[1] (closed_form) = 18.28778184056412 " "
y[1] (numeric) = 18.28778184056782 " "
absolute error = 3.701927653310122000000000000E-12 " "
relative error = 2.02426280321152920000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999795 " "
y[1] (closed_form) = 18.461526936576412 " "
y[1] (numeric) = 18.46152693658018 " "
absolute error = 3.7694292132073315000000000000E-12 " "
relative error = 2.041775431770624600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999794 " "
y[1] (closed_form) = 18.637018199833687 " "
y[1] (numeric) = 18.637018199837513 " "
absolute error = 3.8262726320681395000000000000E-12 " "
relative error = 2.053049791034857700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999793 " "
y[1] (closed_form) = 18.81427317960851 " "
y[1] (numeric) = 18.8142731796124 " "
absolute error = 3.8902214782865485000000000000E-12 " "
relative error = 2.067696924111259700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.889999999999792 " "
y[1] (closed_form) = 18.99330960154657 " "
y[1] (numeric) = 18.993309601550525 " "
absolute error = 3.9541703245049575000000000000E-12 " "
relative error = 2.08187535898587200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997907 " "
y[1] (closed_form) = 19.17414536943926 " "
y[1] (numeric) = 19.174145369443277 " "
absolute error = 4.0181191707233666000000000000E-12 " "
relative error = 2.095592316269622200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997896 " "
y[1] (closed_form) = 19.35679856701406 " "
y[1] (numeric) = 19.35679856701814 " "
absolute error = 4.078515303262975000000000000E-12 " "
relative error = 2.10701955137001700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997885 " "
y[1] (closed_form) = 19.54128745974295 " "
y[1] (numeric) = 19.54128745974709 " "
absolute error = 4.1389114358025836000000000000E-12 " "
relative error = 2.118034159381342600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997874 " "
y[1] (closed_form) = 19.727630496668937 " "
y[1] (numeric) = 19.72763049667314 " "
absolute error = 4.202860282020992600000000000E-12 " "
relative error = 2.130443533363348700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997863 " "
y[1] (closed_form) = 19.915846312251 " "
y[1] (numeric) = 19.915846312255265 " "
absolute error = 4.266809128239401600000000000E-12 " "
relative error = 2.142419187887950600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9499999999997852 " "
y[1] (closed_form) = 20.105953728227544 " "
y[1] (numeric) = 20.105953728231874 " "
absolute error = 4.330757974457810600000000000E-12 " "
relative error = 2.153967940539765800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999784 " "
y[1] (closed_form) = 20.297971755498594 " "
y[1] (numeric) = 20.29797175550299 " "
absolute error = 4.39470682067621960000000000E-12 " "
relative error = 2.165096529649924700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999783 " "
y[1] (closed_form) = 20.49191959602689 " "
y[1] (numeric) = 20.49191959603135 " "
absolute error = 4.462208380573429000000000000E-12 " "
relative error = 2.177545329349521700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999782 " "
y[1] (closed_form) = 20.687816644758108 " "
y[1] (numeric) = 20.687816644762634 " "
absolute error = 4.526157226791838000000000000E-12 " "
relative error = 2.187837075566250700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.989999999999781 " "
y[1] (closed_form) = 20.88568249156037 " "
y[1] (numeric) = 20.88568249156497 " "
absolute error = 4.600764214046648700000000000E-12 " "
relative error = 2.202831636412052600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997797 " "
y[1] (closed_form) = 21.085536923183245 " "
y[1] (numeric) = 21.08553692318792 " "
absolute error = 4.675371201301459000000000000E-12 " "
relative error = 2.21733561651017600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997786 " "
y[1] (closed_form) = 21.28739992523644 " "
y[1] (numeric) = 21.287399925241193 " "
absolute error = 4.75353090223507000000000000E-12 " "
relative error = 2.233025601496643500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997775 " "
y[1] (closed_form) = 21.491291684188383 " "
y[1] (numeric) = 21.491291684193207 " "
absolute error = 4.82458517581108000000000000E-12 " "
relative error = 2.244902375672763200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997764 " "
y[1] (closed_form) = 21.697232589384875 " "
y[1] (numeric) = 21.69723258938977 " "
absolute error = 4.89563944938709030000000000E-12 " "
relative error = 2.256342798197327000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0399999999997753 " "
y[1] (closed_form) = 21.905243235088058 " "
y[1] (numeric) = 21.90524323509303 " "
absolute error = 4.973799150320701300000000000E-12 " "
relative error = 2.27059754458860120000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0499999999997742 " "
y[1] (closed_form) = 22.115344422535845 " "
y[1] (numeric) = 22.115344422540893 " "
absolute error = 5.048406137575512000000000000E-12 " "
relative error = 2.282761706587357300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999773 " "
y[1] (closed_form) = 22.327557162022064 " "
y[1] (numeric) = 22.327557162027183 " "
absolute error = 5.119460411151522000000000000E-12 " "
relative error = 2.292888726698431600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999772 " "
y[1] (closed_form) = 22.541902674997505 " "
y[1] (numeric) = 22.541902675002707 " "
absolute error = 5.201172825763933000000000000E-12 " "
relative error = 2.307335321579951400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999771 " "
y[1] (closed_form) = 22.758402396192093 " "
y[1] (numeric) = 22.75840239619738 " "
absolute error = 5.286437954055145000000000000E-12 " "
relative error = 2.3228510780438902000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.08999999999977 " "
y[1] (closed_form) = 22.977077975758363 " "
y[1] (numeric) = 22.977077975763727 " "
absolute error = 5.364597654988756000000000000E-12 " "
relative error = 2.334760608223812600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997687 " "
y[1] (closed_form) = 23.1979512814365 " "
y[1] (numeric) = 23.197951281441945 " "
absolute error = 5.446310069601168000000000000E-12 " "
relative error = 2.347754766585540300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997676 " "
y[1] (closed_form) = 23.421044400741135 " "
y[1] (numeric) = 23.42104440074666 " "
absolute error = 5.524469770534779000000000000E-12 " "
relative error = 2.358763202874062700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997665 " "
