(%i1) batch("temp/diffeq.expt_lin_sin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.expt_lin_sin.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([30],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([30],convfloat),[arr_b],
completearray([30],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,30,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[30],convfloat)
(%i173) completearray(array_norms,[30],convfloat)
(%i174) completearray(array_fact_1,[30],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[30],convfloat)
(%i184) completearray(array_x,[30],convfloat)
(%i185) completearray(array_tmp0,[30],convfloat)
(%i186) completearray(array_tmp1,[30],convfloat)
(%i187) completearray(array_tmp2,[30],convfloat)
(%i188) completearray(array_tmp3_g,[30],convfloat)
(%i189) completearray(array_tmp3,[30],convfloat)
(%i190) completearray(array_tmp4_c1,[30],convfloat)
(%i191) completearray(array_tmp4_a1,[30],convfloat)
(%i192) completearray(array_tmp4_a2,[30],convfloat)
(%i193) completearray(array_tmp4,[30],convfloat)
(%i194) completearray(array_tmp5,[30],convfloat)
(%i195) completearray(array_m1,[30],convfloat)
(%i196) completearray(array_y_higher,[2,30],convfloat)
(%i197) completearray(array_y_higher_work,[2,30],convfloat)
(%i198) completearray(array_y_higher_work2,[2,30],convfloat)
(%i199) completearray(array_y_set_initial,[2,30],convfloat)
(%i200) completearray(array_given_rad_poles,[2,3],convfloat)
(%i201) completearray(array_given_ord_poles,[2,3],convfloat)
(%i202) completearray(array_rad_test_poles,[2,4],convfloat)
(%i203) completearray(array_ord_test_poles,[2,4],convfloat)
(%i204) completearray(array_fact_2,[30,30],convfloat)
(%i205) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i206) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i207) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i208) 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))
(%i209) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i210) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i211) 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)
(%i212) 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)
(%i213) 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)
(%i214) 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)
(%i215) 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)
(%i216) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i217) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i218) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i219) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i220) log_revs(file,revs):=printf(file,revs)
(%i221) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i222) 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)
(%i223) logstart(file):=(printf(file,""),0)
(%i224) logend(file):=(printf(file,"
~%"),0)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) 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)
(%i229) 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)
(%i230) c(in_val):=(ret:in_val,ret)
(%i231) 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)
(%i232) 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)
(%i233) 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)
(%i234) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i235) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i236) 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)
(%i237) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i238) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i239) 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)
(%i240) log10(x):=log(x)/glob_log_10
(%i241) c(x):=x
(%i242) 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
(%i243) 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)
(%i244) exact_soln_y(x):=block(c(0.0))
(%o244) exact_soln_y(x) := block(c(0.0))
(%i245) 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)
(%i246) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i247) 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)
(%i248) 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)
(%i249) 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))
(%i250) 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))
(%i251) 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(28)
*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)
(%i252) 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)
(%i253) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i254) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D2[1]*array_x[1],
array_tmp2[1]:array_const_0D3[1]+array_tmp1[1],
array_tmp3[1]:sin(array_x[1]),
array_tmp3_g[1]:cos(array_x[1]),
array_tmp4[1]:expt(array_tmp2[1],c(array_tmp3[1])),
array_tmp4_a1[1]:log(array_tmp2[1]),
array_tmp4_a1[2]:array_tmp2[2]/array_tmp2[1],
array_tmp5[1]:array_tmp4[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp5[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_const_0D2[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:array_tmp3_g[1]*array_x[2]/c(1),
array_tmp3_g[2]:neg(array_tmp3[1])*array_x[2]/c(1),
array_tmp4_a2[1]:(array_tmp4_a1[2]*array_tmp3[1]
+array_tmp4_a1[1]*array_tmp3[2])
/glob_h,
array_tmp4[2]:array_tmp4[1]*array_tmp4_a2[1]*glob_h,
array_tmp5[2]:array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp5[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp3[3]:array_tmp3_g[2]*array_x[2]/c(2),
array_tmp3_g[3]:neg(array_tmp3[2])*array_x[2]/c(2),
array_tmp4_a1[3]:neg(array_tmp4_a1[2])
*array_tmp2[2]*c(1)
/array_tmp2[1]
/c(2),
array_tmp4_a2[2]:ats(3,array_tmp3,array_tmp4_a1,1)*c(2)
/glob_h,
array_tmp4[3]:ats(2,array_tmp4,array_tmp4_a2,1)*glob_h
/c(2),array_tmp5[3]:array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp5[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp3[4]:array_tmp3_g[3]*array_x[2]/c(3),
array_tmp3_g[4]:neg(array_tmp3[3])*array_x[2]/c(3),
array_tmp4_a1[4]:neg(array_tmp4_a1[3])
*array_tmp2[2]*c(2)
/array_tmp2[1]
/c(3),
array_tmp4_a2[3]:ats(4,array_tmp3,array_tmp4_a1,1)*c(3)
/glob_h,
array_tmp4[4]:ats(3,array_tmp4,array_tmp4_a2,1)*glob_h
/c(3),array_tmp5[4]:array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp5[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp3[5]:array_tmp3_g[4]*array_x[2]/c(4),
array_tmp3_g[5]:neg(array_tmp3[4])*array_x[2]/c(4),
array_tmp4_a1[5]:neg(array_tmp4_a1[4])
*array_tmp2[2]*c(3)
/array_tmp2[1]
/c(4),
array_tmp4_a2[4]:ats(5,array_tmp3,array_tmp4_a1,1)*c(4)
/glob_h,
array_tmp4[5]:ats(4,array_tmp4,array_tmp4_a2,1)*glob_h
/c(4),array_tmp5[5]:array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp5[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp3[kkk]
:array_tmp3_g[kkk-1]*array_x[2]/c(kkk-1),
array_tmp3_g[kkk]
:neg(array_tmp3[kkk-1])*array_x[2]/c(kkk-1),
array_tmp4_a1[kkk]
:neg(array_tmp4_a1[kkk-1])
*array_tmp2[2]*c(kkk-2)
/array_tmp2[1]
/c(kkk-1),
array_tmp4_a2[kkk-1]
:ats(kkk,array_tmp3,array_tmp4_a1,1)*c(kkk-1)
/glob_h,
array_tmp4[kkk]
:ats(kkk-1,array_tmp4,array_tmp4_a2,1)*glob_h
/c(kkk-1),array_tmp5[kkk]:array_tmp4[kkk],
order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp5[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)
