(%i1) batch("temp/diffeq.expt_sin_sin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.expt_sin_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_g,[30],convfloat)
(%i188) completearray(array_tmp2,[30],convfloat)
(%i189) completearray(array_tmp3,[30],convfloat)
(%i190) completearray(array_tmp4_g,[30],convfloat)
(%i191) completearray(array_tmp4,[30],convfloat)
(%i192) completearray(array_tmp5_c1,[30],convfloat)
(%i193) completearray(array_tmp5_a1,[30],convfloat)
(%i194) completearray(array_tmp5_a2,[30],convfloat)
(%i195) completearray(array_tmp5,[30],convfloat)
(%i196) completearray(array_tmp6,[30],convfloat)
(%i197) completearray(array_m1,[30],convfloat)
(%i198) completearray(array_y_higher,[2,30],convfloat)
(%i199) completearray(array_y_higher_work,[2,30],convfloat)
(%i200) completearray(array_y_higher_work2,[2,30],convfloat)
(%i201) completearray(array_y_set_initial,[2,30],convfloat)
(%i202) completearray(array_given_rad_poles,[2,3],convfloat)
(%i203) completearray(array_given_ord_poles,[2,3],convfloat)
(%i204) completearray(array_rad_test_poles,[2,4],convfloat)
(%i205) completearray(array_ord_test_poles,[2,4],convfloat)
(%i206) completearray(array_fact_2,[30,30],convfloat)
(%i207) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i208) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i209) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i210) 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))
(%i211) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i212) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i213) 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)
(%i214) 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)
(%i215) 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)
(%i216) 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)
(%i217) 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)
(%i218) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i219) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i220) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i221) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i222) log_revs(file,revs):=printf(file,revs)
(%i223) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i224) 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)
(%i225) logstart(file):=(printf(file,""),0)
(%i226) logend(file):=(printf(file,"
~%"),0)
(%i227) 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)
(%i228) 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)
(%i229) 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)
(%i230) 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)
(%i231) 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)
(%i232) c(in_val):=(ret:in_val,ret)
(%i233) 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)
(%i234) 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)
(%i235) 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)
(%i236) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i237) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i238) 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)
(%i239) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i240) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i241) 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)
(%i242) log10(x):=log(x)/glob_log_10
(%i243) c(x):=x
(%i244) 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
(%i245) 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)
(%i246) exact_soln_y(x):=block(c(0.0))
(%o246) exact_soln_y(x) := block(c(0.0))
(%i247) 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)
(%i248) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i249) 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)
(%i250) 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)
(%i251) 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))
(%i252) 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))
(%i253) display_alot(iter):=(
block(mode_declare(
[[abserr,est_rel_err],convfloat,
[closed_form_val_y],convfloat,[ind_var],
convfloat,[numeric_val],convfloat,[relerr],
convfloat,[term_no],fixnum]),
if reached_interval()
then (if iter >= 0
then (ind_var:array_x[1],
omniout_float(always,
"x[1] ",
33,ind_var,20,
" "),
closed_form_val_y
:exact_soln_y(ind_var),
omniout_float(always,
"y[1] (closed_form) ",
33,
closed_form_val_y,
20," "),
term_no:1,
numeric_val:array_y[term_no],
abserr
:abs(
numeric_val
-closed_form_val_y),
omniout_float(always,
"y[1] (numeric) ",
33,numeric_val,
20," "),
if
c(abs(closed_form_val_y))
> c(glob_prec)
then (
relerr
:abserr*glob__100
/abs(closed_form_val_y),
if c(relerr) > c(glob_prec)
then glob_good_digits
:3
-floor(log10(c(relerr)))
else glob_good_digits:16)
else (relerr:glob__m1,
glob_good_digits:-16),
if
glob_good_digits
< glob_min_good_digits
then glob_min_good_digits
:glob_good_digits,
if
glob_apfp_est_good_digits
< glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits
:glob_apfp_est_good_digits,
if
c(abs(numeric_val))
> c(glob_prec)
then (
est_rel_err
:c(array_max_est_error[1])
*glob__100
*c(sqrt(glob_iter))*c(29)
*c(ats_max_terms)
/c(abs(numeric_val)),
if est_rel_err > glob_prec
then glob_est_digits
:3
-floor(
log10(est_rel_err))
else glob_est_digits:16)
else (relerr:glob__m1,
glob_est_digits:-16),
array_est_digits[1]
:glob_est_digits,
if glob_iter = 1
then array_1st_rel_error[1]
:relerr
else array_last_rel_error[
1]
:relerr,
array_est_rel_error[1]
:est_rel_err,
omniout_float(always,
"absolute error ",
4,abserr,20," "),
omniout_float(always,
"relative error ",
4,relerr,20,"%"),