y[1] (closed_form) = 23.646379643170107 " "
y[1] (numeric) = 23.646379643175713 " "
absolute error = 5.6061821851471900000000000000E-12 " "
relative error = 2.370841655148021600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997654 " "
y[1] (closed_form) = 23.873979542435446 " "
y[1] (numeric) = 23.873979542441134 " "
absolute error = 5.687894599759602000000000000E-12 " "
relative error = 2.382466060863251000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1399999999997643 " "
y[1] (closed_form) = 24.10386685871674 " "
y[1] (numeric) = 24.103866858722512 " "
absolute error = 5.773159728050814000000000000E-12 " "
relative error = 2.39511766385444200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999763 " "
y[1] (closed_form) = 24.336064580937187 " "
y[1] (numeric) = 24.336064580943052 " "
absolute error = 5.865530283699627000000000000E-12 " "
relative error = 2.410221366808085500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999762 " "
y[1] (closed_form) = 24.570595929062517 " "
y[1] (numeric) = 24.570595929068467 " "
absolute error = 5.950795411990839000000000000E-12 " "
relative error = 2.421917412655074400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999761 " "
y[1] (closed_form) = 24.80748435642298 " "
y[1] (numeric) = 24.80748435642902 " "
absolute error = 6.0396132539608520000000000000E-12 " "
relative error = 2.43459319259718400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.17999999999976 " "
y[1] (closed_form) = 25.04675355205872 " "
y[1] (numeric) = 25.04675355206485 " "
absolute error = 6.128431095930864000000000000E-12 " "
relative error = 2.446796581119047600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.189999999999759 " "
y[1] (closed_form) = 25.288427443088697 " "
y[1] (numeric) = 25.288427443094914 " "
absolute error = 6.217248937900877000000000000E-12 " "
relative error = 2.45853521413805620000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997577 " "
y[1] (closed_form) = 25.532530197103405 " "
y[1] (numeric) = 25.532530197109715 " "
absolute error = 6.30961949354969000000000000E-12 " "
relative error = 2.471208080374853700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997566 " "
y[1] (closed_form) = 25.779086224581665 " "
y[1] (numeric) = 25.779086224588067 " "
absolute error = 6.401990049198503000000000000E-12 " "
relative error = 2.483404568116103800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997555 " "
y[1] (closed_form) = 26.02812018133169 " "
y[1] (numeric) = 26.028120181338185 " "
absolute error = 6.494360604847316000000000000E-12 " "
relative error = 2.495132402802299200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997544 " "
y[1] (closed_form) = 26.279656970956683 " "
y[1] (numeric) = 26.279656970963273 " "
absolute error = 6.590283874174929000000000000E-12 " "
relative error = 2.50775110248138700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2399999999997533 " "
y[1] (closed_form) = 26.533721747345226 " "
y[1] (numeric) = 26.5337217473519 " "
absolute error = 6.675549002466141000000000000E-12 " "
relative error = 2.515873598898371000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999752 " "
y[1] (closed_form) = 26.79033991718667 " "
y[1] (numeric) = 26.790339917193446 " "
absolute error = 6.775024985472555000000000000E-12 " "
relative error = 2.528905943864568000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999751 " "
y[1] (closed_form) = 27.04953714251186 " "
y[1] (numeric) = 27.049537142518734 " "
absolute error = 6.874500968478969000000000000E-12 " "
relative error = 2.541448651139689400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.26999999999975 " "
y[1] (closed_form) = 27.311339343259313 " "
y[1] (numeric) = 27.311339343266297 " "
absolute error = 6.984635092521785000000000000E-12 " "
relative error = 2.55741214472722500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.279999999999749 " "
y[1] (closed_form) = 27.575772699867287 " "
y[1] (numeric) = 27.57577269987437 " "
absolute error = 7.084111075528199000000000000E-12 " "
relative error = 2.56896194809521800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.289999999999748 " "
y[1] (closed_form) = 27.842863655891794 " "
y[1] (numeric) = 27.842863655898984 " "
absolute error = 7.190692485892214000000000000E-12 " "
relative error = 2.582598031137002000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997467 " "
y[1] (closed_form) = 28.11263892065102 " "
y[1] (numeric) = 28.11263892065831 " "
absolute error = 7.290168468898628000000000000E-12 " "
relative error = 2.59319962436660700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997456 " "
y[1] (closed_form) = 28.38512547189625 " "
y[1] (numeric) = 28.38512547190365 " "
absolute error = 7.400302592941443000000000000E-12 " "
relative error = 2.607105823882437400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997445 " "
y[1] (closed_form) = 28.660350558509684 " "
y[1] (numeric) = 28.66035055851719 " "
absolute error = 7.506884003305458000000000000E-12 " "
relative error = 2.61925756559755400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997434 " "
y[1] (closed_form) = 28.938341703229337 " "
y[1] (numeric) = 28.93834170323695 " "
absolute error = 7.613465413669473000000000000E-12 " "
relative error = 2.630926641114289500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3399999999997423 " "
y[1] (closed_form) = 29.21912670540134 " "
y[1] (numeric) = 29.21912670540906 " "
absolute error = 7.720046824033489000000000000E-12 " "
relative error = 2.642120998984678300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999741 " "
y[1] (closed_form) = 29.5027336437599 " "
y[1] (numeric) = 29.50273364376773 " "
absolute error = 7.830180948076304000000000000E-12 " "
relative error = 2.65405268631181900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.35999999999974 " "
y[1] (closed_form) = 29.789190879235196 " "
y[1] (numeric) = 29.78919087924314 " "
absolute error = 7.94386778579792000000000000E-12 " "
relative error = 2.666694714200935000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.369999999999739 " "
y[1] (closed_form) = 30.078527057789483 " "
y[1] (numeric) = 30.07852705779754 " "
absolute error = 8.057554623519536000000000000E-12 " "
relative error = 2.678839495045306500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.379999999999738 " "
y[1] (closed_form) = 30.370771113281737 " "
y[1] (numeric) = 30.370771113289905 " "
absolute error = 8.167688747562352000000000000E-12 " "
relative error = 2.689325442906011500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.389999999999737 " "
