(%i1) batch("temp/diffeq.diff2.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.diff2.max
(%i2) load("stringproc")
(%i3) keepfloat:true
(%i4) alias(convfloat,float)
(%i5) alias(int_trunc,truncate)
(%i6) alias(elapsed_time_seconds,elapsed_real_time)
(%i7) alias(ln,log)
(%i8) alias(arcsin,asin)
(%i9) alias(arccos,acos)
(%i10) alias(arctan,atan)
(%i11) alias(float_abs,abs)
(%i12) mode_declare(display_poles(),fixnum)
(%i13) mode_declare(est_size_answer(),convfloat)
(%i14) mode_declare(test_suggested_h(),convfloat)
(%i15) mode_declare(reached_interval(),boolean)
(%i16) mode_declare(display_alot([iter],fixnum),fixnum)
(%i17) mode_declare(prog_report([x_start],convfloat,[x_end],convfloat),fixnum)
(%i18) mode_declare(check_for_pole(),fixnum)
(%i19) mode_declare(atomall(),fixnum)
(%i20) mode_declare(log10([x],convfloat),convfloat)
(%i21) mode_declare(logitem_timestr([fd],fixnum,[secs_in],number),fixnum)
(%i22) mode_declare(omniout_timestr(secs_in,number),fixnum)
(%i23) mode_declare(zero_ats_ar(ar,array([40],convfloat)),fixnum)
(%i24) mode_declare(ats([mmm_ats],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_ats],fixnum),
convfloat)
(%i25) mode_declare(att([mmm_att],fixnum,[arr_a],
completearray([40],convfloat),[arr_b],
completearray([40],convfloat),[jjj_att],fixnum),
convfloat)
(%i26) mode_declare(logitem_ditto([file],fixnum),fixnum)
(%i27) mode_declare(logitem_integer([file],fixnum,[n],fixnum),fixnum)
(%i28) mode_declare(logitem_good_digits([file],fixnum,[relerror],convfloat),fixnum)
(%i29) mode_declare(logitem_number([file],fixnum,[x],number),fixnum)
(%i30) mode_declare(logitem_pole([file],fixnum,[pole],fixnum),fixnum)
(%i31) mode_declare(logstart([file],fixnum),fixnum)
(%i32) mode_declare(logend([file],fixnum),fixnum)
(%i33) mode_declare(chk_data(),fixnum)
(%i34) mode_declare(comp_expect_sec([t_end2],convfloat,[t_start2],convfloat,
[t2],convfloat,[clock_sec2],convfloat),
convfloat)
(%i35) mode_declare(comp_percent([t_end2],convfloat,[start2],convfloat,[t2],
convfloat),convfloat)
(%i36) mode_declare(comp_rad_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i37) mode_declare(comp_ord_from_ratio([term1],convfloat,[term2],convfloat,
[last_no],fixnum),convfloat)
(%i38) mode_declare(comp_rad_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i39) mode_declare(comp_ord_from_three_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[last_no],fixnum),convfloat)
(%i40) mode_declare(comp_rad_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i41) mode_declare(comp_ord_from_six_terms([term1],convfloat,[term2],
convfloat,[term3],convfloat,
[term4],convfloat,[term5],
convfloat,[term6],convfloat,
[last_no],fixnum),convfloat)
(%i42) mode_declare(neg([nnn],convfloat),convfloat)
(%i43) mode_declare(factorial_2([nnn],fixnum),convfloat)
(%i44) mode_declare(factorial_1([nnn],fixnum),convfloat)
(%i45) mode_declare(factorial_3([mmm],fixnum,[nnn],fixnum),convfloat)
(%i46) mode_declare(convfloat([mmm],fixnum),convfloat)
(%i47) mode_declare(elaped_time_seconds(),convfloat)
(%i48) mode_declare(Si([x],convfloat),convfloat)
(%i49) mode_declare(Ci([x],convfloat),convfloat)
(%i50) mode_declare(estimated_needed_step_error([x_start],convfloat,[x_end],
convfloat,[estimated_h],
convfloat,[estimated_answer],
convfloat),convfloat)
(%i51) mode_declare(my_check_sign([x0],convfloat,[xf],convfloat),convfloat)
(%i52) mode_declare(main_prog(),fixnum)
(%i53) define_variable(always,1,fixnum)
(%i54) define_variable(info,2,fixnum)
(%i55) define_variable(debugl,3,fixnum)
(%i56) define_variable(debugmassive,4,fixnum)
(%i57) define_variable(glob_iolevel,5,fixnum)
(%i58) define_variable(glob_yes_pole,4,fixnum)
(%i59) define_variable(glob_no_pole,3,fixnum)
(%i60) define_variable(glob_not_given,0,fixnum)
(%i61) define_variable(glob_no_sing_tests,4,fixnum)
(%i62) define_variable(glob_ratio_test,1,fixnum)
(%i63) define_variable(glob_three_term_test,2,fixnum)
(%i64) define_variable(glob_six_term_test,3,fixnum)
(%i65) define_variable(ats_max_terms,40,fixnum)
(%i66) define_variable(glob_log_10,0.0,convfloat)
(%i67) define_variable(max_unchanged,10,fixnum)
(%i68) define_variable(glob__small,1.0E-51,convfloat)
(%i69) define_variable(glob_small_float,1.0E-51,convfloat)
(%i70) define_variable(glob_smallish_float,1.0E-61,convfloat)
(%i71) define_variable(glob_large_float,1.0E+100,convfloat)
(%i72) define_variable(glob_larger_float,1.1E+100,convfloat)
(%i73) define_variable(glob__m2,-2.0,convfloat)
(%i74) define_variable(glob__m1,-1.0,convfloat)
(%i75) define_variable(glob__0,0.0,convfloat)
(%i76) define_variable(glob__1,1.0,convfloat)
(%i77) define_variable(glob__2,2.0,convfloat)
(%i78) define_variable(glob__3,3.0,convfloat)
(%i79) define_variable(glob__4,4.0,convfloat)
(%i80) define_variable(glob__5,5.0,convfloat)
(%i81) define_variable(glob__8,8.0,convfloat)
(%i82) define_variable(glob__10,10.0,convfloat)
(%i83) define_variable(glob__100,100.0,convfloat)
(%i84) define_variable(glob__pi,0.0,convfloat)
(%i85) define_variable(glob__0_5,0.5,convfloat)
(%i86) define_variable(glob__0_8,0.8,convfloat)
(%i87) define_variable(glob__m0_8,-0.8,convfloat)
(%i88) define_variable(glob__0_25,0.25,convfloat)
(%i89) define_variable(glob__0_125,0.125,convfloat)
(%i90) define_variable(glob_prec,1.0E-16,convfloat)
(%i91) define_variable(glob_check_sign,1.0,convfloat)
(%i92) define_variable(glob_desired_digits_correct,8.0,convfloat)
(%i93) define_variable(glob_max_estimated_step_error,0.0,convfloat)
(%i94) define_variable(glob_ratio_of_radius,0.1,convfloat)
(%i95) define_variable(glob_percent_done,0.0,convfloat)
(%i96) define_variable(glob_total_exp_sec,0.1,convfloat)
(%i97) define_variable(glob_optimal_expect_sec,0.1,convfloat)
(%i98) define_variable(glob_estimated_size_answer,100.0,convfloat)
(%i99) define_variable(glob_almost_1,0.999,convfloat)
(%i100) define_variable(glob_clock_sec,0.0,convfloat)
(%i101) define_variable(glob_clock_start_sec,0.0,convfloat)
(%i102) define_variable(glob_disp_incr,0.1,convfloat)
(%i103) define_variable(glob_h,0.1,convfloat)
(%i104) define_variable(glob_diff_rc_fm,0.1,convfloat)
(%i105) define_variable(glob_diff_rc_fmm1,0.1,convfloat)
(%i106) define_variable(glob_diff_rc_fmm2,0.1,convfloat)
(%i107) define_variable(glob_diff_ord_fm,0.1,convfloat)
(%i108) define_variable(glob_diff_ord_fmm1,0.1,convfloat)
(%i109) define_variable(glob_diff_ord_fmm2,0.1,convfloat)
(%i110) define_variable(glob_six_term_ord_save,0.1,convfloat)
(%i111) define_variable(glob_guess_error_rc,0.1,convfloat)
(%i112) define_variable(glob_guess_error_ord,0.1,convfloat)
(%i113) define_variable(glob_least_given_sing,9.9E+200,convfloat)
(%i114) define_variable(glob_least_ratio_sing,9.9E+200,convfloat)
(%i115) define_variable(glob_least_3_sing,9.9E+100,convfloat)
(%i116) define_variable(glob_least_6_sing,9.9E+100,convfloat)
(%i117) define_variable(glob_last_good_h,0.1,convfloat)
(%i118) define_variable(glob_max_h,0.1,convfloat)
(%i119) define_variable(glob_min_h,1.0E-6,convfloat)
(%i120) define_variable(glob_display_interval,0.1,convfloat)
(%i121) define_variable(glob_abserr,1.0E-11,convfloat)
(%i122) define_variable(glob_relerr,1.0E-11,convfloat)
(%i123) define_variable(glob_min_pole_est,1.0E+9,convfloat)
(%i124) define_variable(glob_max_rel_trunc_err,1.0E-11,convfloat)
(%i125) define_variable(glob_max_trunc_err,1.0E-11,convfloat)
(%i126) define_variable(glob_max_hours,0.0,convfloat)
(%i127) define_variable(glob_optimal_clock_start_sec,0.0,convfloat)
(%i128) define_variable(glob_optimal_start,0.0,convfloat)
(%i129) define_variable(glob_upper_ratio_limit,1.0001,convfloat)
(%i130) define_variable(glob_lower_ratio_limit,0.9999,convfloat)
(%i131) define_variable(glob_max_sec,10000.0,convfloat)
(%i132) define_variable(glob_orig_start_sec,0.0,convfloat)
(%i133) define_variable(glob_normmax,0.0,convfloat)
(%i134) define_variable(glob_max_minutes,0.0,convfloat)
(%i135) define_variable(glob_next_display,0.0,convfloat)
(%i136) define_variable(glob_est_digits,1,fixnum)
(%i137) define_variable(glob_subiter_method,3,fixnum)
(%i138) define_variable(glob_html_log,true,boolean)
(%i139) define_variable(glob_min_good_digits,99999,fixnum)
(%i140) define_variable(glob_good_digits,0,fixnum)
(%i141) define_variable(glob_min_apfp_est_good_digits,99999,fixnum)
(%i142) define_variable(glob_apfp_est_good_digits,0,fixnum)
(%i143) define_variable(glob_max_opt_iter,10,fixnum)
(%i144) define_variable(glob_dump,false,boolean)
(%i145) define_variable(glob_djd_debug,true,boolean)
(%i146) define_variable(glob_display_flag,true,boolean)
(%i147) define_variable(glob_djd_debug2,true,boolean)
(%i148) define_variable(glob_h_reason,0,fixnum)
(%i149) define_variable(glob_sec_in_minute,60,fixnum)
(%i150) define_variable(glob_min_in_hour,60,fixnum)
(%i151) define_variable(glob_hours_in_day,24,fixnum)
(%i152) define_variable(glob_days_in_year,365,fixnum)
(%i153) define_variable(glob_sec_in_hour,3600,fixnum)
(%i154) define_variable(glob_sec_in_day,86400,fixnum)
(%i155) define_variable(glob_sec_in_year,31536000,fixnum)
(%i156) define_variable(glob_not_yet_finished,true,boolean)
(%i157) define_variable(glob_initial_pass,true,boolean)
(%i158) define_variable(glob_not_yet_start_msg,true,boolean)