omniout_int(info,
"Desired digits ",
32,
glob_desired_digits_correct,
4," "),
omniout_int(info,
"Estimated correct digits ",
32,glob_est_digits,
4," "),
omniout_int(info,
"Correct digits ",
32,
glob_good_digits,4,
" "),
omniout_float(always,
"h ",
4,glob_h,20,
" ")))),0)
(%i254) 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)
(%i255) 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)
(%i256) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_0D1[1]*array_x[1],
array_tmp2[1]:sin(array_tmp1[1]),
array_tmp2_g[1]:cos(array_tmp1[1]),
array_tmp3[1]:array_const_0D2[1]*array_x[1],
array_tmp4[1]:sin(array_tmp3[1]),
array_tmp4_g[1]:cos(array_tmp3[1]),
array_tmp5[1]:expt(array_tmp2[1],c(array_tmp4[1])),
array_tmp5_a1[1]:log(array_tmp2[1]),
array_tmp6[1]:array_tmp5[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp6[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_0D1[1]*array_x[2],
array_tmp2[2]:array_tmp2_g[1]*array_tmp1[2]/c(1),
array_tmp2_g[2]:neg(array_tmp2[1])*array_tmp1[2]/c(1),
array_tmp3[2]:array_const_0D2[1]*array_x[2],
array_tmp4[2]:array_tmp4_g[1]*array_tmp3[2]/c(1),
array_tmp4_g[2]:neg(array_tmp4[1])*array_tmp3[2]/c(1),
array_tmp5_a1[2]:(array_tmp2[2]
-att(1,array_tmp2,array_tmp5_a1,2))
/array_tmp2[1],
array_tmp5_a2[1]:ats(2,array_tmp2,array_tmp5_a1,1)*c(1)
/glob_h,
array_tmp5[2]:ats(1,array_tmp5,array_tmp5_a2,1)*glob_h
/c(1),array_tmp6[2]:array_tmp5[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp6[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_tmp2[3]:array_tmp2_g[2]*array_tmp1[2]/c(2),
array_tmp2_g[3]:neg(array_tmp2[2])*array_tmp1[2]/c(2),
array_tmp4[3]:array_tmp4_g[2]*array_tmp3[2]/c(2),
array_tmp4_g[3]:neg(array_tmp4[2])*array_tmp3[2]/c(2),
array_tmp5_a1[3]:(array_tmp2[3]
-att(2,array_tmp2,array_tmp5_a1,2))
/array_tmp2[1],
array_tmp5_a2[2]:ats(3,array_tmp2,array_tmp5_a1,1)*c(2)
/glob_h,
array_tmp5[3]:ats(2,array_tmp5,array_tmp5_a2,1)*glob_h
/c(2),array_tmp6[3]:array_tmp5[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp6[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_tmp2[4]:array_tmp2_g[3]*array_tmp1[2]/c(3),
array_tmp2_g[4]:neg(array_tmp2[3])*array_tmp1[2]/c(3),
array_tmp4[4]:array_tmp4_g[3]*array_tmp3[2]/c(3),
array_tmp4_g[4]:neg(array_tmp4[3])*array_tmp3[2]/c(3),
array_tmp5_a1[4]:(array_tmp2[4]
-att(3,array_tmp2,array_tmp5_a1,2))
/array_tmp2[1],
array_tmp5_a2[3]:ats(4,array_tmp2,array_tmp5_a1,1)*c(3)
/glob_h,
array_tmp5[4]:ats(3,array_tmp5,array_tmp5_a2,1)*glob_h
/c(3),array_tmp6[4]:array_tmp5[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp6[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_tmp2[5]:array_tmp2_g[4]*array_tmp1[2]/c(4),
array_tmp2_g[5]:neg(array_tmp2[4])*array_tmp1[2]/c(4),
array_tmp4[5]:array_tmp4_g[4]*array_tmp3[2]/c(4),
array_tmp4_g[5]:neg(array_tmp4[4])*array_tmp3[2]/c(4),
array_tmp5_a1[5]:(array_tmp2[5]
-att(4,array_tmp2,array_tmp5_a1,2))
/array_tmp2[1],
array_tmp5_a2[4]:ats(5,array_tmp2,array_tmp5_a1,1)*c(4)
/glob_h,
array_tmp5[5]:ats(4,array_tmp5,array_tmp5_a2,1)*glob_h
/c(4),array_tmp6[5]:array_tmp5[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp6[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_tmp2[kkk]
:array_tmp2_g[kkk-1]*array_tmp1[2]/c(kkk-1),
array_tmp2_g[kkk]
:neg(array_tmp2[kkk-1])*array_tmp1[2]/c(kkk-1),
array_tmp4[kkk]
:array_tmp4_g[kkk-1]*array_tmp3[2]/c(kkk-1),
array_tmp4_g[kkk]
:neg(array_tmp4[kkk-1])*array_tmp3[2]/c(kkk-1),
array_tmp5_a1[kkk]
:(array_tmp2[kkk]
-att(kkk-1,array_tmp2,array_tmp5_a1,2))
/array_tmp2[1],
array_tmp5_a2[kkk-1]
:ats(kkk,array_tmp2,array_tmp5_a1,1)*c(kkk-1)
/glob_h,
array_tmp5[kkk]
:ats(kkk-1,array_tmp5,array_tmp5_a2,1)*glob_h
/c(kkk-1),array_tmp6[kkk]:array_tmp5[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_tmp6[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)
(%i257) exact_soln_y(x):=block(c(0.0))
(%o257) exact_soln_y(x) := block(c(0.0))
(%i258) 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_g[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 30 do (array_tmp4_g[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_c1[term]:c(0.0),term:1+term),term:1,
while term <= 30 do
(array_tmp5_a1[term]:c(0.0),term:1+term),term:1,
while term <= 30 do
(array_tmp5_a2[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_tmp6[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_g),zero_ats_ar(array_tmp2),
zero_ats_ar(array_tmp3),zero_ats_ar(array_tmp4_g),
zero_ats_ar(array_tmp4),zero_ats_ar(array_tmp5_c1),
zero_ats_ar(array_tmp5_a1),zero_ats_ar(array_tmp5_a2),
zero_ats_ar(array_tmp5),zero_ats_ar(array_tmp6),
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_0D1),
array_const_0D1[1]:c(0.1),zero_ats_ar(array_const_0D2),
array_const_0D2[1]:c(0.2),zero_ats_ar(array_m1),
array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,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_sin_sinpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * 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 ( sin ( 0.1 * x ) , sin ( 0.2 * 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,
"2015-04-24T21:15:11-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"expt_sin_sin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * 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_sin_sin diffeq.max"),
logitem_str(html_log_file,
"expt_sin_sin maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i259) main():=(glob_iolevel:2,compile(all),main_prog())
(%i260) 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_0D1 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp2_g in translation.