y[1] (closed_form) = 30.665952270361043 " "
y[1] (numeric) = 30.665952270369324 " "
absolute error = 8.281375585283968000000000000E-12 " "
relative error = 2.700511470269260600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997357 " "
y[1] (closed_form) = 30.964100047389092 " "
y[1] (numeric) = 30.96410004739749 " "
absolute error = 8.398615136684384000000000000E-12 " "
relative error = 2.712371786627320600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997346 " "
y[1] (closed_form) = 31.26524425939205 " "
y[1] (numeric) = 31.265244259400564 " "
absolute error = 8.5158546880848010000000000E-12 " "
relative error = 2.72374481306879500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997335 " "
y[1] (closed_form) = 31.56941502104206 " "
y[1] (numeric) = 31.5694150210507 " "
absolute error = 8.636646953164018000000000000E-12 " "
relative error = 2.735764013177756000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997324 " "
y[1] (closed_form) = 31.87664274966878 " "
y[1] (numeric) = 31.876642749677536 " "
absolute error = 8.757439218243235000000000000E-12 " "
relative error = 2.747290323832559700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4399999999997313 " "
y[1] (closed_form) = 32.18695816830108 " "
y[1] (numeric) = 32.18695816830997 " "
absolute error = 8.888889624358853000000000000E-12 " "
relative error = 2.76164326491496860000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.44999999999973 " "
y[1] (closed_form) = 32.500392308739436 " "
y[1] (numeric) = 32.50039230874845 " "
absolute error = 9.016787316795671000000000000E-12 " "
relative error = 2.774362608038745000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.459999999999729 " "
y[1] (closed_form) = 32.816976514659075 " "
y[1] (numeric) = 32.816976514668205 " "
absolute error = 9.130474154517287000000000000E-12 " "
relative error = 2.78224112158497570000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999728 " "
y[1] (closed_form) = 33.136742444744414 " "
y[1] (numeric) = 33.13674244475367 " "
absolute error = 9.258371846954105000000000000E-12 " "
relative error = 2.793989741868097000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.479999999999727 " "
y[1] (closed_form) = 33.459722075854934 " "
y[1] (numeric) = 33.45972207586432 " "
absolute error = 9.386269539390923000000000000E-12 " "
relative error = 2.8052443227447500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997258 " "
y[1] (closed_form) = 33.7859477062229 " "
y[1] (numeric) = 33.78594770623242 " "
absolute error = 9.521272659185342000000000000E-12 " "
relative error = 2.818116200846323400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997247 " "
y[1] (closed_form) = 34.115451958683195 " "
y[1] (numeric) = 34.11545195869286 " "
absolute error = 9.663381206337363000000000000E-12 " "
relative error = 2.832552597585565000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997236 " "
y[1] (closed_form) = 34.44826778393566 " "
y[1] (numeric) = 34.448267783945475 " "
absolute error = 9.812595180846984000000000000E-12 " "
relative error = 2.848501771523883000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997225 " "
y[1] (closed_form) = 34.78442846384018 " "
y[1] (numeric) = 34.784428463850126 " "
absolute error = 9.947598300641403000000000000E-12 " "
relative error = 2.859784892249224000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997214 " "
y[1] (closed_form) = 35.123967614744856 " "
y[1] (numeric) = 35.12396761475493 " "
absolute error = 1.00754959930782200000000000E-11 " "
relative error = 2.86855292192234600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5399999999997203 " "
y[1] (closed_form) = 35.46691919084775 " "
y[1] (numeric) = 35.46691919085796 " "
absolute error = 1.02104991128726400000000000E-11 " "
relative error = 2.878879628064075500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.549999999999719 " "
y[1] (closed_form) = 35.81331748759224 " "
y[1] (numeric) = 35.813317487602596 " "
absolute error = 1.03526076600246600000000000E-11 " "
relative error = 2.890714512446770400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999718 " "
y[1] (closed_form) = 36.163197145096696 " "
y[1] (numeric) = 36.1631971451072 " "
absolute error = 1.05018216345342810000000000E-11 " "
relative error = 2.904008069971823500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999717 " "
y[1] (closed_form) = 36.51659315161842 " "
y[1] (numeric) = 36.51659315162907 " "
absolute error = 1.0643930181686301000000000E-11 " "
relative error = 2.91482015791896500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.579999999999716 " "
y[1] (closed_form) = 36.87354084705257 " "
y[1] (numeric) = 36.87354084706336 " "
absolute error = 1.079314415619592200000000000E-11 " "
relative error = 2.92707017233975700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997148 " "
y[1] (closed_form) = 37.23407592646613 " "
y[1] (numeric) = 37.23407592647708 " "
absolute error = 1.094946355806314400000000000E-11 " "
relative error = 2.9407104340892803000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997137 " "
y[1] (closed_form) = 37.59823444366751 " "
y[1] (numeric) = 37.598234443678614 " "
absolute error = 1.110578295993036600000000000E-11 " "
relative error = 2.953804380514165600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997125 " "
y[1] (closed_form) = 37.96605281481188 " "
y[1] (numeric) = 37.96605281482313 " "
absolute error = 1.124789150708238600000000000E-11 " "
relative error = 2.96261809515636300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997114 " "
y[1] (closed_form) = 38.33756782204288 " "
y[1] (numeric) = 38.33756782205429 " "
absolute error = 1.141131633630720900000000000E-11 " "
relative error = 2.976536328354681400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997103 " "
y[1] (closed_form) = 38.71281661717082 " "
y[1] (numeric) = 38.71281661718239 " "
absolute error = 1.156763573817443100000000000E-11 " "
relative error = 2.98806357919296440000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6399999999997092 " "
y[1] (closed_form) = 39.09183672538794 " "
y[1] (numeric) = 39.09183672539966 " "
absolute error = 1.171684971268405200000000000E-11 " "
relative error = 2.997262521838637300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999708 " "
y[1] (closed_form) = 39.4746660490209 " "
y[1] (numeric) = 39.47466604903278 " "
absolute error = 1.188027454190887500000000000E-11 " "
relative error = 3.00959469224022600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999707 " "
