(%i1) batch("temp/diffeq.tan_sqrt_lin.max")
read and interpret file: /home/dennis/src/mine/omni/testtar/omnisode0060dir/temp/diffeq.tan_sqrt_lin.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_tmp4_g,[40],convfloat)
(%i190) completearray(array_tmp4_a1,[40],convfloat)
(%i191) completearray(array_tmp4_a2,[40],convfloat)
(%i192) completearray(array_tmp4,[40],convfloat)
(%i193) completearray(array_tmp5,[40],convfloat)
(%i194) completearray(array_m1,[40],convfloat)
(%i195) completearray(array_y_higher,[2,40],convfloat)
(%i196) completearray(array_y_higher_work,[2,40],convfloat)
(%i197) completearray(array_y_higher_work2,[2,40],convfloat)
(%i198) completearray(array_y_set_initial,[2,40],convfloat)
(%i199) completearray(array_given_rad_poles,[2,3],convfloat)
(%i200) completearray(array_given_ord_poles,[2,3],convfloat)
(%i201) completearray(array_rad_test_poles,[2,4],convfloat)
(%i202) completearray(array_ord_test_poles,[2,4],convfloat)
(%i203) completearray(array_fact_2,[40,40],convfloat)
(%i204) omniout_str(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a~%",string(str))
(%i205) omniout_str_noeol(iolevel,str):=if glob_iolevel >= iolevel
then printf(true,"~a",string(str))
(%i206) omniout_labstr(iolevel,label,str):=if glob_iolevel >= iolevel
then printf(true,"~a = ~a~%",string(label),
string(str))
(%i207) 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))
(%i208) omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel):=if
glob_iolevel >= iolevel
then (printf(true,"~a = ~d ~a~%",prelabel,value,
postlabel),newline())
(%i209) omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,
postlabel):=if glob_iolevel >= iolevel
then (sprint(prelabel,"[",elemnt,"]=",value,
postlabel),newline())
(%i210) 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)
(%i211) 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)
(%i212) 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)
(%i213) 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)
(%i214) 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)
(%i215) logditto(file):=(printf(file,""),printf(file,"ditto"),
printf(file," | "),0)
(%i216) logitem_integer(file,n):=(printf(file,""),printf(file,"~d",n),
printf(file," | "),0)
(%i217) logitem_str(file,str):=(printf(file,""),printf(file,str),
printf(file," | "),0)
(%i218) logitem_good_digits(file,rel_error):=(
block(mode_declare([[good_digits],fixnum]),
printf(file,""),
printf(file,"~d",glob_min_good_digits),
printf(file," | ")),0)
(%i219) log_revs(file,revs):=printf(file,revs)
(%i220) logitem_float(file,x):=(printf(file,""),printf(file,"~g",x),
printf(file," | "),0)
(%i221) 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)
(%i222) logstart(file):=(printf(file,""),0)
(%i223) logend(file):=(printf(file,"
~%"),0)
(%i224) 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)
(%i225) 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)
(%i226) 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)
(%i227) 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)
(%i228) 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)
(%i229) c(in_val):=(ret:in_val,ret)
(%i230) 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)
(%i231) 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)
(%i232) 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)
(%i233) comp_ord_from_six_terms(term1,term2,term3,term4,term5,term6,last_no):=glob_six_term_ord_save
(%i234) factorial_2(nnn):=block(mode_declare([[ret],convfloat]),ret:nnn!,ret)
(%i235) 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)
(%i236) factorial_1(in):=block(mode_declare([[ret],convfloat]),ret:in!,ret)
(%i237) neg(in):=block(mode_declare([[ret],convfloat]),ret:-in,ret)
(%i238) 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)
(%i239) log10(x):=log(x)/glob_log_10
(%i240) c(x):=x
(%i241) 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
(%i242) 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)
(%i243) exact_soln_y(x):=block(c(0.0))
(%o243) exact_soln_y(x) := block(c(0.0))
(%i244) 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)
(%i245) my_check_sign(x0,xf):=block([ret],
if xf > x0 then ret:glob__1 else ret:glob__m1,ret)
(%i246) 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)
(%i247) 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)
(%i248) 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))
(%i249) 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))
(%i250) 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)
(%i251) 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)
(%i252) check_for_pole():=(
block(mode_declare([cnt],fixnum,[dr1,dr2,ds1,ds2,hdrc],
convfloat,[m,n],fixnum,[nr1,nr2],
convfloat,[ord_no],fixnum,
[term1,term2,term3,part1,part2,
part3,part4,part5,part6,part7,
part8,part9,part10,part11,part12,
part13,part14,rad_c,rcs,rm0,rm1,
rm2,rm3,rm4],convfloat,
[found_sing],fixnum,
[h_new,ratio,term,local_test,
tmp_rad,tmp_ord,tmp_ratio,
prev_tmp_rad],convfloat,[last_no],
fixnum),tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,1]:glob_larger_float,
array_ord_test_poles[1,1]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-3
and found_sing = 1 do
(tmp_rad
:comp_rad_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,1]
then (
array_rad_test_poles[1,1]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_ratio(
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,1]:rad_c,
array_ord_test_poles[1,1]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,2]:glob_larger_float,
array_ord_test_poles[1,2]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-4
and found_sing = 1 do
(tmp_rad
:comp_rad_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,2]
then (
array_rad_test_poles[1,2]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_three_terms(
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,2]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,2]
:tmp_ord)),
tmp_rad:glob_larger_float,
prev_tmp_rad:glob_larger_float,
tmp_ratio:glob_larger_float,
rad_c:glob_larger_float,
array_rad_test_poles[1,3]:glob_larger_float,
array_ord_test_poles[1,3]:glob_larger_float,
found_sing:1,last_no:-10-1+ats_max_terms,cnt:0,