(%i255) exact_soln_y(x):=block(c(0.0))
(%o255) exact_soln_y(x) := block(c(0.0))
(%i256) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:30,
glob_html_log:true,term:1,
while term <= 30 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 30 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3_g[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do
(array_tmp4_c1[term]:c(0.0),term:1+term),term:1,
while term <= 30 do
(array_tmp4_a1[term]:c(0.0),term:1+term),term:1,
while term <= 30 do
(array_tmp4_a2[term]:c(0.0),term:1+term),term:1,
while term <= 30 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 30 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 30 do
(term:1,
while term <= 30 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3_g),
zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4_c1),
zero_ats_ar(array_tmp4_a1),zero_ats_ar(array_tmp4_a2),
zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5),
zero_ats_ar(array_m1),zero_ats_ar(array_const_1),
array_const_1[1]:c(1),zero_ats_ar(array_const_0D0),
array_const_0D0[1]:c(0.0),zero_ats_ar(array_const_0D2),
array_const_0D2[1]:c(0.2),zero_ats_ar(array_const_0D3),
array_const_0D3[1]:c(0.3),zero_ats_ar(array_m1),
array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/expt_lin_sinpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:30,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.1),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:0,"),
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(0.0)) "),omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_type_given_pole:0,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T21:10:48-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"expt_lin_sin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"expt_lin_sin diffeq.max"),
logitem_str(html_log_file,
"expt_lin_sin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i257) main():=(glob_iolevel:2,compile(all),main_prog())
(%i258) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_0D3 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp3_g in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp4_a1 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp5 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 array_tmp4_a2 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_tmp4_c1 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_upper_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_lower_ratio_limit (declared type convfloat) assigned type any.
warning: variable glob_h (declared type convfloat) assigned type any.
warning: variable glob_display_interval (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_max_minutes in translation.
warning: encountered undefined variable glob_max_hours in translation.
warning: encountered undefined variable x_end in translation.
warning: variable glob_check_sign (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_larger_float in translation.
warning: variable last_min_pole_est (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_max_h in translation.
warning: encountered undefined variable glob_display_interval in translation.
warning: encountered undefined variable glob__10 in translation.
warning: variable display_max (declared type [found_h]) assigned type any.
warning: encountered undefined variable display_max in translation.
warning: variable min_value (declared type [found_h]) assigned type convfloat.
warning: variable est_answer (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_answer in translation.
warning: variable est_needed_step_err (declared type [found_h]) assigned type any.
warning: encountered undefined variable est_needed_step_err in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable opt_iter in translation.
warning: encountered undefined variable found_h in translation.
warning: variable glob_next_display (declared type convfloat) assigned type any.
warning: variable order_diff (declared type [found_h]) assigned type fixnum.
warning: variable term_no (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable order_diff in translation.
warning: variable term_no (declared type [found_h]) assigned type any.
warning: variable r_order (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable r_order in translation.
warning: encountered undefined variable rows in translation.
warning: variable it (declared type [found_h]) assigned type any.
warning: encountered undefined variable it in translation.
warning: variable r_order (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_look_poles in translation.
warning: variable estimated_step_error (declared type [found_h]) assigned type any.
warning: encountered undefined variable estimated_step_error in translation.
warning: encountered undefined variable glob__2 in translation.
warning: variable opt_iter (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_optimize in translation.
warning: variable html_log_file (declared type [found_h]) assigned type any.
warning: encountered undefined variable glob_html_log in translation.
warning: variable current_iter (declared type [found_h]) assigned type fixnum.
warning: variable glob_clock_start_sec (declared type convfloat) assigned type any.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable debugl in translation.
warning: variable glob_optimal_clock_start_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable current_iter in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: variable calc_term (declared type [found_h]) assigned type fixnum.
warning: variable iii (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable calc_term in translation.
warning: variable iii (declared type [found_h]) assigned type any.
warning: variable temp_sum (declared type [found_h]) assigned type convfloat.
warning: encountered undefined variable temp_sum in translation.
warning: variable temp_sum (declared type [found_h]) assigned type any.
warning: encountered undefined variable html_log_file in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob_percent_done in translation.
warning: encountered undefined variable glob__100 in translation.
WARNING: in $MAIN_PROG : |$Digits| is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MAX_TERMS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_DISPLAY_FLAG is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_NO_EQS is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_UNCHANGED_H_CNT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_WARNED2 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SMALLISH_FLOAT is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_ALMOST_1 is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_SUBITER_METHOD is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_LAST_GOOD_H is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB__PI is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $LAST_MIN_POLE_EST is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $MIN_VALUE is neither declared nor bound,
it will be treated as if it were declared SPECIAL.
WARNING: in $MAIN_PROG : $GLOB_REACHED_OPTIMAL_H is neither declared nor
bound,
it will be treated as if it were declared SPECIAL.