y[1] (closed_form) = 39.86134287132108 " "
y[1] (numeric) = 39.861342871333115 " "
absolute error = 1.203659394377609700000000000E-11 " "
relative error = 3.019615767244015500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999706 " "
y[1] (closed_form) = 40.25190586029296 " "
y[1] (numeric) = 40.25190586030516 " "
absolute error = 1.22000187730009200000000000E-11 " "
relative error = 3.0309170490820897000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.679999999999705 " "
y[1] (closed_form) = 40.646394072560895 " "
y[1] (numeric) = 40.646394072573266 " "
absolute error = 1.237054902958334400000000000E-11 " "
relative error = 3.04345546802989700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997037 " "
y[1] (closed_form) = 41.044846957274856 " "
y[1] (numeric) = 41.0448469572874 " "
absolute error = 1.254107928616576800000000000E-11 " "
relative error = 3.05545768003965430000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997026 " "
y[1] (closed_form) = 41.44730436005536 " "
y[1] (numeric) = 41.44730436006808 " "
absolute error = 1.271871497010579300000000000E-11 " "
relative error = 3.06864708489061440000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997015 " "
y[1] (closed_form) = 41.853806526978076 " "
y[1] (numeric) = 41.85380652699097 " "
absolute error = 1.289635065404581800000000000E-11 " "
relative error = 3.08128500707172350000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997004 " "
y[1] (closed_form) = 42.26439410859843 " "
y[1] (numeric) = 42.264394108611505 " "
absolute error = 1.307398633798584300000000000E-11 " "
relative error = 3.093380755534366000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999996993 " "
y[1] (closed_form) = 42.67910816401676 " "
y[1] (numeric) = 42.67910816403001 " "
absolute error = 1.325162202192586800000000000E-11 " "
relative error = 3.10494351732927330000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7399999999996982 " "
y[1] (closed_form) = 43.097990164984196 " "
y[1] (numeric) = 43.09799016499764 " "
absolute error = 1.344346856058109600000000000E-11 " "
relative error = 3.1192796947416596000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999697 " "
y[1] (closed_form) = 43.5210820000499 " "
y[1] (numeric) = 43.52108200006353 " "
absolute error = 1.362820967187872200000000000E-11 " "
relative error = 3.131404148422388700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999696 " "
y[1] (closed_form) = 43.94842597874997 " "
y[1] (numeric) = 43.94842597876378 " "
absolute error = 1.381295078317634800000000000E-11 " "
relative error = 3.14299101174982100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999695 " "
y[1] (closed_form) = 44.38006483583838 " "
y[1] (numeric) = 44.38006483585237 " "
absolute error = 1.399058646711637300000000000E-11 " "
relative error = 3.15244840647878170000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.779999999999694 " "
y[1] (closed_form) = 44.81604173556055 " "
y[1] (numeric) = 44.816041735574736 " "
absolute error = 1.4182433005771600000000000E-11 " "
relative error = 3.16458849477510850000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996927 " "
y[1] (closed_form) = 45.25640027596977 " "
y[1] (numeric) = 45.25640027598414 " "
absolute error = 1.437427954442682700000000000E-11 " "
relative error = 3.17618711536349900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996916 " "
y[1] (closed_form) = 45.70118449328704 " "
y[1] (numeric) = 45.7011844933016 " "
absolute error = 1.455902065572445300000000000E-11 " "
relative error = 3.18569875532722800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996905 " "
y[1] (closed_form) = 46.15043886630475 " "
y[1] (numeric) = 46.15043886631951 " "
absolute error = 1.476507804909488200000000000E-11 " "
relative error = 3.19933643358592800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996894 " "
y[1] (closed_form) = 46.60420832083457 " "
y[1] (numeric) = 46.604208320849544 " "
absolute error = 1.49711354424653100000000000E-11 " "
relative error = 3.21239990590558200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8299999999996883 " "
y[1] (closed_form) = 47.06253823420012 " "
y[1] (numeric) = 47.06253823421528 " "
absolute error = 1.516298198112053800000000000E-11 " "
relative error = 3.221879343962300600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999687 " "
y[1] (closed_form) = 47.525474439774655 " "
y[1] (numeric) = 47.52547443979003 " "
absolute error = 1.537614480184856800000000000E-11 " "
relative error = 3.235347986127642400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999686 " "
y[1] (closed_form) = 47.993063231564534 " "
y[1] (numeric) = 47.99306323158011 " "
absolute error = 1.557509676786139600000000000E-11 " "
relative error = 3.24528082167045700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999685 " "
y[1] (closed_form) = 48.465351368838576 " "
y[1] (numeric) = 48.46535136885437 " "
absolute error = 1.579536501594702700000000000E-11 " "
relative error = 3.25910461181611500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999684 " "
y[1] (closed_form) = 48.9423860808041 " "
y[1] (numeric) = 48.942386080820114 " "
absolute error = 1.601563326403265800000000000E-11 " "
relative error = 3.27234418803994900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.879999999999683 " "
y[1] (closed_form) = 49.42421507132982 " "
y[1] (numeric) = 49.42421507134606 " "
absolute error = 1.62430069394758900000000000E-11 " "
relative error = 3.286447122333399600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996817 " "
y[1] (closed_form) = 49.910886523716314 " "
y[1] (numeric) = 49.91088652373277 " "
absolute error = 1.64561697602039200000000000E-11 " "
relative error = 3.29711029123563870000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996806 " "
y[1] (closed_form) = 50.40244910551439 " "
y[1] (numeric) = 50.402449105531076 " "
absolute error = 1.668354343564715200000000000E-11 " "
relative error = 3.3100660249110503000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996795 " "
y[1] (closed_form) = 50.89895197339187 " "
y[1] (numeric) = 50.89895197340877 " "
absolute error = 1.690381168373278300000000000E-11 " "
relative error = 3.32105299389454700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996784 " "
y[1] (closed_form) = 51.40044477804928 " "
y[1] (numeric) = 51.4004447780664 " "
absolute error = 1.712407993181841400000000000E-11 " "
relative error = 3.33150423226129530000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9299999999996773 " "
y[1] (closed_form) = 51.906977669185004 " "