warning: encountered undefined variable array_const_0D2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_tmp4_g in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable array_tmp5_a1 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp6 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_tmp5_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_tmp5_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_sin_sinpostode.ode#################"
"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * 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) = 9.089280960289792000E-3 " "
absolute error = 9.089280960289792000E-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) = 1.81149434954783420E-2 " "
absolute error = 1.81149434954783420E-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) = 2.707900099984001400E-2 " "
absolute error = 2.707900099984001400E-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) = 3.59833067222725400E-2 " "
absolute error = 3.59833067222725400E-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) = 4.4829576810029803E-2 " "
absolute error = 4.4829576810029803E-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) = 5.361940864992856000E-2 " "
absolute error = 5.361940864992856000E-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) = 6.23542957146323500E-2 " "
absolute error = 6.23542957146323500E-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) = 7.10356397557373600E-2 " "
absolute error = 7.10356397557373600E-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) = 7.9664760945279700E-2 " "
absolute error = 7.9664760945279700E-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) = 8.82429064051514200E-2 " "
absolute error = 8.82429064051514200E-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) = 9.67712574516755700E-2 " "
absolute error = 9.67712574516755700E-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) = 0.10525093580317364 " "
absolute error = 0.10525093580317364 " "
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) = 0.11368300894106634 " "
absolute error = 0.11368300894106634 " "
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) = 0.12206849477299299 " "
absolute error = 0.12206849477299299 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.13040836571508188 " "
absolute error = 0.13040836571508188 " "
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) = 0.13870355228679676 " "
absolute error = 0.13870355228679676 " "
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) = 0.14695494629363068 " "
absolute error = 0.14695494629363068 " "
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) = 0.1551634036588518 " "
absolute error = 0.1551634036588518 " "
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) = 0.16332974695449096 " "
absolute error = 0.16332974695449096 " "
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) = 0.17145476767305012 " "
absolute error = 0.17145476767305012 " "
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) = 0.1795392282744598 " "
absolute error = 0.1795392282744598 " "
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) = 0.18758386403721863 " "
absolute error = 0.18758386403721863 " "
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) = 0.19558938473811235 " "
absolute error = 0.19558938473811235 " "
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) = 0.20355647618120454 " "
absolute error = 0.20355647618120454 " "
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) = 0.21148580159374042 " "
absolute error = 0.21148580159374042 " "
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) = 0.21937800290408704 " "
absolute error = 0.21937800290408704 " "
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) = 0.22723370191472786 " "
absolute error = 0.22723370191472786 " "
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) = 0.2350535013815758 " "
absolute error = 0.2350535013815758 " "
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) = 0.24283798600938677 " "
absolute error = 0.24283798600938677 " "
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) = 0.25058772337180407 " "
absolute error = 0.25058772337180407 " "
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) = 0.2583032647635016 " "
absolute error = 0.2583032647635016 " "
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) = 0.26598514599098644 " "
absolute error = 0.26598514599098644 " "
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) = 0.27363388810784073 " "
absolute error = 0.27363388810784073 " "
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) = 0.2812499980995182 " "
absolute error = 0.2812499980995182 " "
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) = 0.28883396952222784 " "
absolute error = 0.28883396952222784 " "
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) = 0.2963862830999391 " "
absolute error = 0.2963862830999391 " "
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) = 0.3039074072831066 " "
absolute error = 0.3039074072831066 " "
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) = 0.31139779877233165 " "
absolute error = 0.31139779877233165 " "
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) = 0.3188579030098442 " "
absolute error = 0.3188579030098442 " "
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) = 0.32628815464139926 " "
absolute error = 0.32628815464139926 " "
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) = 0.333688977950923 " "
absolute error = 0.333688977950923 " "
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) = 0.3410607872700138 " "
absolute error = 0.3410607872700138 " "
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) = 0.3484039873642102 " "
absolute error = 0.3484039873642102 " "
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) = 0.35571897379774914 " "
absolute error = 0.35571897379774914 " "
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) = 0.3630061332783897 " "
absolute error = 0.3630061332783897 " "
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) = 0.37026584398372736 " "
absolute error = 0.37026584398372736 " "
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) = 0.37749847587030344 " "
absolute error = 0.37749847587030344 " "
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) = 0.38470439096669845 " "
absolute error = 0.38470439096669845 " "
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) = 0.3918839436516962 " "
absolute error = 0.3918839436516962 " "
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) = 0.3990374809185178 " "
absolute error = 0.3990374809185178 " "
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) = 0.4061653426260372 " "
absolute error = 0.4061653426260372 " "
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) = 0.4132678617378213 " "
absolute error = 0.4132678617378213 " "
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) = 0.4203453645497661 " "
absolute error = 0.4203453645497661 " "
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) = 0.42739817090704246 " "
absolute error = 0.42739817090704246 " "
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) = 0.434426594411009 " "
absolute error = 0.434426594411009 " "
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) = 0.44143094261670024 " "
absolute error = 0.44143094261670024 " "
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) = 0.4484115172214514 " "
absolute error = 0.4484115172214514 " "
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) = 0.4553686142451812 " "
absolute error = 0.4553686142451812 " "
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) = 0.46230252420281587 " "
absolute error = 0.46230252420281587 " "
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) = 0.4692135322693018 " "
absolute error = 0.4692135322693018 " "
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) = 0.4761019184376251 " "
absolute error = 0.4761019184376251 " "
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) = 0.48296795767022427 " "
absolute error = 0.48296795767022427 " "
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) = 0.4898119200441581 " "
absolute error = 0.4898119200441581 " "
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) = 0.49663407089036643 " "
absolute error = 0.49663407089036643 " "
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) = 0.5034346709273362 " "
absolute error = 0.5034346709273362 " "
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) = 0.5102139763894679 " "
absolute error = 0.5102139763894679 " "