(%i159) define_variable(glob_reached_optimal_h,false,boolean)
(%i160) define_variable(glob_optimal_done,false,boolean)
(%i161) define_variable(glob_type_given_pole,0,fixnum)
(%i162) define_variable(glob_optimize,false,boolean)
(%i163) define_variable(glob_look_poles,false,boolean)
(%i164) define_variable(glob_dump_closed_form,false,boolean)
(%i165) define_variable(glob_max_iter,1000,fixnum)
(%i166) define_variable(glob_no_eqs,0,fixnum)
(%i167) define_variable(glob_unchanged_h_cnt,0,fixnum)
(%i168) define_variable(glob_warned,false,boolean)
(%i169) define_variable(glob_warned2,false,boolean)
(%i170) define_variable(glob_start,0,fixnum)
(%i171) define_variable(glob_iter,0,fixnum)
(%i172) completearray(array_y_init,[40],convfloat)
(%i173) completearray(array_norms,[40],convfloat)
(%i174) completearray(array_fact_1,[40],convfloat)
(%i175) completearray(array_1st_rel_error,[2],convfloat)
(%i176) completearray(array_last_rel_error,[2],convfloat)
(%i177) completearray(array_est_rel_error,[2],convfloat)
(%i178) completearray(array_max_est_error,[2],convfloat)
(%i179) completearray(array_type_pole,[2],convfloat)
(%i180) completearray(array_type_real_pole,[2],convfloat)
(%i181) completearray(array_type_complex_pole,[2],convfloat)
(%i182) completearray(array_est_digits,[2],convfloat)
(%i183) completearray(array_y,[40],convfloat)
(%i184) completearray(array_x,[40],convfloat)
(%i185) completearray(array_tmp0,[40],convfloat)
(%i186) completearray(array_tmp1,[40],convfloat)
(%i187) completearray(array_tmp2,[40],convfloat)
(%i188) completearray(array_tmp3,[40],convfloat)
(%i189) completearray(array_m1,[40],convfloat)
(%i190) completearray(array_y_higher,[4,40],convfloat)
(%i191) completearray(array_y_higher_work,[4,40],convfloat)
(%i192) completearray(array_y_higher_work2,[4,40],convfloat)
(%i193) completearray(array_y_set_initial,[2,40],convfloat)
(%i194) completearray(array_given_rad_poles,[2,3],convfloat)
(%i195) completearray(array_given_ord_poles,[2,3],convfloat)
(%i196) completearray(array_rad_test_poles,[2,4],convfloat)
(%i197) completearray(array_ord_test_poles,[2,4],convfloat)
(%i198) completearray(array_fact_2,[40,40],convfloat)
(%i199) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i200) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i201) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i202) 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))
(%i203) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i204) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i205) 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)
(%i206) 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)
(%i207) 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)
(%i208) 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)
(%i209) 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)
(%i210) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i211) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i212) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i213) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i214) log_revs(file,revs):=printf(file,revs)
(%i215) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i216) 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)
(%i217) logstart(file):=(printf(file,""),0)
(%i218) logend(file):=(printf(file,"
~%"),0)
(%i219) 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)
(%i220) 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)
(%i221) 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)
(%i222) 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)
(%i223) 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)
(%i224) c(in_val):=(ret:in_val,ret)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i229) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i230) 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)
(%i231) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i232) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i233) 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)
(%i234) log10(x):=log(x)/glob_log_10
(%i235) c(x):=x
(%i236) 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
(%i237) 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)
(%i238) exact_soln_y(x):=block(neg(cos(c(x))))
(%o238) exact_soln_y(x) := block(neg(cos(c(x))))
(%i239) exact_soln_yp(x):=block(sin(c(x)))
(%o239) exact_soln_yp(x) := block(sin(c(x)))
(%i240) exact_soln_ypp(x):=block(cos(c(x)))
(%o240) exact_soln_ypp(x) := block(cos(c(x)))
(%i241) 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)
(%i242) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i243) 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)
(%i244) 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)
(%i245) 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))
(%i246) 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))
(%i247) 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(24)
*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)
(%i248) 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)
(%i249) 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:-10-3+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:-10-3+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:-10-3+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)
(%i250) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_y_higher[2,1],
array_tmp2[1]:neg(array_tmp1[1]),
array_tmp3[1]:array_tmp2[1]+array_const_0D0[1],
if not array_y_set_initial[1,4]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp3[1])*expt(glob_h,c(3))
*c(factorial_3(0,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[3,2]:c(temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[4,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_y_higher[2,2],
array_tmp2[2]:neg(array_tmp1[2]),
array_tmp3[2]:array_tmp2[2],
if not array_y_set_initial[1,5]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp3[2])*expt(glob_h,c(3))
*c(factorial_3(1,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[3,3]:c(temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[4,2]:c(temporary),0)),
kkk:3,array_tmp1[3]:array_y_higher[2,3],
array_tmp2[3]:neg(array_tmp1[3]),
array_tmp3[3]:array_tmp2[3],
if not array_y_set_initial[1,6]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp3[3])*expt(glob_h,c(3))
*c(factorial_3(2,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[3,4]:c(temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[4,3]:c(temporary),0)),
kkk:4,array_tmp1[4]:array_y_higher[2,4],
array_tmp2[4]:neg(array_tmp1[4]),
array_tmp3[4]:array_tmp2[4],
if not array_y_set_initial[1,7]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp3[4])*expt(glob_h,c(3))
*c(factorial_3(3,6)),
if 7 <= ats_max_terms
then (array_y[7]:temporary,
array_y_higher[1,7]:temporary),
temporary:c(temporary)*c(6)/c(glob_h),
array_y_higher[2,6]:c(temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[3,5]:c(temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[4,4]:c(temporary),0)),
kkk:5,array_tmp1[5]:array_y_higher[2,5],
array_tmp2[5]:neg(array_tmp1[5]),
array_tmp3[5]:array_tmp2[5],
if not array_y_set_initial[1,8]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp3[5])*expt(glob_h,c(3))
*c(factorial_3(4,7)),
if 8 <= ats_max_terms
then (array_y[8]:temporary,
array_y_higher[1,8]:temporary),
temporary:c(temporary)*c(7)/c(glob_h),
array_y_higher[2,7]:c(temporary),
temporary:c(temporary)*c(6)/c(glob_h),
array_y_higher[3,6]:c(temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[4,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(if kkk <= ats_max_terms
then array_tmp1[kkk]:array_y_higher[2,kkk],
array_tmp2[kkk]:neg(array_tmp1[kkk]),
array_tmp3[kkk]:array_tmp2[kkk],order_d:3,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp3[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i251) exact_soln_y(x):=block(neg(cos(c(x))))
(%o251) exact_soln_y(x) := block(neg(cos(c(x))))
(%i252) exact_soln_yp(x):=block(sin(c(x)))
(%o252) exact_soln_yp(x) := block(sin(c(x)))
(%i253) exact_soln_ypp(x):=block(cos(c(x)))
(%o253) exact_soln_ypp(x) := block(cos(c(x)))
(%i254) main_prog():=block(
mode_declare([[d1,d2,d3,d4,est_err_2,display_max],convfloat,
[niii,done_once,term,ord,order_diff,term_no,
html_log_file,iiif,jjjf,rows,r_order,
sub_iter,calc_term,iii],fixnum,[temp_sum],
convfloat,[current_iter],fixnum,
[x_start,x_end],convfloat,[it,opt_iter],
fixnum,[tmp],convfloat,[subiter],fixnum,
[est_needed_step_err,estimated_step_error,
min_value,est_answer,last_min_pole_est],
convfloat,[repeat_it],fixnum],[found_h],
boolean),Digits:32,max_terms:40,
glob_html_log:true,term:1,
while term <= 40 do (array_y_init[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_norms[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_fact_1[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_1st_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_last_rel_error[term]:c(0.0),term:1+term),
term:1,
while term <= 2 do
(array_est_rel_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do
(array_max_est_error[term]:c(0.0),term:1+term),term:1,
while term <= 2 do (array_type_pole[term]:0,term:1+term),
term:1,
while term <= 2 do
(array_type_real_pole[term]:0,term:1+term),term:1,
while term <= 2 do