y[1] (numeric) = 51.90697766920235 " "
absolute error = 1.734434817990404600000000000E-11 " "
relative error = 3.34142902529280860000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999676 " "
y[1] (closed_form) = 52.41860130051027 " "
y[1] (numeric) = 52.41860130052784 " "
absolute error = 1.757172185534727800000000000E-11 " "
relative error = 3.352192050034007000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999675 " "
y[1] (closed_form) = 52.93536683481456 " "
y[1] (numeric) = 52.935366834832365 " "
absolute error = 1.78062009581481100000000000E-11 " "
relative error = 3.36376264543751500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999674 " "
y[1] (closed_form) = 53.45732594908195 " "
y[1] (numeric) = 53.4573259491 " "
absolute error = 1.805489091566414600000000000E-11 " "
relative error = 3.37743996638765900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999673 " "
y[1] (closed_form) = 53.98453083965883 " "
y[1] (numeric) = 53.98453083967712 " "
absolute error = 1.82893700184649800000000000E-11 " "
relative error = 3.38789088911170100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.979999999999672 " "
y[1] (closed_form) = 54.517034227473594 " "
y[1] (numeric) = 54.51703422749213 " "
absolute error = 1.853805997598101400000000000E-11 " "
relative error = 3.40041607887738850000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996707 " "
y[1] (closed_form) = 55.05488936330879 " "
y[1] (numeric) = 55.05488936332759 " "
absolute error = 1.88009607882122500000000000E-11 " "
relative error = 3.41494842794872800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996696 " "
y[1] (closed_form) = 55.5981500331262 " "
y[1] (numeric) = 55.59815003314525 " "
absolute error = 1.904965074572828600000000000E-11 " "
relative error = 3.426310180172942000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999673 " "
y[1] (closed_form) = 56.14687056344578 " "
y[1] (numeric) = 56.14687056346485 " "
absolute error = 1.90709670278010900000000000E-11 " "
relative error = 3.39662154567474230000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999676 " "
y[1] (closed_form) = 56.701105826777585 " "
y[1] (numeric) = 56.70110582679667 " "
absolute error = 1.90851778825162900000000000E-11 " "
relative error = 3.36592692580312100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.02999999999968 " "
y[1] (closed_form) = 57.26091124710981 " "
y[1] (numeric) = 57.26091124712891 " "
absolute error = 1.909938873723149300000000000E-11 " "
relative error = 3.335502059128602000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999683 " "
y[1] (closed_form) = 57.826342805451006 " "
y[1] (numeric) = 57.826342805470105 " "
absolute error = 1.909938873723149300000000000E-11 " "
relative error = 3.30288719822535400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999686 " "
y[1] (closed_form) = 58.39745704542819 " "
y[1] (numeric) = 58.39745704544728 " "
absolute error = 1.909228330987389200000000000E-11 " "
relative error = 3.26936895471693900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.05999999999969 " "
y[1] (closed_form) = 58.9743110789413 " "
y[1] (numeric) = 58.97431107896038 " "
absolute error = 1.90851778825162900000000000E-11 " "
relative error = 3.23618496483484600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999693 " "
y[1] (closed_form) = 59.55696259187439 " "
y[1] (numeric) = 59.556962591893466 " "
absolute error = 1.90780724551586900000000000E-11 " "
relative error = 3.203332007694024700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999696 " "
y[1] (closed_form) = 60.145469849864305 " "
y[1] (numeric) = 60.145469849883376 " "
absolute error = 1.90709670278010900000000000E-11 " "
relative error = 3.17080689125984300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997 " "
y[1] (closed_form) = 60.73989170412726 " "
y[1] (numeric) = 60.73989170414633 " "
absolute error = 1.90709670278010900000000000E-11 " "
relative error = 3.13977626445211770000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999703 " "
y[1] (closed_form) = 61.34028759734405 " "
y[1] (numeric) = 61.34028759736311 " "
absolute error = 1.905675617308588700000000000E-11 " "
relative error = 3.10672755533526700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999706 " "
y[1] (closed_form) = 61.94671756960431 " "
y[1] (numeric) = 61.94671756962336 " "
absolute error = 1.904965074572828600000000000E-11 " "
relative error = 3.07516709409563100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.11999999999971 " "
y[1] (closed_form) = 62.55924226441064 " "
y[1] (numeric) = 62.55924226442967 " "
absolute error = 1.902833446365548300000000000E-11 " "
relative error = 3.04165040606326540000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999713 " "
y[1] (closed_form) = 63.17792293474296 " "
y[1] (numeric) = 63.177922934761966 " "
absolute error = 1.90070181815826800000000000E-11 " "
relative error = 3.008490513563606400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999716 " "
y[1] (closed_form) = 63.80282144918386 " "
y[1] (numeric) = 63.80282144920285 " "
absolute error = 1.899280732686747800000000000E-11 " "
relative error = 2.97679740417034930000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.14999999999972 " "
y[1] (closed_form) = 64.43400029810554 " "
y[1] (numeric) = 64.43400029812452 " "
absolute error = 1.897149104479467500000000000E-11 " "
relative error = 2.944329229447587600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999723 " "
y[1] (closed_form) = 65.07152259991888 " "
y[1] (numeric) = 65.07152259993784 " "
absolute error = 1.895728019007947300000000000E-11 " "
relative error = 2.913299002796517000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999726 " "
y[1] (closed_form) = 65.71545210738533 " "
y[1] (numeric) = 65.71545210740426 " "
absolute error = 1.89288584806490700000000000E-11 " "
relative error = 2.88042733841616200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.17999999999973 " "
y[1] (closed_form) = 66.36585321399225 " "
y[1] (numeric) = 66.36585321401117 " "
absolute error = 1.891464762593386700000000000E-11 " "
relative error = 2.8500571769860100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999733 " "
y[1] (closed_form) = 67.0227909603923 " "
y[1] (numeric) = 67.02279096041119 " "
absolute error = 1.888622591650346300000000000E-11 " "
relative error = 2.817881148468502400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999736 " "
y[1] (closed_form) = 67.68633104090756 " "
y[1] (numeric) = 67.6863310409264 " "
absolute error = 1.884359335235785700000000000E-11 " "