while last_no < ats_max_terms-7
and found_sing = 1 do
(tmp_rad
:comp_rad_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],last_no),
if abs(prev_tmp_rad) > glob__0
then tmp_ratio:tmp_rad/prev_tmp_rad
else tmp_ratio:glob_large_float,
if cnt > 0
and tmp_ratio
< glob_upper_ratio_limit
and tmp_ratio
> glob_lower_ratio_limit
then rad_c:tmp_rad elseif cnt = 0
then rad_c:tmp_rad elseif cnt > 0
then found_sing:0,
prev_tmp_rad:tmp_rad,cnt:1+cnt,
last_no:1+last_no),
if found_sing = 1
then (if rad_c < array_rad_test_poles[1,3]
then (
array_rad_test_poles[1,3]:rad_c,
last_no:last_no-1,
tmp_ord
:comp_ord_from_six_terms(
array_y_higher[1,last_no-5],
array_y_higher[1,last_no-4],
array_y_higher[1,last_no-3],
array_y_higher[1,last_no-2],
array_y_higher[1,last_no-1],
array_y_higher[1,last_no],
last_no),
array_rad_test_poles[1,3]:rad_c,
if rad_c < glob_min_pole_est
then glob_min_pole_est:rad_c,
array_ord_test_poles[1,3]
:tmp_ord)),
if abs(glob_min_pole_est)*glob_ratio_of_radius
< abs(glob_h)
then (h_new
:glob_check_sign*glob_min_pole_est
*glob_ratio_of_radius,
omniout_str(always,
"SETTING H FOR POLE"),
glob_h_reason:6,
if
glob_check_sign*glob_min_h
> glob_check_sign*h_new
then (
omniout_str(always,
"SETTING H FOR MIN H"),
h_new:glob_min_h,glob_h_reason:5),
term:1,ratio:c(1.0),
while term <= ats_max_terms do
(
array_y[term]
:array_y[term]*ratio,
array_y_higher[1,term]
:array_y_higher[1,term]*ratio,
array_x[term]
:array_x[term]*ratio,
ratio:ratio*h_new/abs(glob_h),
term:1+term),glob_h:h_new),
if reached_interval() then display_poles()),0)
(%i253) atomall():=(
block(mode_declare([[kkk,order_d],fixnum,
[adj2,adj3,temporary,term,temp,temp2],
convfloat]),
array_tmp1[1]:array_const_2D0[1]*array_x[1],
array_tmp2[1]:array_const_3D0[1]+array_tmp1[1],
array_tmp3[1]:sqrt(array_tmp2[1]),
array_tmp4_a1[1]:sin(array_tmp3[1]),
array_tmp4_a2[1]:cos(array_tmp3[1]),
array_tmp4[1]:array_tmp4_a1[1]/array_tmp4_a2[1],
array_tmp5[1]:array_tmp4[1]+array_const_0D0[1],
if not array_y_set_initial[1,2]
then (if 1 <= ats_max_terms
then (
temporary
:c(array_tmp5[1])*expt(glob_h,c(1))
*c(factorial_3(0,1)),
if 2 <= ats_max_terms
then (array_y[2]:temporary,
array_y_higher[1,2]:temporary),
temporary:c(temporary)*c(1)/c(glob_h),
array_y_higher[2,1]:c(temporary),0)),
kkk:2,array_tmp1[2]:array_const_2D0[1]*array_x[2],
array_tmp2[2]:array_tmp1[2],
array_tmp3[2]:array_tmp2[2]/array_tmp3[1]/glob__2,
array_tmp4_a1[2]:att(1,array_tmp4_a2,array_tmp3,1),
array_tmp4_a2[2]:neg(att(1,array_tmp4_a1,array_tmp3,1)),
array_tmp4[2]:(array_tmp4_a1[2]
-ats(2,array_tmp4_a2,array_tmp4,2))
/array_tmp4_a2[1],
array_tmp5[2]:array_tmp4[2],
if not array_y_set_initial[1,3]
then (if 2 <= ats_max_terms
then (
temporary
:c(array_tmp5[2])*expt(glob_h,c(1))
*c(factorial_3(1,2)),
if 3 <= ats_max_terms
then (array_y[3]:temporary,
array_y_higher[1,3]:temporary),
temporary:c(temporary)*c(2)/c(glob_h),
array_y_higher[2,2]:c(temporary),0)),
kkk:3,array_tmp3[3]:0,
array_tmp3[3]:neg(ats(3,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/glob__2,
array_tmp4_a1[3]:att(2,array_tmp4_a2,array_tmp3,1),
array_tmp4_a2[3]:neg(att(2,array_tmp4_a1,array_tmp3,1)),
array_tmp4[3]:(array_tmp4_a1[3]
-ats(3,array_tmp4_a2,array_tmp4,2))
/array_tmp4_a2[1],
array_tmp5[3]:array_tmp4[3],
if not array_y_set_initial[1,4]
then (if 3 <= ats_max_terms
then (
temporary
:c(array_tmp5[3])*expt(glob_h,c(1))
*c(factorial_3(2,3)),
if 4 <= ats_max_terms
then (array_y[4]:temporary,
array_y_higher[1,4]:temporary),
temporary:c(temporary)*c(3)/c(glob_h),
array_y_higher[2,3]:c(temporary),0)),
kkk:4,array_tmp3[4]:0,
array_tmp3[4]:neg(ats(4,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/glob__2,
array_tmp4_a1[4]:att(3,array_tmp4_a2,array_tmp3,1),
array_tmp4_a2[4]:neg(att(3,array_tmp4_a1,array_tmp3,1)),
array_tmp4[4]:(array_tmp4_a1[4]
-ats(4,array_tmp4_a2,array_tmp4,2))
/array_tmp4_a2[1],
array_tmp5[4]:array_tmp4[4],
if not array_y_set_initial[1,5]
then (if 4 <= ats_max_terms
then (
temporary
:c(array_tmp5[4])*expt(glob_h,c(1))
*c(factorial_3(3,4)),
if 5 <= ats_max_terms
then (array_y[5]:temporary,
array_y_higher[1,5]:temporary),
temporary:c(temporary)*c(4)/c(glob_h),
array_y_higher[2,4]:c(temporary),0)),
kkk:5,array_tmp3[5]:0,
array_tmp3[5]:neg(ats(5,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/glob__2,
array_tmp4_a1[5]:att(4,array_tmp4_a2,array_tmp3,1),
array_tmp4_a2[5]:neg(att(4,array_tmp4_a1,array_tmp3,1)),
array_tmp4[5]:(array_tmp4_a1[5]
-ats(5,array_tmp4_a2,array_tmp4,2))
/array_tmp4_a2[1],
array_tmp5[5]:array_tmp4[5],
if not array_y_set_initial[1,6]
then (if 5 <= ats_max_terms
then (
temporary
:c(array_tmp5[5])*expt(glob_h,c(1))
*c(factorial_3(4,5)),
if 6 <= ats_max_terms
then (array_y[6]:temporary,
array_y_higher[1,6]:temporary),
temporary:c(temporary)*c(5)/c(glob_h),
array_y_higher[2,5]:c(temporary),0)),
kkk:6,
while kkk <= ats_max_terms do
(array_tmp3[kkk]:0,
array_tmp3[kkk]
:neg(ats(kkk,array_tmp3,array_tmp3,2))
/array_tmp3[1]
/glob__2,
array_tmp4_a1[kkk]
:att(kkk-1,array_tmp4_a2,array_tmp3,1),
array_tmp4_a2[kkk]
:neg(att(kkk-1,array_tmp4_a1,array_tmp3,1)),
array_tmp4[kkk]
:(array_tmp4_a1[kkk]
-ats(kkk,array_tmp4_a2,array_tmp4,2))
/array_tmp4_a2[1],
array_tmp5[kkk]:array_tmp4[kkk],order_d:1,
if order_d+kkk <= ats_max_terms
then (if
not array_y_set_initial[1,order_d+kkk]
then (
temporary
:c(array_tmp5[kkk])*expt(glob_h,c(order_d))
*c(
factorial_3(
kkk-1,
-1+order_d+kkk)),
array_y[order_d+kkk]:c(temporary),
array_y_higher[1,order_d+kkk]:c(temporary),
term:-1+order_d+kkk,adj2:-1+order_d+kkk,
adj3:2,
while term >= 1 and term <= ats_max_terms
and adj3 < 1+order_d do
(
if adj3 <= 1+order_d
then (
if adj2 > 0
then temporary
:c(temporary)*c(adj2)
/c(glob_h)
else temporary:c(temporary),
array_y_higher[adj3,term]
:c(temporary)),term:term-1,
adj2:adj2-1,adj3:1+adj3))),
kkk:1+kkk)),0)
(%i254) exact_soln_y(x):=block(c(0.0))
(%o254) exact_soln_y(x) := block(c(0.0))
(%i255) 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_tmp4_g[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do
(array_tmp4_a1[term]:c(0.0),term:1+term),term:1,
while term <= 40 do
(array_tmp4_a2[term]:c(0.0),term:1+term),term:1,