"##############ECHO OF PROBLEM#################"
"##############temp/expt_lin_sinpostode.ode#################"
"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:0,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (c(0.0)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.0 " "
absolute error = 0.0 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = -16
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 8.877307336040212000E-3 " "
absolute error = 8.877307336040212000E-3 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.766119953132292100E-2 " "
absolute error = 1.766119953132292100E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.635377595127346700E-2 " "
absolute error = 2.635377595127346700E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.49571163778688800E-2 " "
absolute error = 3.49571163778688800E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 4.34732543164380150E-2 " "
absolute error = 4.34732543164380150E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 5.19041782652624600E-2 " "
absolute error = 5.19041782652624600E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 6.02518329472768800E-2 " "
absolute error = 6.02518329472768800E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 6.85181205051429900E-2 " "
absolute error = 6.85181205051429900E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 7.67049016609212100E-2 " "
absolute error = 7.67049016609212100E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 8.48139968415184100E-2 " "
absolute error = 8.48139968415184100E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 9.2847187271044410E-2 " "
absolute error = 9.2847187271044410E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.10080621603116738 " "
absolute error = 0.10080621603116738 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1086927890905172 " "
absolute error = 0.1086927890905172 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.11650857630414688 " "
absolute error = 0.11650857630414688 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.12425521238402366 " "
absolute error = 0.12425521238402366 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1319342978414868 " "
absolute error = 0.1319342978414868 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1395473999025731 " "
absolute error = 0.1395473999025731 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.14709605339707954 " "
absolute error = 0.14709605339707954 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1545817616221994 " "
absolute error = 0.1545817616221994 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1620059971815392 " "
absolute error = 0.1620059971815392 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.16937020280029372 " "
absolute error = 0.16937020280029372 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1766757921173285 " "
absolute error = 0.1766757921173285 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.183924150454893 " "
absolute error = 0.183924150454893 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.19111663556666153 " "
absolute error = 0.19111663556666153 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.1982545783647741 " "
absolute error = 0.1982545783647741 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.20533928362652584 " "
absolute error = 0.20533928362652584 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.21237203068133095 " "
absolute error = 0.21237203068133095 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.21935407407856514 " "
absolute error = 0.21935407407856514 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2262866442368694 " "
absolute error = 0.2262866442368694 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.23317094807547753 " "
absolute error = 0.23317094807547753 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.24000816962811125 " "
absolute error = 0.24000816962811125 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.24679947063996657 " "
absolute error = 0.24679947063996657 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2535459911482984 " "
absolute error = 0.2535459911482984 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2602488500470921 " "
absolute error = 0.2602488500470921 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.26690914563629525 " "
absolute error = 0.26690914563629525 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2735279561560645 " "
absolute error = 0.2735279561560645 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2801063403064703 " "
absolute error = 0.2801063403064703 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2866453377530837 " "
absolute error = 0.2866453377530837 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.29314596961885847 " "
absolute error = 0.29314596961885847 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.2996092389627049 " "
absolute error = 0.2996092389627049 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.30603613124514073 " "
absolute error = 0.30603613124514073 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.312427614781391 " "
absolute error = 0.312427614781391 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3187846411822954 " "
absolute error = 0.3187846411822954 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.32510814578337033 " "
absolute error = 0.32510814578337033 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3313990480623629 " "
absolute error = 0.3313990480623629 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3376582520456198 " "
absolute error = 0.3376582520456198 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3438866467035858 " "
absolute error = 0.3438866467035858 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.350085106335736 " "
absolute error = 0.350085106335736 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3562544909452338 " "
absolute error = 0.3562544909452338 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3623956466036014 " "
absolute error = 0.3623956466036014 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.36850940580567404 " "
absolute error = 0.36850940580567404 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3745965878151063 " "
absolute error = 0.3745965878151063 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.38065799900068703 " "
absolute error = 0.38065799900068703 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3866944331637097 " "
absolute error = 0.3866944331637097 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.39270667185664143 " "
absolute error = 0.39270667185664143 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.3986954846933211 " "
absolute error = 0.3986954846933211 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4046616296509127 " "
absolute error = 0.4046616296509127 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4106058533638322 " "
absolute error = 0.4106058533638322 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.41652889140985705 " "
absolute error = 0.41652889140985705 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4224314685886237 " "
absolute error = 0.4224314685886237 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4283142991927097 " "
absolute error = 0.4283142991927097 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4341780872714919 " "
absolute error = 0.4341780872714919 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4400235268879641 " "
absolute error = 0.4400235268879641 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.44585130236869486 " "
absolute error = 0.44585130236869486 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.45166208854709644 " "
absolute error = 0.45166208854709644 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.45745655100017385 " "
absolute error = 0.45745655100017385 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4632353462789146 " "
absolute error = 0.4632353462789146 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.468999122132477 " "
absolute error = 0.468999122132477 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4747485177263279 " "
absolute error = 0.4747485177263279 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.480484163854477 " "
absolute error = 0.480484163854477 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4862066831459492 " "
absolute error = 0.4862066831459492 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.4919166902656335 " "
absolute error = 0.4919166902656335 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.49761479210963977 " "
absolute error = 0.49761479210963977 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5033015879952941 " "
absolute error = 0.5033015879952941 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5089776698458952 " "
absolute error = 0.5089776698458952 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5146436223703534 " "
absolute error = 0.5146436223703534 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5203000232378285 " "
absolute error = 0.5203000232378285 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5259474432474811 " "
absolute error = 0.5259474432474811 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5315864464934418 " "
absolute error = 0.5315864464934418 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5372175905251101 " "
absolute error = 0.5372175905251101 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.54284142650288 " "
absolute error = 0.54284142650288 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5484584993493944 " "
absolute error = 0.5484584993493944 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5540693478964224 " "
absolute error = 0.5540693478964224 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5596745050274529 " "
absolute error = 0.5596745050274529 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5652744978160936 " "
absolute error = 0.5652744978160936 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5708698476603619 " "
absolute error = 0.5708698476603619 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5764610704129529 " "
absolute error = 0.5764610704129529 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5820486765075642 " "
absolute error = 0.5820486765075642 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5876331710813572 " "
absolute error = 0.5876331710813572 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.5932150540936287 " "
absolute error = 0.5932150540936287 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0099999999999996 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.598794820440771 " "
absolute error = 0.598794820440771 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999985 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.604372960067586 " "
absolute error = 0.604372960067586 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999974 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6099499580750264 " "
absolute error = 0.6099499580750264 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6155262948244299 " "
absolute error = 0.6155262948244299 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6211024460383101 " "
absolute error = 0.6211024460383101 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6266788828977654 " "
absolute error = 0.6266788828977654 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6322560721365716 " "
absolute error = 0.6322560721365716 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.63783447613201 " "
absolute error = 0.63783447613201 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6434145529924937 " "
absolute error = 0.6434145529924937 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6489967566420431 " "
absolute error = 0.6489967566420431 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6545815369016674 " "
absolute error = 0.6545815369016674 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6601693395676997 " "
absolute error = 0.6601693395676997 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6657606064871401 " "
absolute error = 0.6657606064871401 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6713557756300527 " "
absolute error = 0.6713557756300527 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6769552811590634 " "
absolute error = 0.6769552811590634 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6825595534960078 " "