relative error = 2.78395845402956800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.20999999999974 " "
y[1] (closed_form) = 68.35653981009905 " "
y[1] (numeric) = 68.35653981011788 " "
absolute error = 1.882938249764265500000000000E-11 " "
relative error = 2.75458391398284100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999743 " "
y[1] (closed_form) = 69.0334842894022 " "
y[1] (numeric) = 69.03348428942097 " "
absolute error = 1.877253907878184700000000000E-11 " "
relative error = 2.719338198269640000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999746 " "
y[1] (closed_form) = 69.71723217382903 " "
y[1] (numeric) = 69.71723217384776 " "
absolute error = 1.87299065146362400000000000E-11 " "
relative error = 2.68655337147294400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.23999999999975 " "
y[1] (closed_form) = 70.40785183873781 " "
y[1] (numeric) = 70.4078518387565 " "
absolute error = 1.868727395049063500000000000E-11 " "
relative error = 2.654146300797811000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999753 " "
y[1] (closed_form) = 71.10541234667055 " "
y[1] (numeric) = 71.10541234668918 " "
absolute error = 1.863043053162982700000000000E-11 " "
relative error = 2.620114266519991700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999756 " "
y[1] (closed_form) = 71.80998345425932 " "
y[1] (numeric) = 71.8099834542779 " "
absolute error = 1.85735871127690200000000000E-11 " "
relative error = 2.586490933339346000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.26999999999976 " "
y[1] (closed_form) = 72.52163561920204 " "
y[1] (numeric) = 72.52163561922058 " "
absolute error = 1.853095454862341300000000000E-11 " "
relative error = 2.555231192788604000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999763 " "
y[1] (closed_form) = 73.24044000730825 " "
y[1] (numeric) = 73.24044000732671 " "
absolute error = 1.845990027504740300000000000E-11 " "
relative error = 2.520451853266500500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.2899999999997664 " "
y[1] (closed_form) = 73.96646849961576 " "
y[1] (numeric) = 73.96646849963417 " "
absolute error = 1.841726771090179700000000000E-11 " "
relative error = 2.489948227148017800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.29999999999977 " "
y[1] (closed_form) = 74.69979369957883 " "
y[1] (numeric) = 74.6997936995972 " "
absolute error = 1.83604242920409900000000000E-11 " "
relative error = 2.45789491278668780000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999773 " "
y[1] (closed_form) = 75.44048894032856 " "
y[1] (numeric) = 75.44048894034687 " "
absolute error = 1.83035808731801800000000000E-11 " "
relative error = 2.426227763138946400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3199999999997765 " "
y[1] (closed_form) = 76.18862829200629 " "
y[1] (numeric) = 76.18862829202452 " "
absolute error = 1.82325265996041700000000000E-11 " "
relative error = 2.3930771570955198000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.32999999999978 " "
y[1] (closed_form) = 76.9442865691706 " "
y[1] (numeric) = 76.94428656918878 " "
absolute error = 1.817568318074336300000000000E-11 " "
relative error = 2.36218749840561200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999783 " "
y[1] (closed_form) = 77.70753933827896 " "
y[1] (numeric) = 77.70753933829707 " "
absolute error = 1.810462890716735300000000000E-11 " "
relative error = 2.32984200263422310000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3499999999997865 " "
y[1] (closed_form) = 78.47846292524432 " "
y[1] (numeric) = 78.47846292526233 " "
absolute error = 1.80193637788761400000000000E-11 " "
relative error = 2.296090303914428100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.35999999999979 " "
y[1] (closed_form) = 79.25713442306781 " "
y[1] (numeric) = 79.25713442308574 " "
absolute error = 1.79340986505849300000000000E-11 " "
relative error = 2.262774043135882500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999793 " "
y[1] (closed_form) = 80.0436316995481 " "
y[1] (numeric) = 80.04363169956594 " "
absolute error = 1.783462266757851500000000000E-11 " "
relative error = 2.22811262918736400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3799999999997965 " "
y[1] (closed_form) = 80.83803340506827 " "
y[1] (numeric) = 80.83803340508602 " "
absolute error = 1.774935753928730300000000000E-11 " "
relative error = 2.195669141324568300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.3899999999998 " "
y[1] (closed_form) = 81.64041898046086 " "
y[1] (numeric) = 81.64041898047853 " "
absolute error = 1.76640924109960900000000000E-11 " "
relative error = 2.163645487319665300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999803 " "
y[1] (closed_form) = 82.45086866495208 " "
y[1] (numeric) = 82.45086866496965 " "
absolute error = 1.756461642798967700000000000E-11 " "
relative error = 2.130313083706294700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4099999999998065 " "
y[1] (closed_form) = 83.26946350418575 " "
y[1] (numeric) = 83.26946350420323 " "
absolute error = 1.747935129969846500000000000E-11 " "
relative error = 2.099131009631138300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.41999999999981 " "
y[1] (closed_form) = 84.09628535832798 " "
y[1] (numeric) = 84.09628535834533 " "
absolute error = 1.735145360726164700000000000E-11 " "
relative error = 2.063284190654605400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999813 " "
y[1] (closed_form) = 84.93141691025315 " "
y[1] (numeric) = 84.9314169102704 " "
absolute error = 1.725197762425523300000000000E-11 " "
relative error = 2.031283387451943700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4399999999998165 " "
y[1] (closed_form) = 85.77494167381245 " "
y[1] (numeric) = 85.77494167382959 " "
absolute error = 1.713829078653361600000000000E-11 " "
relative error = 1.998053330273033300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.44999999999982 " "
y[1] (closed_form) = 86.62694400218516 " "
y[1] (numeric) = 86.62694400220217 " "
absolute error = 1.7010393094096798000000000E-11 " "
relative error = 1.963637675325094200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999823 " "
y[1] (closed_form) = 87.4875090963141 " "
y[1] (numeric) = 87.48750909633101 " "
absolute error = 1.691091711109038400000000000E-11 " "
relative error = 1.932952176347063600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.469999999999827 " "
y[1] (closed_form) = 88.35672301342585 " "
y[1] (numeric) = 88.35672301344263 " "