(array_type_complex_pole[term]:0,term:1+term),term:1,
while term <= 2 do (array_est_digits[term]:0,term:1+term),
term:1,
while term <= 40 do (array_y[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_x[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp0[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp1[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp2[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp3[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 4 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 4 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 4 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3),
zero_ats_ar(array_m1),zero_ats_ar(array_const_3),
array_const_3[1]:c(3),zero_ats_ar(array_const_0D0),
array_const_0D0[1]:c(0.0),zero_ats_ar(array_const_1),
array_const_1[1]:c(1),zero_ats_ar(array_m1),
array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:true,array_y_set_initial[1,3]:true,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/diff2postode.ode#################"),
omniout_str(always,
"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(-1.0),"),
omniout_str(always,"x_end:c(1.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,
"array_y_init[1 + 1] : exact_soln_yp(x_start),"),
omniout_str(always,
"array_y_init[2 + 1] : exact_soln_ypp(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),omniout_str(always,""),
omniout_str(always,""),
omniout_str(always,"glob_type_given_pole:3,"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (neg(cos(c(x)))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_yp (x) := (block("),
omniout_str(always," (sin(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"exact_soln_ypp (x) := (block("),
omniout_str(always," (cos(c(x))) "),
omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(-1.0),x_end:c(1.0),
array_y_init[1+0]:exact_soln_y(x_start),
array_y_init[1+1]:exact_soln_yp(x_start),
array_y_init[1+2]:exact_soln_ypp(x_start),
glob_look_poles:true,glob_type_given_pole:3,
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:3,
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:3,
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:4,ord:4,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[4,iii]
:array_y_higher[4,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:4,
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:3,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[3,iii]
:array_y_higher[3,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:3,
calc_term: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:3,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[3,iii]
:array_y_higher[3,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:3,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:2,
calc_term:3,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:3,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:2,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:4,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:4,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:3,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:3,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T20:33:05-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"diff2"),
logitem_str(html_log_file,
"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; "),
logitem_float(html_log_file,x_start),
logitem_float(html_log_file,x_end),
logitem_float(html_log_file,array_x[1]),
logitem_float(html_log_file,glob_h),
logitem_h_reason(html_log_file),
logitem_str(html_log_file,"16"),
logitem_float(html_log_file,
glob_desired_digits_correct),
if array_est_digits[1] # -16
then (
logitem_integer(html_log_file,
array_est_digits[
1]),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_min_good_digits # -16
then (
logitem_integer(html_log_file,
glob_min_good_digits),
0)
else (
logitem_str(html_log_file,
"Unknown"),0),
if glob_good_digits # -16
then (
logitem_integer(html_log_file,
glob_good_digits),0)
else (
logitem_str(html_log_file,
"Unknown"),0),
logitem_str(html_log_file,"NA"),
logitem_str(html_log_file,"NA"),
logitem_integer(html_log_file,
ats_max_terms),
if glob_type_given_pole = 0
then (
logitem_str(html_log_file,
"Not Given"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 4
then (
logitem_str(html_log_file,
"No Solution"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 5
then (
logitem_str(html_log_file,
"Some Pole"),
logitem_str(html_log_file,"????"),0)
elseif glob_type_given_pole = 3
then (
logitem_str(html_log_file,
"No Pole"),
logitem_str(html_log_file,"NA"),0)
elseif glob_type_given_pole = 1
then (
logitem_str(html_log_file,
"Real Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0) elseif glob_type_given_pole = 2
then (
logitem_str(html_log_file,
"Complex Sing"),
logitem_float(html_log_file,
glob_least_given_sing),
0),
if
glob_least_ratio_sing
< glob_large_float
then (
logitem_float(html_log_file,
glob_least_ratio_sing),
0)
else (
logitem_str(html_log_file,"NONE"),0),
if glob_least_3_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_3_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
if glob_least_6_sing < glob_large_float
then (
logitem_float(html_log_file,
glob_least_6_sing),0)
else (
logitem_str(html_log_file,"NONE"),
0),
logitem_integer(html_log_file,
glob_iter),
logitem_time(html_log_file,
glob_clock_sec),
if c(glob_percent_done) < glob__100
then (
logitem_time(html_log_file,
glob_total_exp_sec),0)
else (
logitem_str(html_log_file,"Done"),
0),
log_revs(html_log_file,
" 308.maple.seems.ok | "),
logitem_str(html_log_file,
"diff2 diffeq.max"),
logitem_str(html_log_file,
"diff2 maxima results"),
logitem_str(html_log_file,"OK"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i255) main():=(glob_iolevel:2,compile(all),main_prog())
(%i256) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_3 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/diff2postode.ode#################"
"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(-1.0),"
"x_end:c(1.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"array_y_init[1 + 1] : exact_soln_yp(x_start),"
"array_y_init[2 + 1] : exact_soln_ypp(x_start),"
"glob_look_poles:true,"
""
""
""
""
""
""
""
"glob_type_given_pole:3,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (neg(cos(c(x)))) "
"));"
"exact_soln_yp (x) := (block("
" (sin(c(x))) "
"));"
"exact_soln_ypp (x) := (block("
" (cos(c(x))) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -1. " "
y[1] (closed_form) = -0.5403023058681398 " "
y[1] (numeric) = -0.5403023058681398 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 15
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.99 " "
y[1] (closed_form) = -0.5486898605815875 " "
y[1] (numeric) = -0.5486898605815874 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 2.023407218512053600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.98 " "
y[1] (closed_form) = -0.5570225467662173 " "
y[1] (numeric) = -0.5570225467662171 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.986276789227053400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.97 " "
y[1] (closed_form) = -0.5652995311603544 " "
y[1] (numeric) = -0.5652995311603539 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.85582130129329800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.96 " "
y[1] (closed_form) = -0.5735199860724567 " "
y[1] (numeric) = -0.5735199860724564 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.80741587871130300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.95 " "
y[1] (closed_form) = -0.5816830894638836 " "
y[1] (numeric) = -0.5816830894638831 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.6345559617241700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.94 " "
y[1] (closed_form) = -0.5897880250310983 " "
y[1] (numeric) = -0.5897880250310978 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.52964100664211800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9299999999999999 " "
y[1] (closed_form) = -0.5978339822872983 " "
y[1] (numeric) = -0.597833982287298 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.571227418575990000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9199999999999999 " "
y[1] (closed_form) = -0.6058201566434629 " "
y[1] (numeric) = -0.6058201566434627 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.665190114427125400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9099999999999999 " "
y[1] (closed_form) = -0.6137457494888117 " "
y[1] (numeric) = -0.6137457494888114 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.61785975886549200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8999999999999999 " "
y[1] (closed_form) = -0.6216099682706645 " "
y[1] (numeric) = -0.6216099682706642 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.35813330526452100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8899999999999999 " "
y[1] (closed_form) = -0.629412026573697 " "
y[1] (numeric) = -0.6294120265736965 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 7.0556200247321600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799999999999999 " "
y[1] (closed_form) = -0.6371511441985803 " "