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) = 0.5169722391504163 " "
absolute error = 0.5169722391504163 " "
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) = 0.5237097068416643 " "
absolute error = 0.5237097068416643 " "
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) = 0.5304266229665667 " "
absolute error = 0.5304266229665667 " "
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) = 0.5371232270100952 " "
absolute error = 0.5371232270100952 " "
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) = 0.54379975454449 " "
absolute error = 0.54379975454449 " "
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) = 0.5504564373310248 " "
absolute error = 0.5504564373310248 " "
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) = 0.5570935034180629 " "
absolute error = 0.5570935034180629 " "
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) = 0.5637111772355887 " "
absolute error = 0.5637111772355887 " "
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) = 0.5703096796863759 " "
absolute error = 0.5703096796863759 " "
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) = 0.5768892282339473 " "
absolute error = 0.5768892282339473 " "
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) = 0.5834500369874775 " "
absolute error = 0.5834500369874775 " "
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) = 0.5899923167837731 " "
absolute error = 0.5899923167837731 " "
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) = 0.5965162752664622 " "
absolute error = 0.5965162752664622 " "
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) = 0.6030221169625202 " "
absolute error = 0.6030221169625202 " "
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) = 0.6095100433562429 " "
absolute error = 0.6095100433562429 " "
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) = 0.6159802529607834 " "
absolute error = 0.6159802529607834 " "
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) = 0.6224329413873525 " "
absolute error = 0.6224329413873525 " "
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) = 0.6288683014121852 " "
absolute error = 0.6288683014121852 " "
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) = 0.6352865230413652 " "
absolute error = 0.6352865230413652 " "
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) = 0.6416877935735985 " "
absolute error = 0.6416877935735985 " "
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) = 0.6480722976610167 " "
absolute error = 0.6480722976610167 " "
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) = 0.6544402173680944 " "
absolute error = 0.6544402173680944 " "
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) = 0.6607917322287552 " "
absolute error = 0.6607917322287552 " "
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) = 0.6671270193017362 " "
absolute error = 0.6671270193017362 " "
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) = 0.6734462532242853 " "
absolute error = 0.6734462532242853 " "
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) = 0.6797496062642501 " "
absolute error = 0.6797496062642501 " "
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) = 0.6860372483706267 " "
absolute error = 0.6860372483706267 " "
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) = 0.6923093472226234 " "
absolute error = 0.6923093472226234 " "
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) = 0.6985660682772971 " "
absolute error = 0.6985660682772971 " "
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) = 0.7048075748158172 " "
absolute error = 0.7048075748158172 " "
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) = 0.7110340279884075 " "
absolute error = 0.7110340279884075 " "
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) = 0.7172455868580141 " "
absolute error = 0.7172455868580141 " "
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) = 0.7234424084427477 " "
absolute error = 0.7234424084427477 " "
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) = 0.7296246477571435 " "
absolute error = 0.7296246477571435 " "
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) = 0.7357924578522833 " "
absolute error = 0.7357924578522833 " "
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) = 0.741945989854816 " "
absolute error = 0.741945989854816 " "
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) = 0.7480853930049224 " "
absolute error = 0.7480853930049224 " "
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) = 0.7542108146932548 " "
absolute error = 0.7542108146932548 " "
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) = 0.7603224004968904 " "
absolute error = 0.7603224004968904 " "
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) = 0.7664202942143317 " "
absolute error = 0.7664202942143317 " "
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) = 0.7725046378995886 " "
absolute error = 0.7725046378995886 " "
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) = 0.7785755718953684 " "
absolute error = 0.7785755718953684 " "
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) = 0.7846332348654096 " "
absolute error = 0.7846332348654096 " "
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) = 0.7906777638259835 " "
absolute error = 0.7906777638259835 " "
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) = 0.7967092941765941 " "
absolute error = 0.7967092941765941 " "
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) = 0.8027279597299013 " "
absolute error = 0.8027279597299013 " "
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) = 0.8087338927408921 " "
absolute error = 0.8087338927408921 " "
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) = 0.8147272239353271 " "
absolute error = 0.8147272239353271 " "
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) = 0.8207080825374808 " "
absolute error = 0.8207080825374808 " "
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) = 0.826676596297203 " "
absolute error = 0.826676596297203 " "
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) = 0.8326328915163195 " "
absolute error = 0.8326328915163195 " "
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) = 0.8385770930743945 " "
absolute error = 0.8385770930743945 " "
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) = 0.8445093244538736 " "
absolute error = 0.8445093244538736 " "
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) = 0.8504297077646268 " "
absolute error = 0.8504297077646268 " "
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) = 0.8563383637679112 " "
absolute error = 0.8563383637679112 " "
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) = 0.8622354118997687 " "
absolute error = 0.8622354118997687 " "
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) = 0.8681209702938771 " "
absolute error = 0.8681209702938771 " "
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) = 0.8739951558038717 " "
absolute error = 0.8739951558038717 " "
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) = 0.8798580840251521 " "
absolute error = 0.8798580840251521 " "
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) = 0.8857098693161893 " "
absolute error = 0.8857098693161893 " "
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) = 0.8915506248193484 " "
absolute error = 0.8915506248193484 " "
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) = 0.8973804624812411 " "
absolute error = 0.8973804624812411 " "
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) = 0.9031994930726216 " "
absolute error = 0.9031994930726216 " "
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) = 0.9090078262078374 " "
absolute error = 0.9090078262078374 " "
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) = 0.9148055703638511 " "
absolute error = 0.9148055703638511 " "
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) = 0.9205928328988423 " "
absolute error = 0.9205928328988423 " "
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) = 0.9263697200704024 " "
absolute error = 0.9263697200704024 " "
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) = 0.932136337053334 " "
absolute error = 0.932136337053334 " "
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) = 0.9378927879570662 " "
absolute error = 0.9378927879570662 " "
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) = 0.9436391758426959 " "
absolute error = 0.9436391758426959 " "
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) = 0.9493756027396643 " "
absolute error = 0.9493756027396643 " "
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) = 0.9551021696620816 " "