while term <= 40 do (array_tmp4[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_tmp5[term]:c(0.0),term:1+term),
term:1,
while term <= 40 do (array_m1[term]:c(0.0),term:1+term),
ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher[ord,term]:c(0.0),term:1+term),
ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_higher_work2[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 40 do
(array_y_set_initial[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_rad_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 3 do
(array_given_ord_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_rad_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 2 do
(term:1,
while term <= 4 do
(array_ord_test_poles[ord,term]:c(0.0),
term:1+term),ord:1+ord),ord:1,
while ord <= 40 do
(term:1,
while term <= 40 do
(array_fact_2[ord,term]:c(0.0),term:1+term),
ord:1+ord),zero_ats_ar(array_y),zero_ats_ar(array_x),
zero_ats_ar(array_tmp0),zero_ats_ar(array_tmp1),
zero_ats_ar(array_tmp2),zero_ats_ar(array_tmp3),
zero_ats_ar(array_tmp4_g),zero_ats_ar(array_tmp4_a1),
zero_ats_ar(array_tmp4_a2),zero_ats_ar(array_tmp4),
zero_ats_ar(array_tmp5),zero_ats_ar(array_m1),
zero_ats_ar(array_const_1),array_const_1[1]:c(1),
zero_ats_ar(array_const_0D0),array_const_0D0[1]:c(0.0),
zero_ats_ar(array_const_2D0),array_const_2D0[1]:c(2.0),
zero_ats_ar(array_const_3D0),array_const_3D0[1]:c(3.0),
zero_ats_ar(array_m1),array_m1[1]:glob__m1,iiif:0,
while iiif <= ats_max_terms do
(jjjf:0,
while jjjf <= ats_max_terms do
(array_fact_1[iiif]:0,
array_fact_2[iiif,jjjf]:0,jjjf:1+jjjf),
iiif:1+iiif),array_y_set_initial[1,1]:true,
array_y_set_initial[1,2]:false,
array_y_set_initial[1,3]:false,
array_y_set_initial[1,4]:false,
array_y_set_initial[1,5]:false,
array_y_set_initial[1,6]:false,
array_y_set_initial[1,7]:false,
array_y_set_initial[1,8]:false,
array_y_set_initial[1,9]:false,
array_y_set_initial[1,10]:false,
array_y_set_initial[1,11]:false,
array_y_set_initial[1,12]:false,
array_y_set_initial[1,13]:false,
array_y_set_initial[1,14]:false,
array_y_set_initial[1,15]:false,
array_y_set_initial[1,16]:false,
array_y_set_initial[1,17]:false,
array_y_set_initial[1,18]:false,
array_y_set_initial[1,19]:false,
array_y_set_initial[1,20]:false,
array_y_set_initial[1,21]:false,
array_y_set_initial[1,22]:false,
array_y_set_initial[1,23]:false,
array_y_set_initial[1,24]:false,
array_y_set_initial[1,25]:false,
array_y_set_initial[1,26]:false,
array_y_set_initial[1,27]:false,
array_y_set_initial[1,28]:false,
array_y_set_initial[1,29]:false,
array_y_set_initial[1,30]:false,
array_y_set_initial[1,31]:false,
array_y_set_initial[1,32]:false,
array_y_set_initial[1,33]:false,
array_y_set_initial[1,34]:false,
array_y_set_initial[1,35]:false,
array_y_set_initial[1,36]:false,
array_y_set_initial[1,37]:false,
array_y_set_initial[1,38]:false,
array_y_set_initial[1,39]:false,
array_y_set_initial[1,40]:false,glob_log_10:log(10.0),
glob_orig_start_sec:elapsed_time_seconds(),
glob_display_flag:true,glob_no_eqs:1,glob_iter:-1,
opt_iter:-1,glob_max_iter:50000,glob_max_hours:0.0,
glob_max_minutes:15.0,
omniout_str(always,
"##############ECHO OF PROBLEM#################"),
omniout_str(always,
"##############temp/tan_sqrt_linpostode.ode#################"),
omniout_str(always,
"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN FIRST INPUT BLOCK */"),
omniout_str(always,"Digits:32,"),
omniout_str(always,"max_terms:40,"),omniout_str(always,"!"),
omniout_str(always,"/* END FIRST INPUT BLOCK */"),
omniout_str(always,"/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(always,"x_start:c(0.1),"),
omniout_str(always,"x_end:c(5.0),"),
omniout_str(always,
"array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(always,"glob_look_poles:true,"),
omniout_str(always,"glob_min_h:c(0.001),"),
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:1,"),
omniout_str(always,""),
omniout_str(always,"array_given_rad_poles[1,1]:c(-1.5),"),
omniout_str(always,""),
omniout_str(always,"array_given_rad_poles[1,2]:c(0.0),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,1]:c(0.5),"),
omniout_str(always,""),
omniout_str(always,"array_given_ord_poles[1,2]:c(0.0),"),
omniout_str(always,"/* END SECOND INPUT BLOCK */"),
omniout_str(always,"/* BEGIN OVERRIDE BLOCK */"),
omniout_str(always,"glob_desired_digits_correct:8,"),
omniout_str(always,"glob_max_minutes:(3.0),"),
omniout_str(always,"glob_subiter_method:3,"),
omniout_str(always,"glob_max_iter:100000,"),
omniout_str(always,"glob_upper_ratio_limit:c(1.000001),"),
omniout_str(always,"glob_lower_ratio_limit:c(0.999999),"),
omniout_str(always,"glob_look_poles:false,"),
omniout_str(always,"glob_h:c(0.001),"),
omniout_str(always,"glob_display_interval:c(0.01),"),
omniout_str(always,"/* END OVERRIDE BLOCK */"),
omniout_str(always,"!"),
omniout_str(always,"/* BEGIN USER DEF BLOCK */"),
omniout_str(always,"exact_soln_y (x) := (block("),
omniout_str(always," (c(0.0)) "),omniout_str(always,"));"),
omniout_str(always,"/* END USER DEF BLOCK */"),
omniout_str(always,
"#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt:0,glob_warned:false,glob_warned2:false,
glob_small_float:glob__0,glob_smallish_float:glob__0,
glob_large_float:c(1.0E+100),glob_larger_float:c(1.1E+100),
glob_almost_1:c(0.99),x_start:c(0.1),x_end:c(5.0),
array_y_init[1+0]:exact_soln_y(x_start),
glob_look_poles:true,glob_min_h:c(0.001),
glob_type_given_pole:1,array_given_rad_poles[1,1]:c(-1.5),
array_given_rad_poles[1,2]:c(0.0),
array_given_ord_poles[1,1]:c(0.5),
array_given_ord_poles[1,2]:c(0.0),
glob_desired_digits_correct:8,glob_max_minutes:3.0,
glob_subiter_method:3,glob_max_iter:100000,
glob_upper_ratio_limit:c(1.000001),
glob_lower_ratio_limit:c(0.999999),glob_look_poles:false,
glob_h:c(0.001),glob_display_interval:c(0.01),
glob_last_good_h:glob_h,
glob_max_sec:3600.0*glob_max_hours+60.0*glob_max_minutes,
glob_check_sign:c(my_check_sign(x_start,x_end)),
glob__pi:3.141592654,glob_prec:1.0E-16,
if glob_optimize
then (omniout_str(always,"START of Optimize"),
found_h:false,glob_min_pole_est:glob_larger_float,
last_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,