absolute error = 0.6825595534960078 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6881690193857684 " "
absolute error = 0.6881690193857684 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6937841019573483 " "
absolute error = 0.6937841019573483 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.6994052207822222 " "
absolute error = 0.6994052207822222 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7050327919300048 " "
absolute error = 0.7050327919300048 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7106672280214759 " "
absolute error = 0.7106672280214759 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7163089382790034 " "
absolute error = 0.7163089382790034 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7219583285743978 " "
absolute error = 0.7219583285743978 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7276158014742384 " "
absolute error = 0.7276158014742384 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7332817562827045 " "
absolute error = 0.7332817562827045 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7389565890819473 " "
absolute error = 0.7389565890819473 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7446406927700375 " "
absolute error = 0.7446406927700375 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7503344570965192 " "
absolute error = 0.7503344570965192 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7560382686956055 " "
absolute error = 0.7560382686956055 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7617525111170456 " "
absolute error = 0.7617525111170456 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7674775648546954 " "
absolute error = 0.7674775648546954 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7732138073728231 " "
absolute error = 0.7732138073728231 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7789616131301776 " "
absolute error = 0.7789616131301776 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7847213536018517 " "
absolute error = 0.7847213536018517 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7904933972989668 " "
absolute error = 0.7904933972989668 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.7962781097862109 " "
absolute error = 0.7962781097862109 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8020758536972548 " "
absolute error = 0.8020758536972548 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8078869887480776 " "
absolute error = 0.8078869887480776 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8137118717482259 " "
absolute error = 0.8137118717482259 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8195508566100373 " "
absolute error = 0.8195508566100373 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8254042943558542 " "
absolute error = 0.8254042943558542 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.831272533123253 " "
absolute error = 0.831272533123253 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8371559181683192 " "
absolute error = 0.8371559181683192 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8430547918669925 " "
absolute error = 0.8430547918669925 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8489694937145087 " "
absolute error = 0.8489694937145087 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8549003603229669 " "
absolute error = 0.8549003603229669 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8608477254170465 " "
absolute error = 0.8608477254170465 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8668119198279008 " "
absolute error = 0.8668119198279008 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8727932714852578 " "
absolute error = 0.8727932714852578 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8787921054077472 " "
absolute error = 0.8787921054077472 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8848087436914893 " "
absolute error = 0.8848087436914893 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8908435054969671 " "
absolute error = 0.8908435054969671 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.8968967070342095 " "
absolute error = 0.8968967070342095 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.902968661546316 " "
absolute error = 0.902968661546316 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9090596792913469 " "
absolute error = 0.9090596792913469 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.91517006752261 " "
absolute error = 0.91517006752261 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.921300130467371 " "
absolute error = 0.921300130467371 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9274501693040146 " "
absolute error = 0.9274501693040146 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9336204821376872 " "
absolute error = 0.9336204821376872 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9398113639744511 " "
absolute error = 0.9398113639744511 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9460231066939765 " "
absolute error = 0.9460231066939765 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9522559990208063 " "
absolute error = 0.9522559990208063 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.958510326494218 " "
absolute error = 0.958510326494218 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9647863714367212 " "
absolute error = 0.9647863714367212 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9710844129212152 " "
absolute error = 0.9710844129212152 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9774047267368429 " "
absolute error = 0.9774047267368429 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9837475853535719 " "
absolute error = 0.9837475853535719 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9901132578855367 " "
absolute error = 0.9901132578855367 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.9965020100531743 " "
absolute error = 0.9965020100531743 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.002914104144188 " "
absolute error = 1.002914104144188 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.009349798973376 " "
absolute error = 1.009349798973376 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0158093498413547 " "
absolute error = 1.0158093498413547 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0222930084922186 " "
absolute error = 1.0222930084922186 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0288010230701714 " "
absolute error = 1.0288010230701714 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.035333638075163 " "
absolute error = 1.035333638075163 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0418910943175717 " "
absolute error = 1.0418910943175717 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.048473628871973 " "
absolute error = 1.048473628871973 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.055081475030028 " "
absolute error = 1.055081475030028 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0617148622525356 " "
absolute error = 1.0617148622525356 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0683740161206892 " "
absolute error = 1.0683740161206892 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0750591582865743 " "
absolute error = 1.0750591582865743 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.081770506422954 " "
absolute error = 1.081770506422954 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0885082741723793 " "
absolute error = 1.0885082741723793 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.0952726710956748 " "
absolute error = 1.0952726710956748 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.102063902619834 " "
absolute error = 1.102063902619834 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1088821699853737 " "
absolute error = 1.1088821699853737 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1157276701931953 " "
absolute error = 1.1157276701931953 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1226005959509902 " "
absolute error = 1.1226005959509902 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1295011356192441 " "
absolute error = 1.1295011356192441 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.13642947315688 " "
absolute error = 1.13642947315688 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1433857880665914 " "
absolute error = 1.1433857880665914 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1503702553399135 " "
absolute error = 1.1503702553399135 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1573830454020766 " "
absolute error = 1.1573830454020766 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1644243240566976 " "
absolute error = 1.1644243240566976 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.171494252430353 " "
absolute error = 1.171494252430353 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1785929869170886 " "
absolute error = 1.1785929869170886 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1857206791229098 " "
absolute error = 1.1857206791229098 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.1928774758103113 " "
absolute error = 1.1928774758103113 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2000635188428956 " "
absolute error = 1.2000635188428956 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2072789451301258 " "
absolute error = 1.2072789451301258 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2145238865722747 " "
absolute error = 1.2145238865722747 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2217984700056186 " "
absolute error = 1.2217984700056186 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2291028171479255 " "
absolute error = 1.2291028171479255 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2364370445442983 " "
absolute error = 1.2364370445442983 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.243801263513423 " "
absolute error = 1.243801263513423 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.251195580094275 " "
absolute error = 1.251195580094275 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2586200949933377 " "
absolute error = 1.2586200949933377 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2660749035323942 " "
absolute error = 1.2660749035323942 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.273560095596937 " "
absolute error = 1.273560095596937 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.281075755585259 " "
absolute error = 1.281075755585259 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.288621962358272 " "
absolute error = 1.288621962358272 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.2961987891901214 " "
absolute error = 1.2961987891901214 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.303806303719635 " "
absolute error = 1.303806303719635 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3114445679026738 " "
absolute error = 1.3114445679026738 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3191136379654342 " "
absolute error = 1.3191136379654342 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3268135643587584 " "
absolute error = 1.3268135643587584 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3345443917135058 " "
absolute error = 1.3345443917135058 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3423061587970389 " "
absolute error = 1.3423061587970389 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.350098898470884 " "
absolute error = 1.350098898470884 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3579226376496119 " "
absolute error = 1.3579226376496119 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.365777397260999 " "
absolute error = 1.365777397260999 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.373663192207519 " "
absolute error = 1.373663192207519 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.381580031329218 " "
absolute error = 1.381580031329218 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.389527917368025 " "
absolute error = 1.389527917368025 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.3975068469335512 " "
absolute error = 1.3975068469335512 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.405516810470428 " "
absolute error = 1.405516810470428 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4135577922272347 " "