absolute error = 0.9551021696620816 " "
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) = 0.9608189766247055 " "
absolute error = 0.9608189766247055 " "
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) = 0.9665261226585866 " "
absolute error = 0.9665261226585866 " "
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) = 0.972223705826387 " "
absolute error = 0.972223705826387 " "
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) = 0.9779118232373805 " "
absolute error = 0.9779118232373805 " "
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) = 0.9835905710621474 " "
absolute error = 0.9835905710621474 " "
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) = 0.9892600445469647 " "
absolute error = 0.9892600445469647 " "
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) = 0.9949203380279056 " "
absolute error = 0.9949203380279056 " "
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) = 1.0005715449446528 " "
absolute error = 1.0005715449446528 " "
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) = 1.0062137578540344 " "
absolute error = 1.0062137578540344 " "
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) = 1.01184706844329 " "
absolute error = 1.01184706844329 " "
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) = 1.0174715675430697 " "
absolute error = 1.0174715675430697 " "
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) = 1.0230873451401779 " "
absolute error = 1.0230873451401779 " "
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) = 1.028694490390068 " "
absolute error = 1.028694490390068 " "
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) = 1.0342930916290909 " "
absolute error = 1.0342930916290909 " "
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) = 1.0398832363865034 " "
absolute error = 1.0398832363865034 " "
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) = 1.0454650113962467 " "
absolute error = 1.0454650113962467 " "
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) = 1.0510385026084972 " "
absolute error = 1.0510385026084972 " "
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) = 1.056603795200997 " "
absolute error = 1.056603795200997 " "
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) = 1.0621609735901658 " "
absolute error = 1.0621609735901658 " "
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) = 1.0677101214420073 " "
absolute error = 1.0677101214420073 " "
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) = 1.073251321682804 " "
absolute error = 1.073251321682804 " "
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) = 1.0787846565096135 " "
absolute error = 1.0787846565096135 " "
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) = 1.0843102074005733 " "
absolute error = 1.0843102074005733 " "
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) = 1.089828055125008 " "
absolute error = 1.089828055125008 " "
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) = 1.095338279753352 " "
absolute error = 1.095338279753352 " "
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) = 1.1008409606668925 " "
absolute error = 1.1008409606668925 " "
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) = 1.1063361765673307 " "
absolute error = 1.1063361765673307 " "
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) = 1.11182400548617 " "
absolute error = 1.11182400548617 " "
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) = 1.1173045247939366 " "
absolute error = 1.1173045247939366 " "
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) = 1.1227778112092293 " "
absolute error = 1.1227778112092293 " "
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) = 1.1282439408076124 " "
absolute error = 1.1282439408076124 " "
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) = 1.1337029890303456 " "
absolute error = 1.1337029890303456 " "
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) = 1.1391550306929614 " "
absolute error = 1.1391550306929614 " "
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) = 1.1446001399936896 " "
absolute error = 1.1446001399936896 " "
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) = 1.1500383905217335 " "
absolute error = 1.1500383905217335 " "
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) = 1.1554698552654028 " "
absolute error = 1.1554698552654028 " "
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) = 1.1608946066201027 " "
absolute error = 1.1608946066201027 " "
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) = 1.1663127163961862 " "
absolute error = 1.1663127163961862 " "
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) = 1.1717242558266694 " "
absolute error = 1.1717242558266694 " "
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) = 1.177129295574815 " "
absolute error = 1.177129295574815 " "
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) = 1.1825279057415854 " "
absolute error = 1.1825279057415854 " "
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) = 1.18792015587297 " "
absolute error = 1.18792015587297 " "
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) = 1.193306114967187 " "
absolute error = 1.193306114967187 " "
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) = 1.1986858514817644 " "
absolute error = 1.1986858514817644 " "
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) = 1.2040594333405004 " "
absolute error = 1.2040594333405004 " "
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) = 1.2094269279403111 " "
absolute error = 1.2094269279403111 " "
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) = 1.2147884021579587 " "
absolute error = 1.2147884021579587 " "
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) = 1.2201439223566735 " "
absolute error = 1.2201439223566735 " "
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) = 1.2254935543926633 " "
absolute error = 1.2254935543926633 " "
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) = 1.230837363621514 " "
absolute error = 1.230837363621514 " "
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) = 1.236175414904492 " "
absolute error = 1.236175414904492 " "
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) = 1.2415077726147363 " "
absolute error = 1.2415077726147363 " "
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) = 1.2468345006433552 " "
absolute error = 1.2468345006433552 " "
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) = 1.2521556624054215 " "
absolute error = 1.2521556624054215 " "
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) = 1.257471320845872 " "
absolute error = 1.257471320845872 " "
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) = 1.2627815384453134 " "
absolute error = 1.2627815384453134 " "
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) = 1.2680863772257338 " "
absolute error = 1.2680863772257338 " "
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) = 1.273385898756126 " "
absolute error = 1.273385898756126 " "
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) = 1.2786801641580163 " "
absolute error = 1.2786801641580163 " "
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) = 1.2839692341109123 " "
absolute error = 1.2839692341109123 " "
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) = 1.2892531688576616 " "
absolute error = 1.2892531688576616 " "
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) = 1.2945320282097261 " "
absolute error = 1.2945320282097261 " "
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) = 1.2998058715523768 " "
absolute error = 1.2998058715523768 " "
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) = 1.305074757849806 " "
absolute error = 1.305074757849806 " "
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) = 1.3103387456501598 " "
absolute error = 1.3103387456501598 " "
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) = 1.3155978930904937 " "
absolute error = 1.3155978930904937 " "
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) = 1.3208522579016533 " "
absolute error = 1.3208522579016533 " "
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) = 1.3261018974130792 " "
absolute error = 1.3261018974130792 " "
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) = 1.3313468685575371 " "
absolute error = 1.3313468685575371 " "
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) = 1.3365872278757793 " "
absolute error = 1.3365872278757793 " "
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) = 1.3418230315211337 " "
absolute error = 1.3418230315211337 " "