absolute error = 1.678301941865356600000000000E-11 " "
relative error = 1.89946150629685280000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.47999999999983 " "
y[1] (closed_form) = 89.23467267563647 " "
y[1] (numeric) = 89.23467267565314 " "
absolute error = 1.66693325809319500000000000E-11 " "
relative error = 1.868033140158885400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999833 " "
y[1] (closed_form) = 90.1214458786438 " "
y[1] (numeric) = 90.12144587866034 " "
absolute error = 1.654143488849513200000000000E-11 " "
relative error = 1.83546044198731380000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.499999999999837 " "
y[1] (closed_form) = 91.0171313005071 " "
y[1] (numeric) = 91.01713130052352 " "
absolute error = 1.641353719605831400000000000E-11 " "
relative error = 1.80334591538229100000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.50999999999984 " "
y[1] (closed_form) = 91.921818510515 " "
y[1] (numeric) = 91.92181851053127 " "
absolute error = 1.627142864890629400000000000E-11 " "
relative error = 1.770137809778534200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999843 " "
y[1] (closed_form) = 92.83559797814239 " "
y[1] (numeric) = 92.8355979781585 " "
absolute error = 1.611510924703907200000000000E-11 " "
relative error = 1.735876064570972300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.529999999999847 " "
y[1] (closed_form) = 93.75856108209751 " "
y[1] (numeric) = 93.75856108211347 " "
absolute error = 1.59587898451718500000000000E-11 " "
relative error = 1.702115482680872600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.53999999999985 " "
y[1] (closed_form) = 94.69080011945991 " "
y[1] (numeric) = 94.69080011947571 " "
absolute error = 1.580247044330462800000000000E-11 " "
relative error = 1.668849605597224600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999853 " "
y[1] (closed_form) = 95.6324083149102 " "
y[1] (numeric) = 95.63240831492584 " "
absolute error = 1.564615104143740600000000000E-11 " "
relative error = 1.636072051005536800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.559999999999857 " "
y[1] (closed_form) = 96.58347983005257 " "
y[1] (numeric) = 96.58347983006807 " "
absolute error = 1.550404249428538600000000000E-11 " "
relative error = 1.60524786656746700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.56999999999986 " "
y[1] (closed_form) = 97.54410977283113 " "
y[1] (numeric) = 97.54410977284648 " "
absolute error = 1.534772309241816400000000000E-11 " "
relative error = 1.573413620582649600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999863 " "
y[1] (closed_form) = 98.51439420704067 " "
y[1] (numeric) = 98.51439420705584 " "
absolute error = 1.51771928358357400000000000E-11 " "
relative error = 1.540606624849046600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.589999999999867 " "
y[1] (closed_form) = 99.4944301619332 " "
y[1] (numeric) = 99.49443016194819 " "
absolute error = 1.499245172453811400000000000E-11 " "
relative error = 1.506863419403176300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.59999999999987 " "
y[1] (closed_form) = 100.48431564192087 " "
y[1] (numeric) = 100.4843156419357 " "
absolute error = 1.48219214679556900000000000E-11 " "
relative error = 1.475048257359296600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999873 " "
y[1] (closed_form) = 101.48414963637663 " "
y[1] (numeric) = 101.48414963639128 " "
absolute error = 1.465139121137326600000000000E-11 " "
relative error = 1.443712270721094800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.619999999999877 " "
y[1] (closed_form) = 102.4940321295331 " "
y[1] (numeric) = 102.49403212954755 " "
absolute error = 1.445243924536043800000000000E-11 " "
relative error = 1.410076171761423500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.62999999999988 " "
y[1] (closed_form) = 103.51406411048117 " "
y[1] (numeric) = 103.51406411049541 " "
absolute error = 1.423927642463240800000000000E-11 " "
relative error = 1.375588577938041700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999883 " "
y[1] (closed_form) = 104.54434758326896 " "
y[1] (numeric) = 104.54434758328301 " "
absolute error = 1.405453531333478200000000000E-11 " "
relative error = 1.34436109060228510000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999887 " "
y[1] (closed_form) = 105.58498557710234 " "
y[1] (numeric) = 105.58498557711617 " "
absolute error = 1.38271616378915500000000000E-11 " "
relative error = 1.309576504870989300000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.65999999999989 " "
y[1] (closed_form) = 106.63608215664787 " "
y[1] (numeric) = 106.63608215666152 " "
absolute error = 1.364242052659392400000000000E-11 " "
relative error = 1.279343750322079200000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999893 " "
y[1] (closed_form) = 107.69774243243945 " "
y[1] (numeric) = 107.69774243245287 " "
absolute error = 1.341504685115069200000000000E-11 " "
relative error = 1.245620061123023900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999897 " "
y[1] (closed_form) = 108.77007257138935 " "
y[1] (numeric) = 108.77007257140254 " "
absolute error = 1.31876731757074600000000000E-11 " "
relative error = 1.212435816575552900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6899999999999 " "
y[1] (closed_form) = 109.8531798074051 " "
y[1] (numeric) = 109.85317980741807 " "
absolute error = 1.29745103549794300000000000E-11 " "
relative error = 1.181077359592719900000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999903 " "
y[1] (closed_form) = 110.94717245211288 " "
y[1] (numeric) = 110.94717245212561 " "
absolute error = 1.273292582482099500000000000E-11 " "
relative error = 1.147656631836813400000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999907 " "
y[1] (closed_form) = 112.05215990568882 " "
y[1] (numeric) = 112.0521599057013 " "
absolute error = 1.24771304399473590000000000E-11 " "
relative error = 1.113510926558578700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.71999999999991 " "
y[1] (closed_form) = 113.16825266779911 " "
y[1] (numeric) = 113.16825266781136 " "
absolute error = 1.224975676450412700000000000E-11 " "
relative error = 1.082437563162064500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999913 " "
y[1] (closed_form) = 114.29556234865005 " "
y[1] (numeric) = 114.29556234866205 " "
absolute error = 1.199396137963049100000000000E-11 " "
relative error = 1.049381194962216600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999917 " "
y[1] (closed_form) = 115.43420168014914 " "