glob_min_h:abs(glob_min_h)*glob_check_sign,
glob_max_h:abs(glob_max_h)*glob_check_sign,
glob_h:abs(glob_min_h)*glob_check_sign,
glob_display_interval
:c(abs(c(glob_display_interval))
*glob_check_sign),
display_max:c(x_end)-c(x_start)/glob__10,
if glob_display_interval > display_max
then glob_display_interval:c(display_max),
chk_data(),min_value:glob_larger_float,
est_answer:est_size_answer(),opt_iter:1,
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,est_answer),
omniout_float(always,"est_needed_step_err",32,
est_needed_step_err,16,""),
estimated_step_error:glob_small_float,
while opt_iter <= 100 and not found_h do
(omniout_int(always,"opt_iter",32,opt_iter,
4,""),array_x[1]:c(x_start),
array_x[2]:c(glob_h),
glob_next_display:c(x_start),order_diff:1,
term_no:1,
while term_no <= order_diff do
(
array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,
c(term_no-1))
/c(
factorial_1(
term_no-1)),
term_no:1+term_no),
r_order:1+r_order),atomall(),
if glob_check_sign*glob_min_h
>= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR MIN H"),
glob_h:glob_check_sign*abs(glob_min_h),
glob_h_reason:1,found_h:true),
if glob_check_sign*glob_display_interval
<= glob_check_sign*glob_h
then (
omniout_str(always,
"SETTING H FOR DISPLAY INTERVAL"),
glob_h_reason:2,
glob_h:glob_display_interval,
found_h:true),
if glob_look_poles then check_for_pole(),
if not found_h
then (est_answer:est_size_answer(),
est_needed_step_err
:estimated_needed_step_error(
x_start,x_end,glob_h,
est_answer),
omniout_float(always,
"est_needed_step_err",
32,
est_needed_step_err,
16,""),
estimated_step_error
:test_suggested_h(),
omniout_float(always,
"estimated_step_error",
32,
estimated_step_error,
32,""),
if
estimated_step_error
< est_needed_step_err
then (
omniout_str(always,
"Double H and LOOP"),
glob_h:glob_h*glob__2)
else (
omniout_str(always,
"Found H for OPTIMAL"),
found_h:true,glob_h_reason:3,
glob_h:glob_h/glob__2)),
opt_iter:1+opt_iter),
if not found_h and opt_iter = 1
then (omniout_str(always,
"Beginning glob_h too large."),
found_h:false),
if glob_check_sign*glob_max_h
<= glob_check_sign*glob_h
then (omniout_str(always,
"SETTING H FOR MAX H"),
glob_h:glob_check_sign*abs(glob_max_h),
glob_h_reason:1,found_h:true))
else (found_h:true,glob_h:glob_h*glob_check_sign),
if glob_html_log then html_log_file:openw("entry.html"),
if found_h
then (omniout_str(always,"START of Soultion"),
array_x[1]:c(x_start),array_x[2]:c(glob_h),
glob_next_display:c(x_start),
glob_min_pole_est:glob_larger_float,
glob_least_given_sing:glob_larger_float,
glob_least_ratio_sing:glob_larger_float,
glob_least_3_sing:glob_larger_float,
glob_least_6_sing:glob_larger_float,order_diff:1,
term_no:1,
while term_no <= order_diff do
(array_y[term_no]
:array_y_init[term_no]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),rows:order_diff,
r_order:1,
while r_order <= rows do
(term_no:1,
while term_no <= 1-r_order+rows do
(it:-1+r_order+term_no,
if term_no < ats_max_terms
then array_y_higher[
r_order,term_no]
:array_y_init[it]
*expt(glob_h,c(term_no-1))
/c(factorial_1(term_no-1)),
term_no:1+term_no),
r_order:1+r_order),current_iter:1,
glob_clock_start_sec:elapsed_time_seconds(),
glob_clock_sec:elapsed_time_seconds(),glob_iter:0,
omniout_str(debugl," "),
glob_reached_optimal_h:true,
glob_optimal_clock_start_sec
:elapsed_time_seconds(),
while glob_iter < glob_max_iter
and glob_check_sign*array_x[1]
< glob_check_sign*x_end
and glob_clock_sec-glob_orig_start_sec
< glob_max_sec do
(if reached_interval()
then (omniout_str(info," "),
omniout_str(info,
"TOP MAIN SOLVE Loop")),
glob_iter:1+glob_iter,
glob_clock_sec:elapsed_time_seconds(),
track_estimated_error(),atomall(),
track_estimated_error(),
display_alot(current_iter),
if glob_look_poles then check_for_pole(),
if reached_interval()
then glob_next_display
:glob_display_interval
+glob_next_display,
array_x[1]:glob_h+array_x[1],
array_x[2]:glob_h,order_diff:2,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[2,iii]
:array_y_higher[2,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:2,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:2,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
array_y_higher_work[1,iii]
:array_y_higher[1,iii]
/expt(glob_h,c(calc_term-1))
/c(
factorial_3(iii-calc_term,iii-1)),
iii:iii-1),temp_sum:glob__0,ord:1,
calc_term:1,iii:ats_max_terms,
while iii >= calc_term do
(
temp_sum
:array_y_higher_work[ord,iii]
+temp_sum,iii:iii-1),
array_y_higher_work2[ord,calc_term]
:temp_sum*expt(glob_h,c(calc_term-1))
/c(factorial_1(calc_term-1)),
term_no:ats_max_terms,
while term_no >= 1 do
(
array_y[term_no]
:array_y_higher_work2[1,term_no],
ord:1,
while ord <= order_diff do
(
array_y_higher[ord,term_no]
:array_y_higher_work2[
ord,term_no],ord:1+ord),
term_no:term_no-1)),
omniout_str(always,"Finished!"),
if glob_iter >= glob_max_iter
then omniout_str(always,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds()-glob_orig_start_sec
>= glob_max_sec
then omniout_str(always,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec:elapsed_time_seconds(),
omniout_str(info,
"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "),
omniout_int(info,
"Iterations ",32,
glob_iter,4," "),
prog_report(x_start,x_end),
if glob_html_log
then (logstart(html_log_file),
logitem_str(html_log_file,
"2015-04-24T22:57:23-05:00"),
logitem_str(html_log_file,"Maxima"),
logitem_str(html_log_file,
"tan_sqrt_lin"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "),
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,
"tan_sqrt_lin diffeq.max"),
logitem_str(html_log_file,
"tan_sqrt_lin maxima results"),
logitem_str(html_log_file,
"PROBLEM - Singularity not accurate"),
logend(html_log_file)),
if glob_html_log then close(html_log_file)))
(%i256) main():=(glob_iolevel:2,compile(all),main_prog())
(%i257) main()
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
warning: encountered undefined variable glob_iolevel in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable secs in translation.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable sec_temp in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable years_int in translation.