absolute error = 1.4135577922272347 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4216297702270615 " "
absolute error = 1.4216297702270615 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.289999999999859 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4297327162397677 " "
absolute error = 1.4297327162397677 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2999999999998577 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4378665957559706 " "
absolute error = 1.4378665957559706 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3099999999998566 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4460313679628207 " "
absolute error = 1.4460313679628207 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3199999999998555 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4542269857216061 " "
absolute error = 1.4542269857216061 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3299999999998544 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4624533955472356 " "
absolute error = 1.4624533955472356 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3399999999998533 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4707105375896394 " "
absolute error = 1.4707105375896394 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.349999999999852 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.478998345617137 " "
absolute error = 1.478998345617137 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.359999999999851 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4873167470018096 " "
absolute error = 1.4873167470018096 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.36999999999985 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.4956656627069231 " "
absolute error = 1.4956656627069231 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.379999999999849 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.504045007276437 " "
absolute error = 1.504045007276437 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.389999999999848 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5124546888266444 " "
absolute error = 1.5124546888266444 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.3999999999998467 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5208946090399742 " "
absolute error = 1.5208946090399742 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4099999999998456 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5293646631609943 " "
absolute error = 1.5293646631609943 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4199999999998445 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5378647399946557 " "
absolute error = 1.5378647399946557 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4299999999998434 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5463947219068015 " "
absolute error = 1.5463947219068015 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4399999999998423 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5549544848269825 " "
absolute error = 1.5549544848269825 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.449999999999841 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5635438982536003 " "
absolute error = 1.5635438982536003 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.45999999999984 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5721628252614182 " "
absolute error = 1.5721628252614182 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.469999999999839 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5808111225114574 " "
absolute error = 1.5808111225114574 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.479999999999838 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.5894886402633097 " "
absolute error = 1.5894886402633097 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.489999999999837 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.598195222389889 " "
absolute error = 1.598195222389889 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.4999999999998357 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.6069307063946443 " "
absolute error = 1.6069307063946443 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5099999999998346 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.6156949234312548 " "
absolute error = 1.6156949234312548 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5199999999998335 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.624487698325827 " "
absolute error = 1.624487698325827 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5299999999998324 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.6333088496016097 " "
absolute error = 1.6333088496016097 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5399999999998313 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.642158189506241 " "
absolute error = 1.642158189506241 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.54999999999983 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.651035524041545 " "
absolute error = 1.651035524041545 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.559999999999829 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.659940652995884 " "
absolute error = 1.659940652995884 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.569999999999828 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.668873369979079 " "
absolute error = 1.668873369979079 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.579999999999827 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.6778334624599072 " "
absolute error = 1.6778334624599072 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5899999999998258 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.686820711806179 " "
absolute error = 1.686820711806179 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.5999999999998247 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.6958348933273995 " "
absolute error = 1.6958348933273995 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6099999999998236 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7048757763200153 " "
absolute error = 1.7048757763200153 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6199999999998225 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7139431241152503 " "
absolute error = 1.7139431241152503 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6299999999998214 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.723036694129519 " "
absolute error = 1.723036694129519 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6399999999998203 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7321562379174227 " "
absolute error = 1.7321562379174227 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.649999999999819 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.741301501227317 " "
absolute error = 1.741301501227317 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.659999999999818 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7504722240594404 " "
absolute error = 1.7504722240594404 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.669999999999817 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7596681407265966 " "
absolute error = 1.7596681407265966 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.679999999999816 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7688889799173764 " "
absolute error = 1.7688889799173764 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6899999999998148 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.778134464761903 " "
absolute error = 1.778134464761903 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.6999999999998137 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7874043129000867 " "
absolute error = 1.7874043129000867 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7099999999998126 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.7966982365523652 " "
absolute error = 1.7966982365523652 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7199999999998115 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.806015942592913 " "
absolute error = 1.806015942592913 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7299999999998104 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.8153571326252953 " "
absolute error = 1.8153571326252953 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7399999999998093 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.824721503060537 " "
absolute error = 1.824721503060537 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.749999999999808 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.8341087451975875 " "
absolute error = 1.8341087451975875 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.759999999999807 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.8435185453061431 " "
absolute error = 1.8435185453061431 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.769999999999806 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.852950584711803 " "
absolute error = 1.852950584711803 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.779999999999805 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.862404539883521 " "
absolute error = 1.862404539883521 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7899999999998037 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.8718800825233184 " "
absolute error = 1.8718800825233184 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.7999999999998026 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.8813768796582235 " "
absolute error = 1.8813768796582235 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8099999999998015 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.8908945937343942 " "
absolute error = 1.8908945937343942 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8199999999998004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.900432882713387 " "
absolute error = 1.900432882713387 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8299999999997993 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.909991400170527 " "
absolute error = 1.909991400170527 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8399999999997982 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.919569795395333 " "
absolute error = 1.919569795395333 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.849999999999797 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9291677134939564 " "
absolute error = 1.9291677134939564 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.859999999999796 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9387847954935808 " "
absolute error = 1.9387847954935808 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.869999999999795 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9484206784487321 " "
absolute error = 1.9484206784487321 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.879999999999794 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9580749955494534 " "
absolute error = 1.9580749955494534 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8899999999997927 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9677473762312854 " "
absolute error = 1.9677473762312854 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.8999999999997916 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9774374462870001 " "
absolute error = 1.9774374462870001 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9099999999997905 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9871448279800337 " "
absolute error = 1.9871448279800337 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9199999999997894 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 1.9968691401595564 " "
absolute error = 1.9968691401595564 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9299999999997883 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.0066099983771237 " "
absolute error = 2.0066099983771237 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9399999999997872 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.0163670150048487 " "
absolute error = 2.0163670150048487 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.949999999999786 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.0261397993550343 " "
absolute error = 2.0261397993550343 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.959999999999785 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.0359279578011957 " "