y[1] (numeric) = -0.63715114419858 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 5.227439523890116000000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8699999999999999 " "
y[1] (closed_form) = -0.6448265472400013 " "
y[1] (numeric) = -0.6448265472400011 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.443478031036885700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8599999999999999 " "
y[1] (closed_form) = -0.6524374681640519 " "
y[1] (numeric) = -0.6524374681640518 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.701654302211222700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8499999999999999 " "
y[1] (closed_form) = -0.6599831458849823 " "
y[1] (numeric) = -0.6599831458849822 " "
absolute error = 1.11022302462515650000000000000000E-16 " "
relative error = 1.682199055456848300000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8399999999999999 " "
y[1] (closed_form) = -0.6674628258413082 " "
y[1] (numeric) = -0.6674628258413082 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8299999999999998 " "
y[1] (closed_form) = -0.6748757600712673 " "
y[1] (numeric) = -0.6748757600712673 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8199999999999998 " "
y[1] (closed_form) = -0.6822212072876137 " "
y[1] (numeric) = -0.6822212072876137 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8099999999999998 " "
y[1] (closed_form) = -0.6894984329517472 " "
y[1] (numeric) = -0.6894984329517472 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7999999999999998 " "
y[1] (closed_form) = -0.6967067093471655 " "
y[1] (numeric) = -0.6967067093471657 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 3.18705994855559200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7899999999999998 " "
y[1] (closed_form) = -0.7038453156522362 " "
y[1] (numeric) = -0.7038453156522365 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.73210377309824200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7799999999999998 " "
y[1] (closed_form) = -0.7109135380122775 " "
y[1] (numeric) = -0.7109135380122779 " "
absolute error = 3.33066907387546960000000000000000E-16 " "
relative error = 4.68505506757974900000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7699999999999998 " "
y[1] (closed_form) = -0.7179106696109435 " "
y[1] (numeric) = -0.717910669610944 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 6.18585610506008200000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7599999999999998 " "
y[1] (closed_form) = -0.7248360107409053 " "
y[1] (numeric) = -0.7248360107409059 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 7.658442793772899000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7499999999999998 " "
y[1] (closed_form) = -0.731688868873821 " "
y[1] (numeric) = -0.7316888688738216 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 7.58671528196100800000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7399999999999998 " "
y[1] (closed_form) = -0.738468558729588 " "
y[1] (numeric) = -0.7384685587295887 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 9.02047632090208400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7299999999999998 " "
y[1] (closed_form) = -0.7451744023448705 " "
y[1] (numeric) = -0.7451744023448711 " "
absolute error = 5.5511151231257830000000000000000E-16 " "
relative error = 7.44941735204250700000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7199999999999998 " "
y[1] (closed_form) = -0.7518057291408952 " "
y[1] (numeric) = -0.7518057291408956 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 5.90696761991336600000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7099999999999997 " "
y[1] (closed_form) = -0.7583618759905083 " "
y[1] (numeric) = -0.758361875990509 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 8.78385156037869400000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6999999999999997 " "
y[1] (closed_form) = -0.7648421872844886 " "
y[1] (numeric) = -0.7648421872844893 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 8.70942824349359100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6899999999999997 " "
y[1] (closed_form) = -0.7712460149971068 " "
y[1] (numeric) = -0.7712460149971075 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 1.00766305708629820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6799999999999997 " "
y[1] (closed_form) = -0.7775727187509281 " "
y[1] (numeric) = -0.7775727187509289 " "
absolute error = 7.7715611723760960000000000000000E-16 " "
relative error = 9.99464228228084100000000000000E-14 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6699999999999997 " "
y[1] (closed_form) = -0.7838216658808494 " "
y[1] (numeric) = -0.7838216658808506 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.4164229861871722000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6599999999999997 " "
y[1] (closed_form) = -0.7899922314973653 " "
y[1] (numeric) = -0.7899922314973666 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.68643130455217780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6499999999999997 " "
y[1] (closed_form) = -0.796083798549056 " "
y[1] (numeric) = -0.7960837985490574 " "
absolute error = 1.4432899320127035000000000000000E-15 " "
relative error = 1.8129874450946581000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6399999999999997 " "
y[1] (closed_form) = -0.8020957578842928 " "
y[1] (numeric) = -0.8020957578842943 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.9378138073876190000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6299999999999997 " "
y[1] (closed_form) = -0.8080275083121521 " "
y[1] (numeric) = -0.8080275083121538 " "
absolute error = 1.6653345369377348000000000000000E-15 " "
relative error = 2.06098742902499470000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6199999999999997 " "
y[1] (closed_form) = -0.8138784566625341 " "
y[1] (numeric) = -0.813878456662536 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.3189938576361010000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.6099999999999997 " "
y[1] (closed_form) = -0.8196480178454797 " "
y[1] (numeric) = -0.8196480178454816 " "
absolute error = 1.887379141862766000000000000000E-15 " "
relative error = 2.30267029355346430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5999999999999996 " "
y[1] (closed_form) = -0.8253356149096785 " "
y[1] (numeric) = -0.8253356149096805 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 2.421319773706819800000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5899999999999996 " "
y[1] (closed_form) = -0.8309406791001637 " "
y[1] (numeric) = -0.8309406791001658 " "
absolute error = 2.1094237467877974000000000000000E-15 " "
relative error = 2.5385972787758077000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5799999999999996 " "
y[1] (closed_form) = -0.8364626499151872 " "
y[1] (numeric) = -0.8364626499151894 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 2.65456688290320430000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5699999999999996 " "
y[1] (closed_form) = -0.8419009751622689 " "
y[1] (numeric) = -0.8419009751622714 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.90116145037672140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5599999999999996 " "
y[1] (closed_form) = -0.8472551110134163 " "
y[1] (numeric) = -0.847255111013419 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 3.1449031401100420000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5499999999999996 " "
y[1] (closed_form) = -0.8525245220595059 " "
y[1] (numeric) = -0.8525245220595088 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 3.3859200402260390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5399999999999996 " "
y[1] (closed_form) = -0.8577086813638244 " "
y[1] (numeric) = -0.8577086813638273 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 3.36545487616555060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5299999999999996 " "
y[1] (closed_form) = -0.8628070705147612 " "
y[1] (numeric) = -0.8628070705147645 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.7315952562744680000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5199999999999996 " "
y[1] (closed_form) = -0.8678191796776501 " "
y[1] (numeric) = -0.8678191796776533 " "
absolute error = 3.219646771412954000000000000000E-15 " "
relative error = 3.71004334406262600000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.5099999999999996 " "
y[1] (closed_form) = -0.8727445076457515 " "
y[1] (numeric) = -0.8727445076457548 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 3.8163162812218970000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.49999999999999956 " "
y[1] (closed_form) = -0.877582561890373 " "
y[1] (numeric) = -0.8775825618903765 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 4.04829566251602800000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.48999999999999955 " "
y[1] (closed_form) = -0.8823328586101217 " "
y[1] (numeric) = -0.8823328586101253 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 4.152328620101769500000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.47999999999999954 " "
y[1] (closed_form) = -0.8869949227792844 " "