warning: encountered undefined variable days_int in translation.
warning: encountered undefined variable hours_int in translation.
warning: encountered undefined variable minutes_int in translation.
warning: encountered undefined variable sec_int in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_sec_in_year in translation.
warning: encountered undefined variable glob_sec_in_day in translation.
warning: encountered undefined variable glob_sec_in_hour in translation.
warning: encountered undefined variable glob_sec_in_minute in translation.
warning: encountered undefined variable iii in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_ats in translation.
warning: encountered undefined variable ma_ats in translation.
warning: encountered undefined variable ret_ats in translation.
warning: encountered undefined variable lll_ats in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable iii_att in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable ma_att in translation.
warning: encountered undefined variable lll_att in translation.
warning: encountered undefined variable ret_att in translation.
warning: encountered undefined variable al_att in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_h_reason in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_max_iter in translation.
warning: encountered undefined variable errflag in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable sub1 in translation.
warning: encountered undefined variable sub2 in translation.
warning: encountered undefined variable rrr in translation.
warning: encountered undefined variable ms2 in translation.
warning: encountered undefined variable sec_left in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable glob_small_float in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ret in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__m2 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temp in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable glob__4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm0 in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable rm1 in translation.
warning: encountered undefined variable rm2 in translation.
warning: encountered undefined variable rm3 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable rm4 in translation.
warning: encountered undefined variable glob__3 in translation.
warning: encountered undefined variable glob__8 in translation.
warning: encountered undefined variable glob__5 in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable nr1 in translation.
warning: encountered undefined variable dr2 in translation.
warning: encountered undefined variable nr2 in translation.
warning: encountered undefined variable dr1 in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable ds1 in translation.
warning: encountered undefined variable ds2 in translation.
warning: encountered undefined variable rcs in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable ord_no in translation.
warning: variable glob_six_term_ord_save (declared type convfloat) assigned type any.
warning: encountered undefined variable rad_c in translation.
warning: encountered undefined variable glob_six_term_ord_save in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_fact_2 in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob_log_10 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob__10 in translation.
warning: encountered undefined variable ats_max_terms in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_x in translation.
warning: encountered undefined variable array_given_rad_poles in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable rad_given in translation.
warning: encountered undefined variable array_given_ord_poles in translation.
warning: variable glob_least_given_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_given_sing in translation.
warning: encountered undefined variable glob_type_given_pole in translation.
warning: encountered undefined variable array_rad_test_poles in translation.
warning: variable glob_least_ratio_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_ratio_sing in translation.
warning: encountered undefined variable array_ord_test_poles in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: variable glob_least_3_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_3_sing in translation.
warning: encountered undefined variable glob__small in translation.
warning: variable glob_least_6_sing (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_least_6_sing in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_estimated_size_answer in translation.
warning: encountered undefined variable array_y in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__1 in translation.
warning: encountered undefined variable glob__small in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable glob__0_5 in translation.
warning: encountered undefined variable glob__0_25 in translation.
warning: encountered undefined variable glob__0_125 in translation.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable array_max_est_error in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_next_display in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob__10 in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable ind_var in translation.
warning: encountered undefined variable closed_form_val_y in translation.
warning: encountered undefined variable term_no in translation.
warning: encountered undefined variable numeric_val in translation.
warning: encountered undefined variable abserr in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable relerr in translation.
warning: variable glob_good_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_prec in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: encountered undefined variable glob_good_digits in translation.
warning: encountered undefined variable glob_min_good_digits in translation.
warning: encountered undefined variable glob_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_min_apfp_est_good_digits in translation.
warning: encountered undefined variable glob_iter in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable est_rel_err in translation.
warning: variable glob_est_digits (declared type fixnum) assigned type any.
warning: encountered undefined variable glob_est_digits in translation.
warning: encountered undefined variable array_est_digits in translation.
warning: encountered undefined variable array_1st_rel_error in translation.
warning: encountered undefined variable array_last_rel_error in translation.
warning: encountered undefined variable array_est_rel_error in translation.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_desired_digits_correct in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable clock_sec1 in translation.
warning: encountered undefined variable glob_orig_start_sec in translation.
warning: encountered undefined variable glob_clock_start_sec in translation.
warning: variable glob_clock_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_max_sec in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable glob_optimal_clock_start_sec in translation.
warning: encountered undefined variable opt_clock_sec in translation.
warning: variable glob_optimal_expect_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable glob_optimal_expect_sec in translation.
warning: encountered undefined variable total_clock_sec in translation.
warning: variable glob_total_exp_sec (declared type convfloat) assigned type any.
warning: encountered undefined variable percent_done in translation.
warning: variable glob_percent_done (declared type convfloat) assigned type any.
warning: encountered undefined variable info in translation.
warning: encountered undefined variable glob_clock_sec in translation.
warning: encountered undefined variable expect_sec in translation.
warning: encountered undefined variable glob_total_exp_sec in translation.
warning: encountered undefined variable glob__100 in translation.
warning: encountered undefined variable left_sec in translation.
warning: encountered undefined variable glob_larger_float in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable last_no in translation.
warning: encountered undefined variable found_sing in translation.
warning: encountered undefined variable array_y_higher in translation.
warning: variable tmp_rad (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_rad in translation.
warning: encountered undefined variable prev_tmp_rad in translation.
warning: encountered undefined variable glob__0 in translation.
warning: encountered undefined variable glob_large_float in translation.
warning: encountered undefined variable cnt in translation.
warning: encountered undefined variable tmp_ratio in translation.
warning: encountered undefined variable glob_upper_ratio_limit in translation.
warning: encountered undefined variable glob_lower_ratio_limit in translation.
warning: variable tmp_ord (declared type convfloat) assigned type any.
warning: encountered undefined variable tmp_ord in translation.
warning: encountered undefined variable glob_min_pole_est in translation.
warning: encountered undefined variable glob_check_sign in translation.
warning: encountered undefined variable glob_ratio_of_radius in translation.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob_min_h in translation.
warning: encountered undefined variable h_new in translation.
warning: variable ratio (declared type convfloat) assigned type any.
warning: encountered undefined variable term in translation.
warning: encountered undefined variable ratio in translation.
warning: encountered undefined variable glob_h in translation.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: encountered undefined variable array_const_2D0 in translation.
warning: encountered undefined variable array_tmp1 in translation.
warning: encountered undefined variable array_const_3D0 in translation.
warning: encountered undefined variable array_tmp2 in translation.
warning: encountered undefined variable array_tmp3 in translation.
warning: encountered undefined variable array_tmp4_a1 in translation.
warning: encountered undefined variable array_tmp4_a2 in translation.
warning: encountered undefined variable array_tmp4 in translation.
warning: encountered undefined variable array_const_0D0 in translation.
warning: encountered undefined variable array_tmp5 in translation.
warning: encountered undefined variable glob_h in translation.
warning: encountered undefined variable temporary in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: encountered undefined variable array_y_set_initial in translation.
warning: encountered undefined variable glob__2 in translation.