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) = 1.3470543352640232 " "
absolute error = 1.3470543352640232 " "
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) = 1.352281194496419 " "
absolute error = 1.352281194496419 " "
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) = 1.3575036642362253 " "
absolute error = 1.3575036642362253 " "
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) = 1.3627217991315996 " "
absolute error = 1.3627217991315996 " "
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) = 1.3679356534652098 " "
absolute error = 1.3679356534652098 " "
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) = 1.373145281158426 " "
absolute error = 1.373145281158426 " "
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) = 1.3783507357754516 " "
absolute error = 1.3783507357754516 " "
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) = 1.3835520705273956 " "
absolute error = 1.3835520705273956 " "
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) = 1.3887493382762806 " "
absolute error = 1.3887493382762806 " "
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) = 1.393942591538997 " "
absolute error = 1.393942591538997 " "
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) = 1.3991318824911974 " "
absolute error = 1.3991318824911974 " "
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) = 1.404317262971135 " "
absolute error = 1.404317262971135 " "
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) = 1.4094987844834452 " "
absolute error = 1.4094987844834452 " "
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) = 1.4146764982028754 " "
absolute error = 1.4146764982028754 " "
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) = 1.419850454977959 " "
absolute error = 1.419850454977959 " "
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) = 1.4250207053346375 " "
absolute error = 1.4250207053346375 " "
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) = 1.4301872994798326 " "
absolute error = 1.4301872994798326 " "
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) = 1.435350287304964 " "
absolute error = 1.435350287304964 " "
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) = 1.4405097183894207 " "
absolute error = 1.4405097183894207 " "
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) = 1.4456656420039815 " "
absolute error = 1.4456656420039815 " "
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) = 1.4508181071141881 " "
absolute error = 1.4508181071141881 " "
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) = 1.4559671623836696 " "
absolute error = 1.4559671623836696 " "
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) = 1.461112856177424 " "
absolute error = 1.461112856177424 " "
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) = 1.4662552365650485 " "
absolute error = 1.4662552365650485 " "
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) = 1.47139435132393 " "
absolute error = 1.47139435132393 " "
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) = 1.4765302479423885 " "
absolute error = 1.4765302479423885 " "
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) = 1.4816629736227769 " "
absolute error = 1.4816629736227769 " "
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) = 1.4867925752845417 " "
absolute error = 1.4867925752845417 " "
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) = 1.4919190995672351 " "
absolute error = 1.4919190995672351 " "
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) = 1.4970425928334945 " "
absolute error = 1.4970425928334945 " "
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) = 1.5021631011719725 " "
absolute error = 1.5021631011719725 " "
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) = 1.5072806704002342 " "
absolute error = 1.5072806704002342 " "
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) = 1.5123953460676094 " "
absolute error = 1.5123953460676094 " "
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) = 1.517507173458012 " "
absolute error = 1.517507173458012 " "
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) = 1.5226161975927155 " "
absolute error = 1.5226161975927155 " "
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) = 1.5277224632330957 " "
absolute error = 1.5277224632330957 " "
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) = 1.532826014883335 " "
absolute error = 1.532826014883335 " "
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) = 1.5379268967930886 " "
absolute error = 1.5379268967930886 " "
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) = 1.5430251529601198 " "
absolute error = 1.5430251529601198 " "
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) = 1.5481208271328954 " "
absolute error = 1.5481208271328954 " "
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) = 1.553213962813149 " "
absolute error = 1.553213962813149 " "
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) = 1.55830460325841 " "
absolute error = 1.55830460325841 " "
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) = 1.5633927914845007 " "
absolute error = 1.5633927914845007 " "
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) = 1.5684785702679975 " "
absolute error = 1.5684785702679975 " "
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) = 1.573561982148662 " "
absolute error = 1.573561982148662 " "
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) = 1.5786430694318403 " "
absolute error = 1.5786430694318403 " "
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) = 1.5837218741908297 " "
absolute error = 1.5837218741908297 " "
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) = 1.5887984382692155 " "
absolute error = 1.5887984382692155 " "
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) = 1.5938728032831773 " "
absolute error = 1.5938728032831773 " "
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) = 1.5989450106237657 " "
absolute error = 1.5989450106237657 " "
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) = 1.604015101459149 " "
absolute error = 1.604015101459149 " "
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) = 1.609083116736831 " "
absolute error = 1.609083116736831 " "
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) = 1.6141490971858405 " "
absolute error = 1.6141490971858405 " "
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) = 1.6192130833188931 " "
absolute error = 1.6192130833188931 " "
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) = 1.6242751154345254 " "
absolute error = 1.6242751154345254 " "
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) = 1.6293352336191989 " "
absolute error = 1.6293352336191989 " "
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) = 1.634393477749383 " "
absolute error = 1.634393477749383 " "
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) = 1.6394498874936065 " "
absolute error = 1.6394498874936065 " "
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) = 1.6445045023144855 " "
absolute error = 1.6445045023144855 " "
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) = 1.6495573614707237 " "
absolute error = 1.6495573614707237 " "
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) = 1.6546085040190903 " "
absolute error = 1.6546085040190903 " "
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) = 1.6596579688163702 " "
absolute error = 1.6596579688163702 " "
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) = 1.6647057945212922 " "
absolute error = 1.6647057945212922 " "
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) = 1.6697520195964304 " "
absolute error = 1.6697520195964304 " "
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) = 1.674796682310084 " "
absolute error = 1.674796682310084 " "
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) = 1.6798398207381322 " "
absolute error = 1.6798398207381322 " "
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) = 1.6848814727658685 " "
absolute error = 1.6848814727658685 " "
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) = 1.689921676089807 " "
absolute error = 1.689921676089807 " "
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) = 1.694960468219473 " "
absolute error = 1.694960468219473 " "
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) = 1.6999978864791656 " "
absolute error = 1.6999978864791656 " "
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) = 1.7050339680097024 " "
absolute error = 1.7050339680097024 " "
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) = 1.7100687497701401 " "