absolute error = 2.0359279578011957 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.969999999999784 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.0457310939004234 " "
absolute error = 2.0457310939004234 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.979999999999783 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.055548808517003 " "
absolute error = 2.055548808517003 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9899999999997817 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.065380699947244 " "
absolute error = 2.065380699947244 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.9999999999997806 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.0752263640454376 " "
absolute error = 2.0752263640454376 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0099999999997795 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.085085394350879 " "
absolute error = 2.085085394350879 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0199999999997784 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.094957382215889 " "
absolute error = 2.094957382215889 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0299999999997773 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.1048419169347636 " "
absolute error = 2.1048419169347636 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.039999999999776 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.11473858587357 " "
absolute error = 2.11473858587357 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.049999999999775 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.124646974600742 " "
absolute error = 2.124646974600742 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.059999999999774 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.1345666670183796 " "
absolute error = 2.1345666670183796 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.069999999999773 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.144497245494191 " "
absolute error = 2.144497245494191 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.079999999999772 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.154438290994004 " "
absolute error = 2.154438290994004 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0899999999997707 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.1643893832147745 " "
absolute error = 2.1643893832147745 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0999999999997696 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.174350100718018 " "
absolute error = 2.174350100718018 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1099999999997685 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.184320021063583 " "
absolute error = 2.184320021063583 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1199999999997674 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.194298720943711 " "
absolute error = 2.194298720943711 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1299999999997663 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2042857763172883 " "
absolute error = 2.2042857763172883 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.139999999999765 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2142807625442313 " "
absolute error = 2.2142807625442313 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.149999999999764 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.224283254519919 " "
absolute error = 2.224283254519919 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.159999999999763 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.234292826809613 " "
absolute error = 2.234292826809613 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.169999999999762 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2443090537827817 " "
absolute error = 2.2443090537827817 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.179999999999761 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2543315097472556 " "
absolute error = 2.2543315097472556 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1899999999997597 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2643597690831463 " "
absolute error = 2.2643597690831463 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.1999999999997586 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2743934063764555 " "
absolute error = 2.2743934063764555 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2099999999997575 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2844319965522937 " "
absolute error = 2.2844319965522937 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2199999999997564 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.2944751150076494 " "
absolute error = 2.2944751150076494 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2299999999997553 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.3045223377436344 " "
absolute error = 2.3045223377436344 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.239999999999754 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.314573241497123 " "
absolute error = 2.314573241497123 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.249999999999753 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.3246274038717387 " "
absolute error = 2.3246274038717387 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.259999999999752 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.3346844034680974 " "
absolute error = 2.3346844034680974 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.269999999999751 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.344743820013252 " "
absolute error = 2.344743820013252 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.27999999999975 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.3548052344892674 " "
absolute error = 2.3548052344892674 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2899999999997487 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.364868229260859 " "
absolute error = 2.364868229260859 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.2999999999997476 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.37493238820204 " "
absolute error = 2.37493238820204 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3099999999997465 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.3849972968216906 " "
absolute error = 2.3849972968216906 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3199999999997454 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.3950625423880125 " "
absolute error = 2.3950625423880125 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3299999999997443 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.4051277140517957 " "
absolute error = 2.4051277140517957 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.339999999999743 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.4151924029684277 " "
absolute error = 2.4151924029684277 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.349999999999742 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.4252562024186055 " "
absolute error = 2.4252562024186055 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.359999999999741 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.4353187079276797 " "
absolute error = 2.4353187079276797 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.36999999999974 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.445379517383577 " "
absolute error = 2.445379517383577 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3799999999997388 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.455438231153248 " "
absolute error = 2.455438231153248 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3899999999997377 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.4654944521975866 " "
absolute error = 2.4654944521975866 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.3999999999997366 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.475547786184768 " "
absolute error = 2.475547786184768 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4099999999997355 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.485597841601956 " "
absolute error = 2.485597841601956 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4199999999997344 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.4956442298653276 " "
absolute error = 2.4956442298653276 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4299999999997333 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.50568656542838 " "
absolute error = 2.50568656542838 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.439999999999732 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.51572446588845 " "
absolute error = 2.51572446588845 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.449999999999731 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.5257575520914344 " "
absolute error = 2.5257575520914344 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.45999999999973 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.535785448234638 " "
absolute error = 2.535785448234638 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.469999999999729 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.5458077819677287 " "
absolute error = 2.5458077819677287 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4799999999997278 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.55582418449176 " "
absolute error = 2.55582418449176 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4899999999997267 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.56583429065621 " "
absolute error = 2.56583429065621 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.4999999999997256 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.5758377390540184 " "
absolute error = 2.5758377390540184 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5099999999997245 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.585834172114578 " "
absolute error = 2.585834172114578 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5199999999997234 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.5958232361946507 " "
absolute error = 2.5958232361946507 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5299999999997222 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.6058045816671838 " "
absolute error = 2.6058045816671838 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.539999999999721 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.6157778630079918 " "
absolute error = 2.6157778630079918 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.54999999999972 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.625742738880282 " "
absolute error = 2.625742738880282 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.559999999999719 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.635698872216997 " "
absolute error = 2.635698872216997 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.569999999999718 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.6456459303009567 " "
absolute error = 2.6456459303009567 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5799999999997167 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.6555835848427725 " "
absolute error = 2.6555835848427725 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5899999999997156 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.665511512056516 " "
absolute error = 2.665511512056516 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.5999999999997145 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.675429392733136 " "
absolute error = 2.675429392733136 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6099999999997134 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.685336912311595 " "
absolute error = 2.685336912311595 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6199999999997123 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.695233760947717 " "
absolute error = 2.695233760947717 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6299999999997112 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.7051196335807393 " "
absolute error = 2.7051196335807393 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.63999999999971 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.714994229997557 " "