warning: encountered undefined variable kkk in translation.
warning: encountered undefined variable order_d in translation.
warning: encountered undefined variable adj3 in translation.
warning: encountered undefined variable adj2 in translation.
modedeclare: [found_h]
is not a built-in type; assuming it is a Maxima extension type.
modedeclare: false
is not a built-in type; assuming it is a Maxima extension type.
warning: variable term (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable array_y_init in translation.
warning: variable term (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_norms in translation.
warning: encountered undefined variable array_fact_1 in translation.
warning: encountered undefined variable array_type_pole in translation.
warning: encountered undefined variable array_type_real_pole in translation.
warning: encountered undefined variable array_type_complex_pole in translation.
warning: encountered undefined variable array_tmp0 in translation.
warning: encountered undefined variable array_tmp4_g in translation.
warning: encountered undefined variable array_m1 in translation.
warning: variable ord (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable ord in translation.
warning: variable ord (declared type [found_h]) assigned type any.
warning: encountered undefined variable array_y_higher_work in translation.
warning: encountered undefined variable array_y_higher_work2 in translation.
warning: encountered undefined variable array_const_1 in translation.
warning: encountered undefined variable glob__m1 in translation.
warning: variable iiif (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable iiif in translation.
warning: encountered undefined variable ats_max_terms in translation.
warning: variable jjjf (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable jjjf in translation.
warning: variable jjjf (declared type [found_h]) assigned type any.
warning: variable iiif (declared type [found_h]) assigned type any.
warning: variable glob_orig_start_sec (declared type convfloat) assigned type any.
warning: variable opt_iter (declared type [found_h]) assigned type fixnum.
warning: encountered undefined variable always in translation.
warning: encountered undefined variable glob__0 in translation.
warning: variable glob_large_float (declared type convfloat) assigned type any.
warning: variable glob_larger_float (declared type convfloat) assigned type any.
warning: variable glob_almost_1 (declared type convfloat) assigned type any.
warning: variable x_start (declared type [found_h]) assigned type any.
warning: variable x_end (declared type [found_h]) assigned type any.
warning: encountered undefined variable x_start in translation.
warning: variable glob_min_h (declared type convfloat) assigned type any.
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/tan_sqrt_linpostode.ode#################"
"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:40,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:c(0.1),"
"x_end:c(5.0),"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_min_h:c(0.001),"
""
""
""
""
""
""
""
"glob_type_given_pole:1,"
""
"array_given_rad_poles[1,1]:c(-1.5),"
""
"array_given_rad_poles[1,2]:c(0.0),"
""
"array_given_ord_poles[1,1]:c(0.5),"
""
"array_given_ord_poles[1,2]:c(0.0),"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:8,"
"glob_max_minutes:(3.0),"
"glob_subiter_method:3,"
"glob_max_iter:100000,"
"glob_upper_ratio_limit:c(1.000001),"
"glob_lower_ratio_limit:c(0.999999),"
"glob_look_poles:false,"
"glob_h:c(0.001),"
"glob_display_interval:c(0.01),"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (c(0.0)) "
"));"
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.1 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = 0.0 " "
absolute error = 0.0 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = -16
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.11000000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -4.46016139604182400E-2 " "
absolute error = 4.46016139604182400E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.12000000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -8.80668840755199200E-2 " "
absolute error = 8.80668840755199200E-2 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.13000000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.13045284233220727 " "
absolute error = 0.13045284233220727 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.14000000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.17181225586825383 " "
absolute error = 0.17181225586825383 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.15000000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.2121940422665403 " "
absolute error = 0.2121940422665403 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.16000000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.25164363549036245 " "
absolute error = 0.25164363549036245 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.17000000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.2902033093365848 " "
absolute error = 0.2902033093365848 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.18000000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.3279124641909628 " "
absolute error = 0.3279124641909628 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.19000000000000009 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.3648078819714537 " "
absolute error = 0.3648078819714537 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2000000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.40092395340288095 " "
absolute error = 0.40092395340288095 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 14
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2100000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.4362928811500712 " "
absolute error = 0.4362928811500712 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2200000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.47094486182290834 " "
absolute error = 0.47094486182290834 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.23000000000000012 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.5049082494368342 " "
absolute error = 0.5049082494368342 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.24000000000000013 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.538209702551104 " "
absolute error = 0.538209702551104 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2500000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.5708743170024797 " "
absolute error = 0.5708743170024797 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.2600000000000001 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.6029257458942242 " "
absolute error = 0.6029257458942242 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.27000000000000013 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.6343863082813075 " "
absolute error = 0.6343863082813075 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.28000000000000014 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.6652770878061821 " "
absolute error = 0.6652770878061821 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.29000000000000015 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.6956180223800379 " "
absolute error = 0.6956180223800379 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.30000000000000016 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.7254279858677435 " "
absolute error = 0.7254279858677435 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.31000000000000016 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.754724862617151 " "
absolute error = 0.754724862617151 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3200000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.7835256155720971 " "
absolute error = 0.7835256155720971 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3300000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.8118463486208162 " "
absolute error = 0.8118463486208162 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3400000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.8397023637555378 " "
absolute error = 0.8397023637555378 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3500000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.8671082135530415 " "
absolute error = 0.8671082135530415 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3600000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.8940777494284503 " "
absolute error = 0.8940777494284503 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3700000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.9206241660643479 " "
absolute error = 0.9206241660643479 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.3800000000000002 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.946760042373372 " "
absolute error = 0.946760042373372 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.39000000000000024 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.9724973793139108 " "
absolute error = 0.9724973793139108 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.40000000000000024 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -0.9978476348446635 " "
absolute error = 0.9978476348446635 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.41000000000000025 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.0228217562739996 " "
absolute error = 1.0228217562739996 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.42000000000000026 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.047430210233738 " "
absolute error = 1.047430210233738 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.43000000000000027 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.071683010483691 " "
absolute error = 1.071683010483691 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4400000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.0955897437327056 " "
absolute error = 1.0955897437327056 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4500000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.1191595936436507 " "
absolute error = 1.1191595936436507 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4600000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.1424013631735124 " "
absolute error = 1.1424013631735124 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4700000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.1653234953853058 " "
absolute error = 1.1653234953853058 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4800000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.1879340928555768 " "
absolute error = 1.1879340928555768 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.4900000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.2102409357897244 " "
absolute error = 1.2102409357897244 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5000000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.2322514989470617 " "
absolute error = 1.2322514989470617 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5100000000000003 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.2539729674682571 " "
absolute error = 1.2539729674682571 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5200000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.2754122516895088 " "
absolute error = 1.2754122516895088 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5300000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.2965760010203304 " "
absolute error = 1.2965760010203304 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5400000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.317470616955102 " "
absolute error = 1.317470616955102 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5500000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.3381022652824879 " "
absolute error = 1.3381022652824879 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5600000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.3584768875513609 " "
absolute error = 1.3584768875513609 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5700000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.378600211846917 " "
absolute error = 1.378600211846917 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5800000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.3984777629262068 " "
absolute error = 1.3984777629262068 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.5900000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.4181148717582601 " "
absolute error = 1.4181148717582601 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6000000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.4375166845102956 " "
absolute error = 1.4375166845102956 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6100000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.456688171018183 " "
absolute error = 1.456688171018183 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6200000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.475634132776286 " "
absolute error = 1.475634132776286 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6300000000000004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.4943592104790573 " "
absolute error = 1.4943592104790573 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6400000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.5128678911442313 " "
absolute error = 1.5128678911442313 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6500000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.5311645148451887 " "
absolute error = 1.5311645148451887 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6600000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.5492532810779411 " "
absolute error = 1.5492532810779411 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6700000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.5671382547862958 " "
absolute error = 1.5671382547862958 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6800000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.584823372066991 " "
absolute error = 1.584823372066991 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.6900000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.6023124455749997 " "
absolute error = 1.6023124455749997 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7000000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.619609169647714 " "