absolute error = 1.7100687497701401 " "
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) = 1.7151022685394774 " "
absolute error = 1.7151022685394774 " "
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) = 1.7201345609183316 " "
absolute error = 1.7201345609183316 " "
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) = 1.7251656633306005 " "
absolute error = 1.7251656633306005 " "
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) = 1.7301956120250996 " "
absolute error = 1.7301956120250996 " "
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) = 1.7352244430771808 " "
absolute error = 1.7352244430771808 " "
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) = 1.7402521923903327 " "
absolute error = 1.7402521923903327 " "
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) = 1.7452788956977603 " "
absolute error = 1.7452788956977603 " "
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) = 1.750304588563944 " "
absolute error = 1.750304588563944 " "
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) = 1.7553293063861826 " "
absolute error = 1.7553293063861826 " "
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) = 1.760353084396115 " "
absolute error = 1.760353084396115 " "
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) = 1.765375957661227 " "
absolute error = 1.765375957661227 " "
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) = 1.7703979610863347 " "
absolute error = 1.7703979610863347 " "
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) = 1.775419129415055 " "
absolute error = 1.775419129415055 " "
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) = 1.7804394972312565 " "
absolute error = 1.7804394972312565 " "
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) = 1.7854590989604915 " "
absolute error = 1.7854590989604915 " "
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) = 1.7904779688714136 " "
absolute error = 1.7904779688714136 " "
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) = 1.7954961410771766 " "
absolute error = 1.7954961410771766 " "
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) = 1.8005136495368175 " "
absolute error = 1.8005136495368175 " "
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) = 1.805530528056622 " "
absolute error = 1.805530528056622 " "
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) = 1.8105468102914746 " "
absolute error = 1.8105468102914746 " "
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) = 1.815562529746193 " "
absolute error = 1.815562529746193 " "
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) = 1.8205777197768458 " "
absolute error = 1.8205777197768458 " "
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) = 1.8255924135920547 " "
absolute error = 1.8255924135920547 " "
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) = 1.8306066442542817 " "
absolute error = 1.8306066442542817 " "
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) = 1.8356204446811004 " "
absolute error = 1.8356204446811004 " "
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) = 1.8406338476464532 " "
absolute error = 1.8406338476464532 " "
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) = 1.8456468857818944 " "
absolute error = 1.8456468857818944 " "
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) = 1.8506595915778143 " "
absolute error = 1.8506595915778143 " "
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) = 1.8556719973846565 " "
absolute error = 1.8556719973846565 " "
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) = 1.8606841354141122 " "
absolute error = 1.8606841354141122 " "
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) = 1.8656960377403065 " "
absolute error = 1.8656960377403065 " "
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) = 1.870707736300971 " "
absolute error = 1.870707736300971 " "
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) = 1.8757192628985986 " "
absolute error = 1.8757192628985986 " "
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) = 1.8807306492015867 " "
absolute error = 1.8807306492015867 " "
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) = 1.885741926745369 " "
absolute error = 1.885741926745369 " "
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) = 1.8907531269335314 " "
absolute error = 1.8907531269335314 " "
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) = 1.8957642810389155 " "
absolute error = 1.8957642810389155 " "
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) = 1.9007754202047114 " "
absolute error = 1.9007754202047114 " "
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) = 1.9057865754455334 " "
absolute error = 1.9057865754455334 " "
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) = 1.9107977776484883 " "
absolute error = 1.9107977776484883 " "
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) = 1.9158090575742286 " "
absolute error = 1.9158090575742286 " "
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) = 1.920820445857992 " "
absolute error = 1.920820445857992 " "
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) = 1.9258319730106321 " "
absolute error = 1.9258319730106321 " "
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) = 1.9308436694196347 " "
absolute error = 1.9308436694196347 " "
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) = 1.9358555653501253 " "
absolute error = 1.9358555653501253 " "
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) = 1.9408676909458593 " "
absolute error = 1.9408676909458593 " "
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) = 1.9458800762302078 " "
absolute error = 1.9458800762302078 " "
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) = 1.9508927511071275 " "
absolute error = 1.9508927511071275 " "
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) = 1.9559057453621207 " "
absolute error = 1.9559057453621207 " "
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) = 1.960919088663183 " "
absolute error = 1.960919088663183 " "
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) = 1.9659328105617424 " "
absolute error = 1.9659328105617424 " "
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) = 1.9709469404935855 " "
absolute error = 1.9709469404935855 " "
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) = 1.975961507779775 " "
absolute error = 1.975961507779775 " "
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) = 1.9809765416275535 " "
absolute error = 1.9809765416275535 " "
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) = 1.9859920711312409 " "
absolute error = 1.9859920711312409 " "
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) = 1.9910081252731187 " "
absolute error = 1.9910081252731187 " "
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) = 1.9960247329243042 " "
absolute error = 1.9960247329243042 " "
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) = 2.001041922845617 " "
absolute error = 2.001041922845617 " "
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) = 2.006059723688432 " "
absolute error = 2.006059723688432 " "
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) = 2.011078163995526 " "
absolute error = 2.011078163995526 " "
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) = 2.016097272201914 " "
absolute error = 2.016097272201914 " "
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) = 2.0211170766356714 " "
absolute error = 2.0211170766356714 " "
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) = 2.0261376055187537 " "
absolute error = 2.0261376055187537 " "
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) = 2.031158886967803 " "
absolute error = 2.031158886967803 " "
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) = 2.036180948994944 " "
absolute error = 2.036180948994944 " "
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) = 2.0412038195085738 " "
absolute error = 2.0412038195085738 " "
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) = 2.0462275263141425 " "
absolute error = 2.0462275263141425 " "
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) = 2.0512520971149226 " "
absolute error = 2.0512520971149226 " "
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) = 2.05627755951277 " "
absolute error = 2.05627755951277 " "
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) = 2.0613039410088785 " "
absolute error = 2.0613039410088785 " "
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) = 2.066331269004524 " "