absolute error = 2.714994229997557 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.649999999999709 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.724857254894647 " "
absolute error = 2.724857254894647 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.659999999999708 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.7347084179376693 " "
absolute error = 2.7347084179376693 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.669999999999707 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.7445474338187483 " "
absolute error = 2.7445474338187483 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6799999999997057 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.754374022311418 " "
absolute error = 2.754374022311418 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6899999999997046 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.7641879083232457 " "
absolute error = 2.7641879083232457 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.6999999999997035 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.7739888219461197 " "
absolute error = 2.7739888219461197 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7099999999997024 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.783776498504214 " "
absolute error = 2.783776498504214 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7199999999997013 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.7935506785996354 " "
absolute error = 2.7935506785996354 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7299999999997 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.80331110815575 " "
absolute error = 2.80331110815575 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.739999999999699 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8130575384582053 " "
absolute error = 2.8130575384582053 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.749999999999698 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8227897261936543 " "
absolute error = 2.8227897261936543 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.759999999999697 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8325074334861875 " "
absolute error = 2.8325074334861875 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.769999999999696 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8422104279314944 " "
absolute error = 2.8422104279314944 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7799999999996947 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8518984826287603 " "
absolute error = 2.8518984826287603 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7899999999996936 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.86157137621032 " "
absolute error = 2.86157137621032 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.7999999999996925 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8712288928690737 " "
absolute error = 2.8712288928690737 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8099999999996914 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.8808708223837005 " "
absolute error = 2.8808708223837005 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8199999999996903 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.890496960141671 " "
absolute error = 2.890496960141671 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.829999999999689 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9001071071600903 " "
absolute error = 2.9001071071600903 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.839999999999688 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.909701070104395 " "
absolute error = 2.909701070104395 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.849999999999687 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9192786613049138 " "
absolute error = 2.9192786613049138 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.859999999999686 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9288396987713337 " "
absolute error = 2.9288396987713337 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.869999999999685 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9383840062050806 " "
absolute error = 2.9383840062050806 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8799999999996837 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9479114130096553 " "
absolute error = 2.9479114130096553 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8899999999996826 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9574217542989407 " "
absolute error = 2.9574217542989407 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.8999999999996815 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9669148709035174 " "
absolute error = 2.9669148709035174 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9099999999996804 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9763906093750108 " "
absolute error = 2.9763906093750108 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9199999999996793 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.985848821988504 " "
absolute error = 2.985848821988504 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.929999999999678 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 2.9952893667430485 " "
absolute error = 2.9952893667430485 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.939999999999677 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0047121073602994 " "
absolute error = 3.0047121073602994 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.949999999999676 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0141169132813173 " "
absolute error = 3.0141169132813173 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.959999999999675 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.02350365966156 " "
absolute error = 3.02350365966156 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.969999999999674 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.032872227364108 " "
absolute error = 3.032872227364108 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9799999999996727 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.042222502951153 " "
absolute error = 3.042222502951153 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9899999999996716 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0515543786737855 " "
absolute error = 3.0515543786737855 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.9999999999996705 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.060867752460126 " "
absolute error = 3.060867752460126 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.009999999999674 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0701625279018234 " "
absolute error = 3.0701625279018234 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.019999999999677 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0794386142389683 " "
absolute error = 3.0794386142389683 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0299999999996805 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0886959263434544 " "
absolute error = 3.0886959263434544 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.039999999999684 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.0979343847008325 " "
absolute error = 3.0979343847008325 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.049999999999687 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.1071539153906857 " "
absolute error = 3.1071539153906857 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0599999999996905 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.116354450065573 " "
absolute error = 3.116354450065573 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.069999999999694 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.1255359259285798 " "
absolute error = 3.1255359259285798 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.079999999999697 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.1346982857095105 " "
absolute error = 3.1346982857095105 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.0899999999997005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.14384147763977 " "
absolute error = 3.14384147763977 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.099999999999704 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.152965455425969 " "
absolute error = 3.152965455425969 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.109999999999707 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.16207017822229 " "
absolute error = 3.16207017822229 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.119999999999710 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.171155610601671 " "
absolute error = 3.171155610601671 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.129999999999714 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.1802217225258222 " "
absolute error = 3.1802217225258222 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.139999999999717 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.1892684893141388 " "
absolute error = 3.1892684893141388 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.149999999999720 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.1982958916115387 " "
absolute error = 3.1982958916115387 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.159999999999724 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.2073039153552694 " "
absolute error = 3.2073039153552694 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.169999999999727 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.216292551740718 " "
absolute error = 3.216292551740718 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.179999999999730 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.22526179718628 " "
absolute error = 3.22526179718628 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.189999999999734 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.2342116532973075 " "
absolute error = 3.2342116532973075 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.199999999999737 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.2431421268291953 " "
absolute error = 3.2431421268291953 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.209999999999740 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.2520532296496283 " "
absolute error = 3.2520532296496283 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.219999999999744 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.260944978700043 " "
absolute error = 3.260944978700043 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.229999999999747 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.269817395956337 " "
absolute error = 3.269817395956337 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.239999999999750 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.2786705083888634 " "
absolute error = 3.2786705083888634 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.249999999999754 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.2875043479217565 " "
absolute error = 3.2875043479217565 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.259999999999757 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.296318951391615 " "
absolute error = 3.296318951391615 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.269999999999760 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.3051143605055984 " "
absolute error = 3.3051143605055984 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.279999999999764 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.313890621798956 " "
absolute error = 3.313890621798956 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.289999999999767 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.322647786592039 " "
absolute error = 3.322647786592039 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.299999999999770 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.3313859109468296 " "
absolute error = 3.3313859109468296 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.309999999999774 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.340105055623018 " "
absolute error = 3.340105055623018 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.319999999999777 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.3488052860336732 " "
absolute error = 3.3488052860336732 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.329999999999780 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.3574866722005323 " "