y[1] (numeric) = 115.43420168016087 " "
absolute error = 1.172395514004165300000000000E-11 " "
relative error = 1.015639643138605700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.74999999999992 " "
y[1] (closed_form) = 116.58428452717843 " "
y[1] (numeric) = 116.58428452718988 " "
absolute error = 1.145394890045281500000000000E-11 " "
relative error = 9.824607962304422000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999923 " "
y[1] (closed_form) = 117.74592589898097 " "
y[1] (numeric) = 117.74592589899216 " "
absolute error = 1.118394266086397700000000000E-11 " "
relative error = 9.498369115937937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999927 " "
y[1] (closed_form) = 118.91924196066203 " "
y[1] (numeric) = 118.91924196067292 " "
absolute error = 1.088551471184473500000000000E-11 " "
relative error = 9.153703414495036000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.77999999999993 " "
y[1] (closed_form) = 120.10435004480551 " "
y[1] (numeric) = 120.10435004481616 " "
absolute error = 1.0643930181686301000000000E-11 " "
relative error = 8.862235362595552000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999933 " "
y[1] (closed_form) = 121.30136866320746 " "
y[1] (numeric) = 121.3013686632178 " "
absolute error = 1.034550223266705900000000000E-11 " "
relative error = 8.52875968892921900000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999937 " "
y[1] (closed_form) = 122.5104175187272 " "
y[1] (numeric) = 122.51041751873726 " "
absolute error = 1.006128513836301900000000000E-11 " "
relative error = 8.212595583412349000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.80999999999994 " "
y[1] (closed_form) = 123.73161751725783 " "
y[1] (numeric) = 123.73161751726757 " "
absolute error = 9.734435479913373000000000000E-12 " "
relative error = 7.867379151133811000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999943 " "
y[1] (closed_form) = 124.9650907798169 " "
y[1] (numeric) = 124.96509077982628 " "
absolute error = 9.379164112033322000000000000E-12 " "
relative error = 7.505427358556482000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999947 " "
y[1] (closed_form) = 126.21096065475854 " "
y[1] (numeric) = 126.2109606547676 " "
absolute error = 9.066525308298878000000000000E-12 " "
relative error = 7.1836275243160050000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.83999999999995 " "
y[1] (closed_form) = 127.46935173010847 " "
y[1] (numeric) = 127.46935173011724 " "
absolute error = 8.768097359279636000000000000E-12 " "
relative error = 6.878592571682937000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8499999999999535 " "
y[1] (closed_form) = 128.7403898460229 " "
y[1] (numeric) = 128.74038984603135 " "
absolute error = 8.44124770082999000000000000E-12 " "
relative error = 6.556798306208298000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999957 " "
y[1] (closed_form) = 130.02420210737264 " "
y[1] (numeric) = 130.02420210738075 " "
absolute error = 8.100187187665142000000000000E-12 " "
relative error = 6.229753427731932000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.86999999999996 " "
y[1] (closed_form) = 131.32091689645364 " "
y[1] (numeric) = 131.32091689646143 " "
absolute error = 7.787548383930698000000000000E-12 " "
relative error = 5.9301660146579460000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.8799999999999635 " "
y[1] (closed_form) = 132.6306638858254 " "
y[1] (numeric) = 132.63066388583283 " "
absolute error = 7.418066161335446000000000000E-12 " "
relative error = 5.5930249792923150000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999967 " "
y[1] (closed_form) = 133.95357405127837 " "
y[1] (numeric) = 133.95357405128544 " "
absolute error = 7.077005648170598000000000000E-12 " "
relative error = 5.283177920629031000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.89999999999997 " "
y[1] (closed_form) = 135.2897796849315 " "
y[1] (numeric) = 135.28977968493817 " "
absolute error = 6.679101716144942000000000000E-12 " "
relative error = 4.936885647755147000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9099999999999735 " "
y[1] (closed_form) = 136.63941440846162 " "
y[1] (numeric) = 136.63941440846793 " "
absolute error = 6.30961949354969000000000000E-12 " "
relative error = 4.617715555109227000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999977 " "
y[1] (closed_form) = 138.00261318646582 " "
y[1] (numeric) = 138.0026131864717 " "
absolute error = 5.8832938520936300000000000000E-12 " "
relative error = 4.263175686495344600000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.92999999999998 " "
y[1] (closed_form) = 139.3795123399579 " "
y[1] (numeric) = 139.37951233996338 " "
absolute error = 5.4853899200679730000000000000E-12 " "
relative error = 3.935578355797848000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9399999999999835 " "
y[1] (closed_form) = 140.77024956000065 " "
y[1] (numeric) = 140.7702495600057 " "
absolute error = 5.059064278611913000000000000E-12 " "
relative error = 3.5938447892397773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999987 " "
y[1] (closed_form) = 142.17496392147498 " "
y[1] (numeric) = 142.1749639214796 " "
absolute error = 4.604316927725449000000000000E-12 " "
relative error = 3.238486440037693000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.95999999999999 " "
y[1] (closed_form) = 143.5937958969877 " "
y[1] (numeric) = 143.59379589699185 " "
absolute error = 4.149569576838985000000000000E-12 " "
relative error = 2.8897972582435466000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.9699999999999935 " "
y[1] (closed_form) = 145.02688737091864 " "
y[1] (numeric) = 145.0268873709224 " "
absolute error = 3.751665644813329000000000000E-12 " "
relative error = 2.5868759323353085000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999997 " "
y[1] (closed_form) = 146.47438165360953 " "
y[1] (numeric) = 146.47438165361282 " "
absolute error = 3.296918293926865000000000000E-12 " "
relative error = 2.250849777760860800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.99 " "
y[1] (closed_form) = 147.9364234956948 " "
y[1] (numeric) = 147.93642349569768 " "
absolute error = 2.8705926524708050000000000000E-12 " "
relative error = 1.9404231795250504000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ; "
Iterations = 4000
"Total Elapsed Time "= 1 Minutes 22 Seconds
"Elapsed Time(since restart) "= 1 Minutes 22 Seconds
"Time to Timeout "= 1 Minutes 37 Seconds
Percent Done = 100.02500000000009 "%"
(%o255) temp/diffeq.diff_B.max