absolute error = 1.619609169647714 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7100000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.6367171251653936 " "
absolute error = 1.6367171251653936 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7200000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.6536397841639985 " "
absolute error = 1.6536397841639985 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7300000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.6703805142154027 " "
absolute error = 1.6703805142154027 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7400000000000005 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.6869425825889328 " "
absolute error = 1.6869425825889328 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7500000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.7033291602072071 " "
absolute error = 1.7033291602072071 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7600000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.7195433254083619 " "
absolute error = 1.7195433254083619 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7700000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.735588067525935 " "
absolute error = 1.735588067525935 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7800000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.7514662902969143 " "
absolute error = 1.7514662902969143 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.7900000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.767180815107758 " "
absolute error = 1.767180815107758 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8000000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.7827343840875516 " "
absolute error = 1.7827343840875516 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8100000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.7981296630568642 " "
absolute error = 1.7981296630568642 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8200000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.8133692443403089 " "
absolute error = 1.8133692443403089 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8300000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.8284556494503075 " "
absolute error = 1.8284556494503075 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8400000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.8433913316490733 " "
absolute error = 1.8433913316490733 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8500000000000006 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.8581786783953873 " "
absolute error = 1.8581786783953873 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8600000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.8728200136823367 " "
absolute error = 1.8728200136823367 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8700000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.887317600271795 " "
absolute error = 1.887317600271795 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8800000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.901673641831076 " "
absolute error = 1.901673641831076 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.8900000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9158902849768564 " "
absolute error = 1.9158902849768564 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9000000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9299696212311617 " "
absolute error = 1.9299696212311617 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9100000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9439136888939164 " "
absolute error = 1.9439136888939164 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9200000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9577244748362994 " "
absolute error = 1.9577244748362994 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9300000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9714039162188919 " "
absolute error = 1.9714039162188919 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9400000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9849539021383709 " "
absolute error = 1.9849539021383709 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9500000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -1.9983762752062944 " "
absolute error = 1.9983762752062944 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9600000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.0116728330633067 " "
absolute error = 2.0116728330633067 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9700000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.0248453298319142 " "
absolute error = 2.0248453298319142 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9800000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.0378954775107996 " "
absolute error = 2.0378954775107996 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 0.9900000000000008 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.0508249473134783 " "
absolute error = 2.0508249473134783 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0000000000000007 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.063635370953942 " "
absolute error = 2.063635370953942 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0099999999999996 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.0763283418817924 " "
absolute error = 2.0763283418817924 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0199999999999985 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.088905416469229 " "
absolute error = 2.088905416469229 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0299999999999974 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.101368115152131 " "
absolute error = 2.101368115152131 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0399999999999963 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.1137179235273447 " "
absolute error = 2.1137179235273447 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0499999999999952 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.1259562934081773 " "
absolute error = 2.1259562934081773 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.059999999999994 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.1380846438400027 " "
absolute error = 2.1380846438400027 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.069999999999993 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.150104362077771 " "
absolute error = 2.150104362077771 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0799999999999919 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.1620168045271284 " "
absolute error = 2.1620168045271284 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0899999999999908 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.173823297650754 " "
absolute error = 2.173823297650754 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.0999999999999897 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.1855251388414576 " "
absolute error = 2.1855251388414576 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1099999999999886 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.197123597263486 " "
absolute error = 2.197123597263486 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999875 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.2086199146634207 " "
absolute error = 2.2086199146634207 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999863 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.2200153061519683 " "
absolute error = 2.2200153061519683 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999852 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.231310960957906 " "
absolute error = 2.231310960957906 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999841 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.242508043155352 " "
absolute error = 2.242508043155352 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.159999999999983 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.2536076923654926 " "
absolute error = 2.2536076923654926 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.169999999999982 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.2646110244338296 " "
absolute error = 2.2646110244338296 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999808 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.275519132083977 " "
absolute error = 2.275519132083977 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999797 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.2863330855489643 " "
absolute error = 2.2863330855489643 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1999999999999786 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.2970539331809787 " "
absolute error = 2.2970539331809787 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2099999999999775 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.307682702040417 " "
absolute error = 2.307682702040417 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999764 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.3182203984650935 " "
absolute error = 2.3182203984650935 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999753 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.3286680086203932 " "
absolute error = 2.3286680086203932 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999742 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.3390264990311356 " "
absolute error = 2.3390264990311356 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999731 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.349296817095873 " "
absolute error = 2.349296817095873 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.259999999999972 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.3594798915843174 " "
absolute error = 2.3594798915843174 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.269999999999971 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.369576633118558 " "
absolute error = 2.369576633118558 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999698 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.3795879346386863 " "
absolute error = 2.3795879346386863 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999687 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.389514671853458 " "
absolute error = 2.389514671853458 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2999999999999676 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.3993577036765363 " "
absolute error = 2.3993577036765363 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3099999999999665 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.4091178726488893 " "
absolute error = 2.4091178726488893 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3199999999999654 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.418796005347851 " "
absolute error = 2.418796005347851 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3299999999999643 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.4283929127833614 " "
absolute error = 2.4283929127833614 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3399999999999632 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.437909390781853 " "
absolute error = 2.437909390781853 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3499999999999621 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.447346220358251 " "
absolute error = 2.447346220358251 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.359999999999961 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.456704168076526 " "
absolute error = 2.456704168076526 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.36999999999996 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.4659839863992166 " "
absolute error = 2.4659839863992166 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3799999999999588 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.4751864140263318 " "
absolute error = 2.4751864140263318 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3899999999999577 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.4843121762239986 " "
absolute error = 2.4843121762239986 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.3999999999999566 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.493361985143258 " "
absolute error = 2.493361985143258 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4099999999999555 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.5023365401293294 " "
absolute error = 2.5023365401293294 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4199999999999544 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.511236528021704 " "
absolute error = 2.511236528021704 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4299999999999533 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.5200626234453867 " "
absolute error = 2.5200626234453867 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4399999999999522 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.5288154890935908 " "
absolute error = 2.5288154890935908 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.449999999999951 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.5374957760021966 " "
absolute error = 2.5374957760021966 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.45999999999995 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.546104123816253 " "
absolute error = 2.546104123816253 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.469999999999949 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.5546411610488 " "
absolute error = 2.5546411610488 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4799999999999478 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.563107505332271 " "
absolute error = 2.563107505332271 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4899999999999467 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.571503763662744 " "
absolute error = 2.571503763662744 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.4999999999999456 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.579830532637258 " "
absolute error = 2.579830532637258 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5099999999999445 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.5880883986844636 " "