absolute error = 3.3574866722005323 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.339999999999784 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.366149288708957 " "
absolute error = 3.366149288708957 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.349999999999787 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.3747932146625783 " "
absolute error = 3.3747932146625783 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.359999999999790 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.3834185336376703 " "
absolute error = 3.3834185336376703 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.369999999999794 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.392025333637291 " "
absolute error = 3.392025333637291 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.379999999999797 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.400613707045213 " "
absolute error = 3.400613707045213 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.389999999999800 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.409183750579682 " "
absolute error = 3.409183750579682 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.399999999999804 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.4177355652470425 " "
absolute error = 3.4177355652470425 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.409999999999807 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.426269256295244 " "
absolute error = 3.426269256295244 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.419999999999810 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.43478493316728 " "
absolute error = 3.43478493316728 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.429999999999814 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.4432827094545657 " "
absolute error = 3.4432827094545657 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.439999999999817 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.451762702850314 " "
absolute error = 3.451762702850314 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.449999999999820 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.460225035102905 " "
absolute error = 3.460225035102905 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.459999999999824 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.468669831969308 " "
absolute error = 3.468669831969308 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4699999999998274 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.47709722316856 " "
absolute error = 3.47709722316856 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.479999999999830 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.4855073423353438 " "
absolute error = 3.4855073423353438 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.489999999999834 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.4939003269736806 " "
absolute error = 3.4939003269736806 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.4999999999998375 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5022763184107712 " "
absolute error = 3.5022763184107712 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.509999999999840 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.510635461751005 " "
absolute error = 3.510635461751005 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.519999999999844 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.518977905830171 " "
absolute error = 3.518977905830171 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5299999999998475 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.527303803169868 " "
absolute error = 3.527303803169868 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.539999999999850 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5356133099321774 " "
absolute error = 3.5356133099321774 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.549999999999854 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5439065858745855 " "
absolute error = 3.5439065858745855 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5599999999998575 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5521837943051957 " "
absolute error = 3.5521837943051957 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.569999999999860 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5604451020382415 " "
absolute error = 3.5604451020382415 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.579999999999864 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5686906793499307 " "
absolute error = 3.5686906793499307 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.5899999999998675 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5769206999346315 " "
absolute error = 3.5769206999346315 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.599999999999870 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.585135340861423 " "
absolute error = 3.585135340861423 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.609999999999874 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.5933347825310276 " "
absolute error = 3.5933347825310276 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.6199999999998775 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6015192086331442 " "
absolute error = 3.6015192086331442 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.629999999999880 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6096888061041956 " "
absolute error = 3.6096888061041956 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.639999999999884 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6178437650855115 " "
absolute error = 3.6178437650855115 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.649999999999888 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6259842788819543 " "
absolute error = 3.6259842788819543 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.659999999999891 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.634110543921013 " "
absolute error = 3.634110543921013 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.669999999999894 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6422227597123724 " "
absolute error = 3.6422227597123724 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.679999999999898 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6503211288079713 " "
absolute error = 3.6503211288079713 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.689999999999901 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.658405856762563 " "
absolute error = 3.658405856762563 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.699999999999904 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6664771520947954 " "
absolute error = 3.6664771520947954 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.709999999999908 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6745352262488127 " "
absolute error = 3.6745352262488127 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.719999999999911 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.682580293556401 " "
absolute error = 3.682580293556401 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.729999999999914 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6906125711996753 " "
absolute error = 3.6906125711996753 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.739999999999918 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.6986322791743294 " "
absolute error = 3.6986322791743294 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.749999999999921 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7066396402534503 " "
absolute error = 3.7066396402534503 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.759999999999924 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.714634879951909 " "
absolute error = 3.714634879951909 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.769999999999928 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.722618226491334 " "
absolute error = 3.722618226491334 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.779999999999931 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.730589910765673 " "
absolute error = 3.730589910765673 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.789999999999934 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.738550166307358 " "
absolute error = 3.738550166307358 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.799999999999938 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7464992292540655 " "
absolute error = 3.7464992292540655 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.809999999999941 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7544373383160923 " "
absolute error = 3.7544373383160923 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.819999999999944 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7623647347443416 " "
absolute error = 3.7623647347443416 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.829999999999948 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7702816622989275 " "
absolute error = 3.7702816622989275 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.839999999999951 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7781883672184 " "
absolute error = 3.7781883672184 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.849999999999954 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.786085098189601 " "
absolute error = 3.786085098189601 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.859999999999958 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.7939721063181415 " "
absolute error = 3.7939721063181415 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.869999999999961 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.801849645099513 " "
absolute error = 3.801849645099513 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.879999999999964 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.809717970390833 " "
absolute error = 3.809717970390833 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.889999999999968 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.817577340383216 " "
absolute error = 3.817577340383216 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.899999999999971 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.8254280155747886 " "
absolute error = 3.8254280155747886 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.909999999999974 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.833270258744333 " "
absolute error = 3.833270258744333 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.919999999999978 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.841104334925567 " "
absolute error = 3.841104334925567 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.929999999999981 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.848930511382056 " "
absolute error = 3.848930511382056 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.939999999999984 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.8567490575827588 " "
absolute error = 3.8567490575827588 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.949999999999988 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.8645602451782044 " "
absolute error = 3.8645602451782044 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.959999999999991 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.872364347977294 " "
absolute error = 3.872364347977294 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.969999999999994 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.880161641924736 " "
absolute error = 3.880161641924736 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.979999999999998 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.8879524050791003 " "
absolute error = 3.8879524050791003 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.990000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 3.89573691759149 " "
absolute error = 3.89573691759149 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 1 ) = expt ( ( 0.2 * x + 0.3 ) , sin ( x ) ) ; "
Iterations = 4900
"Total Elapsed Time "= 2 Minutes 31 Seconds
"Elapsed Time(since restart) "= 2 Minutes 31 Seconds
"Time to Timeout "= 28 Seconds
Percent Done = 100.0204081632654 "%"
(%o258) temp/diffeq.expt_lin_sin.max