absolute error = 2.066331269004524 " "
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) = 2.0713595708017993 " "
absolute error = 2.0713595708017993 " "
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) = 2.0763888736043414 " "
absolute error = 2.0763888736043414 " "
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) = 2.0814192045180526 " "
absolute error = 2.0814192045180526 " "
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) = 2.08645059055181 " "
absolute error = 2.08645059055181 " "
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) = 2.091483058618168 " "
absolute error = 2.091483058618168 " "
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) = 2.0965166355340528 " "
absolute error = 2.0965166355340528 " "
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) = 2.1015513480214496 " "
absolute error = 2.1015513480214496 " "
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) = 2.106587222708081 " "
absolute error = 2.106587222708081 " "
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) = 2.1116242861280767 " "
absolute error = 2.1116242861280767 " "
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) = 2.116662564722639 " "
absolute error = 2.116662564722639 " "
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) = 2.1217020848406984 " "
absolute error = 2.1217020848406984 " "
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) = 2.1267428727395576 " "
absolute error = 2.1267428727395576 " "
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) = 2.1317849545855374 " "
absolute error = 2.1317849545855374 " "
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) = 2.1368283564546053 " "
absolute error = 2.1368283564546053 " "
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) = 2.1418731043330057 " "
absolute error = 2.1418731043330057 " "
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) = 2.146919224117874 " "
absolute error = 2.146919224117874 " "
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) = 2.15196674161785 " "
absolute error = 2.15196674161785 " "
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) = 2.1570156825536855 " "
absolute error = 2.1570156825536855 " "
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) = 2.1620660725588356 " "
absolute error = 2.1620660725588356 " "
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) = 2.1671179371800537 " "
absolute error = 2.1671179371800537 " "
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) = 2.1721713018779734 " "
absolute error = 2.1721713018779734 " "
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) = 2.177226192027686 " "
absolute error = 2.177226192027686 " "
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) = 2.1822826329193092 " "
absolute error = 2.1822826329193092 " "
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) = 2.1873406497585535 " "
absolute error = 2.1873406497585535 " "
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) = 2.192400267667277 " "
absolute error = 2.192400267667277 " "
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) = 2.1974615116840357 " "
absolute error = 2.1974615116840357 " "
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) = 2.2025244067646286 " "
absolute error = 2.2025244067646286 " "
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) = 2.2075889777826343 " "
absolute error = 2.2075889777826343 " "
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) = 2.2126552495299454 " "
absolute error = 2.2126552495299454 " "
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) = 2.2177232467172883 " "
absolute error = 2.2177232467172883 " "
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) = 2.2227929939747466 " "
absolute error = 2.2227929939747466 " "
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) = 2.227864515852274 " "
absolute error = 2.227864515852274 " "
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) = 2.2329378368201978 " "
absolute error = 2.2329378368201978 " "
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) = 2.2380129812697223 " "
absolute error = 2.2380129812697223 " "
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) = 2.243089973513425 " "
absolute error = 2.243089973513425 " "
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) = 2.248168837785742 " "
absolute error = 2.248168837785742 " "
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) = 2.253249598243455 " "
absolute error = 2.253249598243455 " "
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) = 2.2583322789661677 " "
absolute error = 2.2583322789661677 " "
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) = 2.2634169039567764 " "
absolute error = 2.2634169039567764 " "
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) = 2.2685034971419373 " "
absolute error = 2.2685034971419373 " "
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) = 2.273592082372529 " "
absolute error = 2.273592082372529 " "
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) = 2.2786826834241047 " "
absolute error = 2.2786826834241047 " "
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) = 2.2837753239973444 " "
absolute error = 2.2837753239973444 " "
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) = 2.288870027718497 " "
absolute error = 2.288870027718497 " "
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) = 2.2939668181398236 " "
absolute error = 2.2939668181398236 " "
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) = 2.299065718740026 " "
absolute error = 2.299065718740026 " "
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) = 2.304166752924678 " "
absolute error = 2.304166752924678 " "
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) = 2.3092699440266498 " "
absolute error = 2.3092699440266498 " "
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) = 2.314375315306524 " "
absolute error = 2.314375315306524 " "
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) = 2.3194828899530107 " "
absolute error = 2.3194828899530107 " "
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) = 2.3245926910833545 " "
absolute error = 2.3245926910833545 " "
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) = 2.329704741743737 " "
absolute error = 2.329704741743737 " "
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) = 2.3348190649096767 " "
absolute error = 2.3348190649096767 " "
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) = 2.339935683486421 " "
absolute error = 2.339935683486421 " "
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) = 2.3450546203093348 " "
absolute error = 2.3450546203093348 " "
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) = 2.350175898144286 " "
absolute error = 2.350175898144286 " "
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) = 2.3552995396880214 " "
absolute error = 2.3552995396880214 " "
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) = 2.3604255675685435 " "
absolute error = 2.3604255675685435 " "
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) = 2.3655540043454786 " "
absolute error = 2.3655540043454786 " "
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) = 2.3706848725104415 " "
absolute error = 2.3706848725104415 " "
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) = 2.3758181944873997 " "
absolute error = 2.3758181944873997 " "
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) = 2.3809539926330223 " "
absolute error = 2.3809539926330223 " "
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) = 2.3860922892370375 " "
absolute error = 2.3860922892370375 " "
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) = 2.3912331065225767 " "
absolute error = 2.3912331065225767 " "
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) = 2.396376466646519 " "
absolute error = 2.396376466646519 " "
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) = 2.401522391699826 " "
absolute error = 2.401522391699826 " "
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) = 2.4066709037078793 " "
absolute error = 2.4066709037078793 " "
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) = 2.4118220246308084 " "
absolute error = 2.4118220246308084 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; "
Iterations = 4207
"Total Elapsed Time "= 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 3 Minutes 0 Seconds
"Expected Time Remaining "= 29 Seconds
"Optimized Time Remaining "= 29 Seconds
"Expected Total Time "= 3 Minutes 29 Seconds
"Time to Timeout "= 0.0 Seconds
Percent Done = 85.87755102040354 "%"
(%o260) temp/diffeq.expt_sin_sin.max