y[1] (numeric) = -0.886994922779288 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 4.1305038926076060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.46999999999999953 " "
y[1] (closed_form) = -0.8915682881953292 " "
y[1] (numeric) = -0.8915682881953328 " "
absolute error = 3.6637359812630166000000000000000E-15 " "
relative error = 4.10931616767009460000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4599999999999995 " "
y[1] (closed_form) = -0.8960524975255254 " "
y[1] (numeric) = -0.8960524975255293 " "
absolute error = 3.885780586188048000000000000000E-15 " "
relative error = 4.336554606921740000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4499999999999995 " "
y[1] (closed_form) = -0.9004471023526771 " "
y[1] (numeric) = -0.9004471023526811 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 4.4386870458106487000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4399999999999995 " "
y[1] (closed_form) = -0.9047516632199636 " "
y[1] (numeric) = -0.9047516632199678 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 4.6629894865967290000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4299999999999995 " "
y[1] (closed_form) = -0.9089657496748853 " "
y[1] (numeric) = -0.9089657496748897 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.8856539425044604000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4199999999999995 " "
y[1] (closed_form) = -0.9130889403123085 " "
y[1] (numeric) = -0.9130889403123129 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 4.8635920362606580000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.4099999999999995 " "
y[1] (closed_form) = -0.9171208228166053 " "
y[1] (numeric) = -0.91712082281661 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 5.0843210484580780000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.39999999999999947 " "
y[1] (closed_form) = -0.9210609940028853 " "
y[1] (numeric) = -0.9210609940028901 " "
absolute error = 4.773959005888173000000000000000E-15 " "
relative error = 5.1831084336128320000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.38999999999999946 " "
y[1] (closed_form) = -0.9249090598573132 " "
y[1] (numeric) = -0.9249090598573183 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 5.5216519492884920000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.37999999999999945 " "
y[1] (closed_form) = -0.9286646355765105 " "
y[1] (numeric) = -0.9286646355765157 " "
absolute error = 5.218048215738236000000000000000E-15 " "
relative error = 5.6188725357231860000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.36999999999999944 " "
y[1] (closed_form) = -0.9323273456060346 " "
y[1] (numeric) = -0.93232734560604 " "
absolute error = 5.440092820663267000000000000000E-15 " "
relative error = 5.834960055930870000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.35999999999999943 " "
y[1] (closed_form) = -0.935896823677935 " "
y[1] (numeric) = -0.9358968236779407 " "
absolute error = 5.662137425588298000000000000000E-15 " "
relative error = 6.0499590150727760000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3499999999999994 " "
y[1] (closed_form) = -0.9393727128473791 " "
y[1] (numeric) = -0.9393727128473849 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 6.1457605156014220000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3399999999999994 " "
y[1] (closed_form) = -0.9427546655283464 " "
y[1] (numeric) = -0.9427546655283524 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 6.3592412238193090000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3299999999999994 " "
y[1] (closed_form) = -0.9460423435283871 " "
y[1] (numeric) = -0.9460423435283932 " "
absolute error = 6.106226635438361000000000000000E-15 " "
relative error = 6.4544961197660560000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3199999999999994 " "
y[1] (closed_form) = -0.949235418082441 " "
y[1] (numeric) = -0.9492354180824473 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 6.5497439512533120000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.3099999999999994 " "
y[1] (closed_form) = -0.9523335698857136 " "
y[1] (numeric) = -0.95233356988572 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 6.761594620253350000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2999999999999994 " "
y[1] (closed_form) = -0.9553364891256062 " "
y[1] (numeric) = -0.9553364891256129 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.9727663745450390000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.28999999999999937 " "
y[1] (closed_form) = -0.9582438755126973 " "
y[1] (numeric) = -0.9582438755127041 " "
absolute error = 6.772360450213455000000000000000E-15 " "
relative error = 7.0674706338091450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.27999999999999936 " "
y[1] (closed_form) = -0.9610554383107711 " "
y[1] (numeric) = -0.9610554383107778 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 6.9312735584322250000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.26999999999999935 " "
y[1] (closed_form) = -0.9637708963658906 " "
y[1] (numeric) = -0.9637708963658975 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 7.1421359356578150000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.25999999999999934 " "
y[1] (closed_form) = -0.9663899781345134 " "
y[1] (numeric) = -0.9663899781345204 " "
absolute error = 6.994405055138486000000000000000E-15 " "
relative error = 7.2376630691475610000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.24999999999999933 " "
y[1] (closed_form) = -0.968912421710645 " "
y[1] (numeric) = -0.9689124217106523 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 7.5625740761885930000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.23999999999999932 " "
y[1] (closed_form) = -0.9713379748520298 " "
y[1] (numeric) = -0.9713379748520374 " "
absolute error = 7.66053886991358000000000000000E-15 " "
relative error = 7.8865843488519640000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.22999999999999932 " "
y[1] (closed_form) = -0.973666395005375 " "
y[1] (numeric) = -0.9736663950053829 " "
absolute error = 7.882583474838611000000000000000E-15 " "
relative error = 8.0957744000141820000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2199999999999993 " "
y[1] (closed_form) = -0.9758974493306056 " "
y[1] (numeric) = -0.9758974493306136 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 8.191030505084480000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.2099999999999993 " "
y[1] (closed_form) = -0.9780309147241484 " "
y[1] (numeric) = -0.9780309147241565 " "
absolute error = 8.104628079763643000000000000000E-15 " "
relative error = 8.2866788337151240000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.1999999999999993 " "
y[1] (closed_form) = -0.9800665778412417 " "
y[1] (numeric) = -0.98006657784125 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 8.3827472214413060000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.18999999999999928 " "
y[1] (closed_form) = -0.9820042351172704 " "
y[1] (numeric) = -0.9820042351172789 " "
absolute error = 8.43769498715119000000000000000E-15 " "
relative error = 8.5923203642228340000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.17999999999999927 " "
y[1] (closed_form) = -0.9838436927881216 " "
y[1] (numeric) = -0.9838436927881301 " "
absolute error = 8.548717289613705000000000000000E-15 " "
relative error = 8.6891010759925050000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.16999999999999926 " "
y[1] (closed_form) = -0.9855847669095609 " "
y[1] (numeric) = -0.9855847669095698 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 9.0116898060948450000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.15999999999999925 " "
y[1] (closed_form) = -0.987227283375627 " "
y[1] (numeric) = -0.9872272833756361 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 9.2216138626128260000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.14999999999999925 " "
y[1] (closed_form) = -0.9887710779360424 " "
y[1] (numeric) = -0.9887710779360516 " "
absolute error = 9.2148511043887990000000000000E-15 " "
relative error = 9.3194990327021410000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.13999999999999924 " "
y[1] (closed_form) = -0.9902159962126372 " "
y[1] (numeric) = -0.9902159962126467 " "
absolute error = 9.43689570931383100000000000000E-15 " "
relative error = 9.5301386216824650000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.12999999999999923 " "
y[1] (closed_form) = -0.9915618937147881 " "
y[1] (numeric) = -0.9915618937147976 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 9.6291699714336750000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.11999999999999922 " "
y[1] (closed_form) = -0.9928086358538664 " "
y[1] (numeric) = -0.992808635853876 " "
absolute error = 9.658940314238862000000000000000E-15 " "
relative error = 9.7289044085839140000000000000E-13 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.10999999999999921 " "
y[1] (closed_form) = -0.9939560979566969 " "
y[1] (numeric) = -0.993956097956707 " "
absolute error = 1.010302952408892500000000000000E-14 " "
relative error = 1.0164462540003531000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -9.9999999999999200E-2 " "
y[1] (closed_form) = -0.9950041652780258 " "