absolute error = 2.5880883986844636 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5199999999999434 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.596277938288797 " "
absolute error = 2.596277938288797 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5299999999999423 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.604399718208421 " "
absolute error = 2.604399718208421 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5399999999999412 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6124542956871286 " "
absolute error = 2.6124542956871286 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.54999999999994 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6204422186604006 " "
absolute error = 2.6204422186604006 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.559999999999939 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.628364025955833 " "
absolute error = 2.628364025955833 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.569999999999938 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6362202474880903 " "
absolute error = 2.6362202474880903 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5799999999999368 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6440114044485887 " "
absolute error = 2.6440114044485887 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5899999999999357 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6517380094900562 " "
absolute error = 2.6517380094900562 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.5999999999999346 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6594005669061525 " "
absolute error = 2.6594005669061525 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6099999999999335 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6669995728062967 " "
absolute error = 2.6669995728062967 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6199999999999324 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6745355152858594 " "
absolute error = 2.6745355152858594 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6299999999999313 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.6820088745918644 " "
absolute error = 2.6820088745918644 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6399999999999302 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.689420123284341 " "
absolute error = 2.689420123284341 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.649999999999929 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.696769726393467 " "
absolute error = 2.696769726393467 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.659999999999928 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7040581415726237 " "
absolute error = 2.7040581415726237 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6699999999999269 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7112858192475042 " "
absolute error = 2.7112858192475042 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6799999999999258 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7184532027613835 " "
absolute error = 2.7184532027613835 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6899999999999247 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.725560728516673 " "
absolute error = 2.725560728516673 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.6999999999999236 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7326088261128745 " "
absolute error = 2.7326088261128745 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7099999999999225 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7395979184810444 " "
absolute error = 2.7395979184810444 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7199999999999214 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7465284220148654 " "
absolute error = 2.7465284220148654 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7299999999999203 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7534007466984347 " "
absolute error = 2.7534007466984347 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7399999999999192 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7602152962308644 " "
absolute error = 2.7602152962308644 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.749999999999918 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7669724681477925 " "
absolute error = 2.7669724681477925 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.759999999999917 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.773672653939889 " "
absolute error = 2.773672653939889 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7699999999999159 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.780316239168449 " "
absolute error = 2.780316239168449 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7799999999999148 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.7869036035781627 " "
absolute error = 2.7869036035781627 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7899999999999137 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.793435121207136 " "
absolute error = 2.793435121207136 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.7999999999999126 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.79991116049425 " "
absolute error = 2.79991116049425 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8099999999999115 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8063320843839263 " "
absolute error = 2.8063320843839263 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8199999999999104 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.812698250428382 " "
absolute error = 2.812698250428382 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8299999999999093 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8190100108874465 " "
absolute error = 2.8190100108874465 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8399999999999082 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8252677128259953 " "
absolute error = 2.8252677128259953 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.849999999999907 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.831471698209088 " "
absolute error = 2.831471698209088 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.859999999999906 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8376223039948583 " "
absolute error = 2.8376223039948583 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8699999999999048 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8437198622252344 " "
absolute error = 2.8437198622252344 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8799999999999037 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.849764700114534 " "
absolute error = 2.849764700114534 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8899999999999026 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8557571401360047 " "
absolute error = 2.8557571401360047 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.8999999999999015 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8616975001063643 " "
absolute error = 2.8616975001063643 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9099999999999004 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8675860932683923 " "
absolute error = 2.8675860932683923 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9199999999998993 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8734232283716303 " "
absolute error = 2.8734232283716303 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9299999999998982 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8792092097512394 " "
absolute error = 2.8792092097512394 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9399999999998971 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.884944337405067 " "
absolute error = 2.884944337405067 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.949999999999896 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8906289070689706 " "
absolute error = 2.8906289070689706 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.959999999999895 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.8962632102904458 " "
absolute error = 2.8962632102904458 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9699999999998938 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9018475345006007 " "
absolute error = 2.9018475345006007 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9799999999998927 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9073821630845256 " "
absolute error = 2.9073821630845256 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9899999999998916 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9128673754501 " "
absolute error = 2.9128673754501 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.9999999999998905 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9183034470952744 " "
absolute error = 2.9183034470952744 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0099999999998897 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9236906496738664 " "
absolute error = 2.9236906496738664 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0199999999998886 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9290292510599185 " "
absolute error = 2.9290292510599185 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0299999999998875 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.934319515410643 " "
absolute error = 2.934319515410643 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0399999999998863 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9395617032280033 " "
absolute error = 2.9395617032280033 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0499999999998852 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.944756071418955 " "
absolute error = 2.944756071418955 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.059999999999884 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9499028733543877 " "
absolute error = 2.9499028733543877 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.069999999999883 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.955002358926799 " "
absolute error = 2.955002358926799 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.079999999999882 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.96005477460674 " "
absolute error = 2.96005477460674 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.089999999999881 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.965060363498042 " "
absolute error = 2.965060363498042 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.0999999999998797 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9700193653918885 " "
absolute error = 2.9700193653918885 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1099999999998786 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.974932016819728 " "
absolute error = 2.974932016819728 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1199999999998775 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.979798551105081 " "
absolute error = 2.979798551105081 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1299999999998764 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.9846191984142543 " "
absolute error = 2.9846191984142543 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1399999999998753 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.989394185805994 " "
absolute error = 2.989394185805994 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1499999999998742 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.994123737280114 " "
absolute error = 2.994123737280114 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.159999999999873 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -2.998808073825099 " "
absolute error = 2.998808073825099 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.169999999999872 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.003447413464739 " "
absolute error = 3.003447413464739 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.179999999999871 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.008041971303795 " "
absolute error = 3.008041971303795 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.18999999999987 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.012591959572729 " "
absolute error = 3.012591959572729 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.1999999999998687 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.0170975876715187 " "
absolute error = 3.0170975876715187 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2099999999998676 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.0215590622125856 " "
absolute error = 3.0215590622125856 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2199999999998665 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.0259765870628463 " "
absolute error = 3.0259765870628463 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2299999999998654 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.030350363384914 " "
absolute error = 3.030350363384914 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.2399999999998643 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.0346805896774742 " "
absolute error = 3.0346805896774742 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.249999999999863 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.0389674618148437 " "
absolute error = 3.0389674618148437 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.259999999999862 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.043211173085746 " "
absolute error = 3.043211173085746 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.269999999999861 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.0474119142313087 " "
absolute error = 3.0474119142313087 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 2.27999999999986 " "
y[1] (closed_form) = 0.0 " "
y[1] (numeric) = -3.051569873482306 " "
absolute error = 3.051569873482306 " "
relative error = -1. "%"
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 1.000E-3 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; "
Iterations = 2183
"Total Elapsed Time "= 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 3 Minutes 0 Seconds
"Expected Time Remaining "= 3 Minutes 43 Seconds
"Optimized Time Remaining "= 3 Minutes 43 Seconds
"Expected Total Time "= 6 Minutes 44 Seconds
"Time to Timeout "= 0.0 Seconds
Percent Done = 44.5714285714257 "%"
(%o257) temp/diffeq.tan_sqrt_lin.max