y[1] (numeric) = -0.995004165278036 " "
absolute error = 1.02140518265514400000000000000E-14 " "
relative error = 1.0265335747310575000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -8.99999999999991900E-2 " "
y[1] (closed_form) = -0.9959527330119943 " "
y[1] (numeric) = -0.9959527330120048 " "
absolute error = 1.054711873393898700000000000000E-14 " "
relative error = 1.0589979207187905000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -7.99999999999991800E-2 " "
y[1] (closed_form) = -0.9968017063026194 " "
y[1] (numeric) = -0.9968017063026303 " "
absolute error = 1.088018564132653400000000000000E-14 " "
relative error = 1.0915095321900878000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -6.99999999999991700E-2 " "
y[1] (closed_form) = -0.9975510002532796 " "
y[1] (numeric) = -0.9975510002532906 " "
absolute error = 1.09912079437890500000000000000E-14 " "
relative error = 1.1018191491962183000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -5.999999999999917000E-2 " "
y[1] (closed_form) = -0.9982005399352042 " "
y[1] (numeric) = -0.9982005399352154 " "
absolute error = 1.121325254871408100000000000000E-14 " "
relative error = 1.1233466723472182000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -4.999999999999915600E-2 " "
y[1] (closed_form) = -0.9987502603949663 " "
y[1] (numeric) = -0.9987502603949777 " "
absolute error = 1.143529715363911200000000000000E-14 " "
relative error = 1.1449606179944227000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -3.99999999999991500E-2 " "
y[1] (closed_form) = -0.999200106660978 " "
y[1] (numeric) = -0.9992001066609897 " "
absolute error = 1.165734175856414400000000000000E-14 " "
relative error = 1.1666673853267914000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -2.99999999999991400E-2 " "
y[1] (closed_form) = -0.9995500337489875 " "
y[1] (numeric) = -0.9995500337489995 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 1.199580637397366000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -1.99999999999991300E-2 " "
y[1] (closed_form) = -0.9998000066665778 " "
y[1] (numeric) = -0.9998000066665899 " "
absolute error = 1.210143096841420600000000000000E-14 " "
relative error = 1.2103851658054549000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -9.99999999999912100E-3 " "
y[1] (closed_form) = -0.9999500004166653 " "
y[1] (numeric) = -0.9999500004166777 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 1.24351196266018000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.812395257962180000000000000000E-16 " "
y[1] (closed_form) = -1. " "
y[1] (numeric) = -1.0000000000000127 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 1.2656542480726785000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.000000000000088300E-2 " "
y[1] (closed_form) = -0.9999500004166653 " "
y[1] (numeric) = -0.9999500004166781 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 1.2879231041837577000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.000000000000089200E-2 " "
y[1] (closed_form) = -0.9998000066665778 " "
y[1] (numeric) = -0.999800006666591 " "
absolute error = 1.321165399303936300000000000000E-14 " "
relative error = 1.3214296764298086000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 3.0000000000000904E-2 " "
y[1] (closed_form) = -0.9995500337489875 " "
y[1] (numeric) = -0.9995500337490009 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.3328673748859624000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 4.00000000000009100E-2 " "
y[1] (closed_form) = -0.9992001066609779 " "
y[1] (numeric) = -0.9992001066609917 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.3777786264811630000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 5.00000000000009200E-2 " "
y[1] (closed_form) = -0.9987502603949662 " "
y[1] (numeric) = -0.9987502603949805 " "
absolute error = 1.43218770176645200000000000000E-14 " "
relative error = 1.4339798031192288000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 6.00000000000009300E-2 " "
y[1] (closed_form) = -0.9982005399352041 " "
y[1] (numeric) = -0.9982005399352187 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.4681362450478494000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 7.00000000000009400E-2 " "
y[1] (closed_form) = -0.9975510002532795 " "
y[1] (numeric) = -0.9975510002532945 " "
absolute error = 1.498801083243961300000000000000E-14 " "
relative error = 1.502480657994843000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 8.00000000000009500E-2 " "
y[1] (closed_form) = -0.9968017063026193 " "
y[1] (numeric) = -0.9968017063026345 " "
absolute error = 1.521005543736464500000000000000E-14 " "
relative error = 1.5258857745922658000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 9.00000000000009600E-2 " "
y[1] (closed_form) = -0.9959527330119942 " "
y[1] (numeric) = -0.9959527330120097 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.5606285147434812000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.10000000000000096 " "
y[1] (closed_form) = -0.9950041652780257 " "
y[1] (numeric) = -0.9950041652780415 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.584432256650111200000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000097 " "
y[1] (closed_form) = -0.9939560979566967 " "
y[1] (numeric) = -0.9939560979567128 " "
absolute error = 1.60982338570647700000000000000E-14 " "
relative error = 1.6196121629675958000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000098 " "
y[1] (closed_form) = -0.9928086358538661 " "
y[1] (numeric) = -0.9928086358538827 " "
absolute error = 1.654232306691483200000000000000E-14 " "
relative error = 1.6662146630793145000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000098 " "
y[1] (closed_form) = -0.9915618937147879 " "
y[1] (numeric) = -0.9915618937148047 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.7018998089045567000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000098 " "
y[1] (closed_form) = -0.990215996212637 " "
y[1] (numeric) = -0.9902159962126542 " "
absolute error = 1.720845688168992600000000000000E-14 " "
relative error = 1.7378488074832732000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.150000000000001 " "
y[1] (closed_form) = -0.9887710779360421 " "
y[1] (numeric) = -0.9887710779360598 " "
absolute error = 1.76525460915399900000000000000E-14 " "
relative error = 1.785301621927278000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.160000000000001 " "
y[1] (closed_form) = -0.9872272833756268 " "
y[1] (numeric) = -0.9872272833756448 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.8218310313942418000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.170000000000001 " "
y[1] (closed_form) = -0.9855847669095605 " "
y[1] (numeric) = -0.9855847669095789 " "
absolute error = 1.831867990631508300000000000000E-14 " "
relative error = 1.858661022507062000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000102 " "
y[1] (closed_form) = -0.9838436927881212 " "
y[1] (numeric) = -0.98384369278814 " "
absolute error = 1.876276911616514600000000000000E-14 " "
relative error = 1.907088417977576000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000103 " "
y[1] (closed_form) = -0.9820042351172701 " "
y[1] (numeric) = -0.9820042351172893 " "
absolute error = 1.920685832601520800000000000000E-14 " "
relative error = 1.9558834513296716000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.20000000000000104 " "
y[1] (closed_form) = -0.9800665778412414 " "
y[1] (numeric) = -0.9800665778412609 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.993734474288744000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.21000000000000105 " "
y[1] (closed_form) = -0.978030914724148 " "
y[1] (numeric) = -0.9780309147241679 " "
absolute error = 1.987299214079030200000000000000E-14 " "
relative error = 2.0319390564863124000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.22000000000000106 " "
y[1] (closed_form) = -0.9758974493306053 " "
y[1] (numeric) = -0.9758974493306254 " "
absolute error = 2.009503674571533300000000000000E-14 " "
relative error = 2.0591340575281827000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000106 " "
y[1] (closed_form) = -0.9736663950053746 " "
y[1] (numeric) = -0.9736663950053952 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 2.1208648428206175000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000107 " "
y[1] (closed_form) = -0.9713379748520293 " "
y[1] (numeric) = -0.9713379748520504 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 2.1716681540317012000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.25000000000000105 " "
y[1] (closed_form) = -0.9689124217106445 " "
y[1] (numeric) = -0.968912421710666 " "
absolute error = 2.153832667772803700000000000000E-14 " "
relative error = 2.222938440576647800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.26000000000000106 " "
y[1] (closed_form) = -0.966389978134513 " "
y[1] (numeric) = -0.9663899781345348 " "
absolute error = 2.176037128265306800000000000000E-14 " "
relative error = 2.251717399290353000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2700000000000011 " "
y[1] (closed_form) = -0.9637708963658902 " "
y[1] (numeric) = -0.9637708963659123 " "
absolute error = 2.209343819004061500000000000000E-14 " "
relative error = 2.292395243864363800000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2800000000000011 " "
y[1] (closed_form) = -0.9610554383107707 " "
y[1] (numeric) = -0.961055438310793 " "
absolute error = 2.231548279496564600000000000000E-14 " "
relative error = 2.321976642074796100000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2900000000000011 " "
y[1] (closed_form) = -0.9582438755126969 " "
y[1] (numeric) = -0.9582438755127196 " "
absolute error = 2.27595720048157100000000000000E-14 " "
relative error = 2.375133573657173000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3000000000000011 " "
y[1] (closed_form) = -0.9553364891256056 " "
y[1] (numeric) = -0.9553364891256286 " "
absolute error = 2.29816166097407400000000000000E-14 " "
relative error = 2.40560439921804000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3100000000000011 " "
y[1] (closed_form) = -0.952333569885713 " "
y[1] (numeric) = -0.9523335698857365 " "
absolute error = 2.342570581959080300000000000000E-14 " "
relative error = 2.4598214911611332000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000011 " "
y[1] (closed_form) = -0.9492354180824405 " "
y[1] (numeric) = -0.9492354180824645 " "
absolute error = 2.39808173319033800000000000000E-14 " "
relative error = 2.526329809769136000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000011 " "
y[1] (closed_form) = -0.9460423435283866 " "
y[1] (numeric) = -0.946042343528411 " "
absolute error = 2.442490654175344400000000000000E-14 " "
relative error = 2.5817984479064240000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.34000000000000113 " "
y[1] (closed_form) = -0.9427546655283459 " "
y[1] (numeric) = -0.9427546655283705 " "
absolute error = 2.464695114667847500000000000000E-14 " "
relative error = 2.61435472534794000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.35000000000000114 " "
y[1] (closed_form) = -0.9393727128473786 " "
y[1] (numeric) = -0.9393727128474035 " "
absolute error = 2.498001805406602200000000000000E-14 " "
relative error = 2.6592233000198473000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.36000000000000115 " "
y[1] (closed_form) = -0.9358968236779345 " "
y[1] (numeric) = -0.9358968236779597 " "
absolute error = 2.520206265899105300000000000000E-14 " "
relative error = 2.692824894944158000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.37000000000000116 " "
y[1] (closed_form) = -0.932327345606034 " "
y[1] (numeric) = -0.9323273456060596 " "
absolute error = 2.5535129566378600000000000000E-14 " "
relative error = 2.738858801763471300000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.38000000000000117 " "
y[1] (closed_form) = -0.9286646355765098 " "
y[1] (numeric) = -0.9286646355765359 " "
absolute error = 2.60902410786911800000000000000E-14 " "
relative error = 2.809436267861595000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3900000000000012 " "
y[1] (closed_form) = -0.9249090598573126 " "
y[1] (numeric) = -0.9249090598573392 " "
absolute error = 2.65343302885412400000000000000E-14 " "
relative error = 2.8688582953911970000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4000000000000012 " "
y[1] (closed_form) = -0.9210609940028847 " "
y[1] (numeric) = -0.9210609940029116 " "
absolute error = 2.697841949839130400000000000000E-14 " "
relative error = 2.9290589520184160000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4100000000000012 " "
y[1] (closed_form) = -0.9171208228166047 " "
y[1] (numeric) = -0.9171208228166321 " "
absolute error = 2.742250870824136700000000000000E-14 " "
relative error = 2.9900649975455856000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4200000000000012 " "
y[1] (closed_form) = -0.9130889403123078 " "
y[1] (numeric) = -0.9130889403123357 " "
absolute error = 2.78665979180914300000000000000E-14 " "
relative error = 3.051904002753565000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4300000000000012 " "
y[1] (closed_form) = -0.9089657496748846 " "
y[1] (numeric) = -0.908965749674913 " "
absolute error = 2.831068712794149000000000000000E-14 " "
relative error = 3.114604388346596000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000012 " "
y[1] (closed_form) = -0.9047516632199629 " "
y[1] (numeric) = -0.9047516632199918 " "
absolute error = 2.88657986402540700000000000000E-14 " "
relative error = 3.1904664908293434000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.45000000000000123 " "
y[1] (closed_form) = -0.9004471023526763 " "
y[1] (numeric) = -0.9004471023527059 " "
absolute error = 2.953193245502916400000000000000E-14 " "
relative error = 3.2796965394045385000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.46000000000000124 " "
y[1] (closed_form) = -0.8960524975255247 " "
y[1] (numeric) = -0.8960524975255546 " "
absolute error = 2.98649993624167100000000000000E-14 " "
relative error = 3.332951969319854000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.47000000000000125 " "
y[1] (closed_form) = -0.8915682881953284 " "
y[1] (numeric) = -0.8915682881953587 " "
absolute error = 3.030908857226677400000000000000E-14 " "
relative error = 3.399525193254354000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.48000000000000126 " "
y[1] (closed_form) = -0.8869949227792836 " "
y[1] (numeric) = -0.8869949227793146 " "
absolute error = 3.09752223870418700000000000000E-14 " "
relative error = 3.4921532910227965000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.49000000000000127 " "
y[1] (closed_form) = -0.8823328586101209 " "
y[1] (numeric) = -0.8823328586101523 " "
absolute error = 3.14193115968919300000000000000E-14 " "
relative error = 3.5609363620872786000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000012 " "
y[1] (closed_form) = -0.8775825618903721 " "
y[1] (numeric) = -0.877582561890404 " "
absolute error = 3.18634008067419900000000000000E-14 " "
relative error = 3.6308151723190670000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000012 " "
y[1] (closed_form) = -0.8727445076457506 " "
y[1] (numeric) = -0.8727445076457832 " "
absolute error = 3.252953462151708700000000000000E-14 " "
relative error = 3.727268901326723500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000012 " "
y[1] (closed_form) = -0.8678191796776493 " "
y[1] (numeric) = -0.8678191796776823 " "
absolute error = 3.29736238313671500000000000000E-14 " "
relative error = 3.799596114436556000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000012 " "
y[1] (closed_form) = -0.8628070705147604 " "
y[1] (numeric) = -0.8628070705147938 " "
absolute error = 3.34177130412172100000000000000E-14 " "
relative error = 3.8731385246159183000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000013 " "
y[1] (closed_form) = -0.8577086813638235 " "
y[1] (numeric) = -0.8577086813638576 " "
absolute error = 3.408384685599230600000000000000E-14 " "
relative error = 3.973825565318558000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000013 " "
y[1] (closed_form) = -0.8525245220595051 " "
y[1] (numeric) = -0.8525245220595398 " "
absolute error = 3.463895836830488400000000000000E-14 " "
relative error = 4.06310404827125000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000013 " "
y[1] (closed_form) = -0.8472551110134154 " "
y[1] (numeric) = -0.8472551110134509 " "
absolute error = 3.541611448554249400000000000000E-14 " "
relative error = 4.180100423729602400000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000013 " "
y[1] (closed_form) = -0.841900975162268 " "
y[1] (numeric) = -0.841900975162304 " "
absolute error = 3.59712259978550700000000000000E-14 " "
relative error = 4.272619590554813000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000013 " "
y[1] (closed_form) = -0.8364626499151863 " "
y[1] (numeric) = -0.8364626499152228 " "
absolute error = 3.65263375101676500000000000000E-14 " "
relative error = 4.3667625223757767000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000013 " "
y[1] (closed_form) = -0.8309406791001628 " "
y[1] (numeric) = -0.8309406791001998 " "
absolute error = 3.69704267200177130000000000000E-14 " "
relative error = 4.4492257570123420000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000013 " "
y[1] (closed_form) = -0.8253356149096776 " "
y[1] (numeric) = -0.8253356149097151 " "
absolute error = 3.75255382323302900000000000000E-14 " "
relative error = 4.5467004639605896000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000013 " "
y[1] (closed_form) = -0.8196480178454788 " "
y[1] (numeric) = -0.8196480178455171 " "
absolute error = 3.8302694349567900000000000000E-14 " "
relative error = 4.673066183976154000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000013 " "
y[1] (closed_form) = -0.8138784566625331 " "
y[1] (numeric) = -0.8138784566625721 " "
absolute error = 3.896882816434299500000000000000E-14 " "
relative error = 4.788040259001602500000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000013 " "
y[1] (closed_form) = -0.8080275083121511 " "
y[1] (numeric) = -0.8080275083121906 " "
absolute error = 3.95239396766555730000000000000E-14 " "
relative error = 4.8914101648859926000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000013 " "
y[1] (closed_form) = -0.8020957578842918 " "
y[1] (numeric) = -0.802095757884332 " "
absolute error = 4.019007349143066700000000000000E-14 " "
relative error = 5.010632844816564000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000014 " "
y[1] (closed_form) = -0.796083798549055 " "
y[1] (numeric) = -0.796083798549096 " "
absolute error = 4.096722960866827600000000000000E-14 " "
relative error = 5.146095132614843000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000014 " "
y[1] (closed_form) = -0.7899922314973643 " "
y[1] (numeric) = -0.7899922314974056 " "
absolute error = 4.130029651605582300000000000000E-14 " "
relative error = 5.2279370441117580000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000014 " "
y[1] (closed_form) = -0.7838216658808485 " "
y[1] (numeric) = -0.7838216658808904 " "
absolute error = 4.19664303308309200000000000000E-14 " "
relative error = 5.354078887787517000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000014 " "
y[1] (closed_form) = -0.777572718750927 " "
y[1] (numeric) = -0.7775727187509699 " "
absolute error = 4.28546087505310400000000000000E-14 " "
relative error = 5.51133131565773000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000014 " "
y[1] (closed_form) = -0.7712460149971058 " "
y[1] (numeric) = -0.7712460149971493 " "
absolute error = 4.352074256530613600000000000000E-14 " "
relative error = 5.642913119683277000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000014 " "
y[1] (closed_form) = -0.7648421872844875 " "
y[1] (numeric) = -0.7648421872845317 " "
absolute error = 4.41868763800812300000000000000E-14 " "
relative error = 5.77725406818409000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000014 " "
y[1] (closed_form) = -0.7583618759905072 " "
y[1] (numeric) = -0.758361875990552 " "
absolute error = 4.485301019485632400000000000000E-14 " "
relative error = 5.914460050654995000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000014 " "
y[1] (closed_form) = -0.751805729140894 " "
y[1] (numeric) = -0.7518057291409395 " "
absolute error = 4.5408121707168900000000000000E-14 " "
relative error = 6.039874391361425000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000014 " "
y[1] (closed_form) = -0.7451744023448694 " "
y[1] (numeric) = -0.7451744023449155 " "
absolute error = 4.607425552194399600000000000000E-14 " "
relative error = 6.183016402195289000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000014 " "
y[1] (closed_form) = -0.7384685587295869 " "
y[1] (numeric) = -0.7384685587296336 " "
absolute error = 4.662936703425657500000000000000E-14 " "
relative error = 6.3143334246314690000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000014 " "
y[1] (closed_form) = -0.7316888688738199 " "
y[1] (numeric) = -0.7316888688738672 " "
absolute error = 4.72955008490316700000000000000E-14 " "
relative error = 6.46388142023079000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000015 " "
y[1] (closed_form) = -0.7248360107409042 " "
y[1] (numeric) = -0.7248360107409522 " "
absolute error = 4.79616346638067600000000000000E-14 " "
relative error = 6.616894573819795000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000015 " "
y[1] (closed_form) = -0.7179106696109423 " "
y[1] (numeric) = -0.7179106696109913 " "
absolute error = 4.896083538596940300000000000000E-14 " "
relative error = 6.819906355828751000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000015 " "
y[1] (closed_form) = -0.7109135380122763 " "
y[1] (numeric) = -0.7109135380123259 " "
absolute error = 4.9626969200744500000000000000E-14 " "
relative error = 6.980732050693839000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000015 " "
y[1] (closed_form) = -0.7038453156522351 " "
y[1] (numeric) = -0.7038453156522855 " "
absolute error = 5.04041253179821100000000000000E-14 " "
relative error = 7.161250376622017000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000015 " "
y[1] (closed_form) = -0.6967067093471644 " "
y[1] (numeric) = -0.6967067093472156 " "
absolute error = 5.118128143521972000000000000000E-14 " "
relative error = 7.346173181420651000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000015 " "
y[1] (closed_form) = -0.689498432951746 " "
y[1] (numeric) = -0.6894984329517979 " "
absolute error = 5.195843755245733000000000000000E-14 " "
relative error = 7.53568609721461000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000015 " "
y[1] (closed_form) = -0.6822212072876125 " "
y[1] (numeric) = -0.6822212072876652 " "
absolute error = 5.273559366969494000000000000000E-14 " "
relative error = 7.729984513287423000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000015 " "
y[1] (closed_form) = -0.674875760071266 " "
y[1] (numeric) = -0.6748757600713196 " "
absolute error = 5.351274978693255000000000000000E-14 " "
relative error = 7.929274238754948000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000015 " "
y[1] (closed_form) = -0.667462825841307 " "
y[1] (numeric) = -0.6674628258413612 " "
absolute error = 5.41788836017076400000000000000E-14 " "
relative error = 8.117138738538373000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000015 " "
y[1] (closed_form) = -0.659983145884981 " "
y[1] (numeric) = -0.6599831458850359 " "
absolute error = 5.49560397189452500000000000000E-14 " "
relative error = 8.326885324511417000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000015 " "
y[1] (closed_form) = -0.6524374681640507 " "
y[1] (numeric) = -0.6524374681641062 " "
absolute error = 5.55111512312578300000000000000E-14 " "
relative error = 8.508271511056129000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000015 " "
y[1] (closed_form) = -0.64482654724 " "
y[1] (numeric) = -0.6448265472400564 " "
absolute error = 5.63993296509579500000000000000E-14 " "
relative error = 8.746434198833708000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000016 " "
y[1] (closed_form) = -0.637151144198579 " "
y[1] (numeric) = -0.6371511441986363 " "
absolute error = 5.72875080706580800000000000000E-14 " "
relative error = 8.991195981091018000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000016 " "
y[1] (closed_form) = -0.6294120265736957 " "
y[1] (numeric) = -0.6294120265737538 " "
absolute error = 5.8175686490358200000000000000E-14 " "
relative error = 9.242862232399147000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000016 " "
y[1] (closed_form) = -0.6216099682706632 " "
y[1] (numeric) = -0.6216099682707222 " "
absolute error = 5.90638649100583300000000000000E-14 " "
relative error = 9.501756394669104000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000016 " "
y[1] (closed_form) = -0.6137457494888103 " "
y[1] (numeric) = -0.6137457494888702 " "
absolute error = 5.98410210272959400000000000000E-14 " "
relative error = 9.750132050142523000000000000E-12 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 15
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000016 " "
y[1] (closed_form) = -0.6058201566434616 " "
y[1] (numeric) = -0.6058201566435224 " "
absolute error = 6.08402217494585800000000000000E-14 " "
relative error = 1.004262091353034800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000016 " "
y[1] (closed_form) = -0.597833982287297 " "
y[1] (numeric) = -0.5978339822873586 " "
absolute error = 6.16173778666961900000000000000E-14 " "
relative error = 1.030677072436560600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000016 " "
y[1] (closed_form) = -0.589788025031097 " "
y[1] (numeric) = -0.5897880250311592 " "
absolute error = 6.22835116814712800000000000000E-14 " "
relative error = 1.056032151181559700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000016 " "
y[1] (closed_form) = -0.5816830894638821 " "
y[1] (numeric) = -0.5816830894639452 " "
absolute error = 6.30606677987088900000000000000E-14 " "
relative error = 1.084106946564834800000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000016 " "
y[1] (closed_form) = -0.5735199860724554 " "
y[1] (numeric) = -0.5735199860725192 " "
absolute error = 6.3837823915946500000000000000E-14 " "
relative error = 1.113088043419668700000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000016 " "
y[1] (closed_form) = -0.5652995311603529 " "
y[1] (numeric) = -0.5652995311604178 " "
absolute error = 6.48370246381091400000000000000E-14 " "
relative error = 1.146949909988824500000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000016 " "
y[1] (closed_form) = -0.557022546766216 " "
y[1] (numeric) = -0.5570225467662815 " "
absolute error = 6.55031584528842400000000000000E-14 " "
relative error = 1.175951652821983600000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000017 " "
y[1] (closed_form) = -0.5486898605815862 " "
y[1] (numeric) = -0.5486898605816527 " "
absolute error = 6.65023591750468800000000000000E-14 " "
relative error = 1.212020923888723000000000000E-11 "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = 14
h = 1.000E-3 " "
"Finished!"
"diff ( y , x , 3 ) = neg ( diff ( y , x , 1 ) ) ; "
Iterations = 2000
"Total Elapsed Time "= 1 Minutes 22 Seconds
"Elapsed Time(since restart) "= 1 Minutes 22 Seconds
"Time to Timeout "= 1 Minutes 37 Seconds
Percent Done = 100.05000000000007 "%"
(%o256) temp/diffeq.diff2.max