(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 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, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 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, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
array_tmp1
1
temp2], array_tmp1 : array_m1 array_const_3D0 , array_tmp2 : -----------,
1 1 1 1 array_x
1
array_tmp2 array_tmp3
1 1
array_tmp3 : -----------, array_tmp4 : -----------,
1 array_x 1 array_x
1 1
array_tmp4
1
array_tmp5 : -----------, array_tmp6 : array_tmp5 + array_const_0D0 ,
1 array_x 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_m1 array_const_3D0 ,
2 2 1
array_tmp1 - array_tmp2 array_x
2 1 2
array_tmp2 : ----------------------------------,
2 array_x
1
array_tmp2 - array_tmp3 array_x
2 1 2
array_tmp3 : ----------------------------------,
2 array_x
1
array_tmp3 - array_tmp4 array_x
2 1 2
array_tmp4 : ----------------------------------,
2 array_x
1
array_tmp4 - array_tmp5 array_x
2 1 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
2 array_x 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_3D0 ,
3 3 1
array_tmp1 - array_tmp2 array_x
3 2 2
array_tmp2 : ----------------------------------,
3 array_x
1
array_tmp2 - array_tmp3 array_x
3 2 2
array_tmp3 : ----------------------------------,
3 array_x
1
array_tmp3 - array_tmp4 array_x
3 2 2
array_tmp4 : ----------------------------------,
3 array_x
1
array_tmp4 - array_tmp5 array_x
3 2 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
3 array_x 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_m1 array_const_3D0 ,
4 4 1
array_tmp1 - array_tmp2 array_x
4 3 2
array_tmp2 : ----------------------------------,
4 array_x
1
array_tmp2 - array_tmp3 array_x
4 3 2
array_tmp3 : ----------------------------------,
4 array_x
1
array_tmp3 - array_tmp4 array_x
4 3 2
array_tmp4 : ----------------------------------,
4 array_x
1
array_tmp4 - array_tmp5 array_x
4 3 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
4 array_x 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_m1 array_const_3D0 ,
5 5 1
array_tmp1 - array_tmp2 array_x
5 4 2
array_tmp2 : ----------------------------------,
5 array_x
1
array_tmp2 - array_tmp3 array_x
5 4 2
array_tmp3 : ----------------------------------,
5 array_x
1
array_tmp3 - array_tmp4 array_x
5 4 2
array_tmp4 : ----------------------------------,
5 array_x
1
array_tmp4 - array_tmp5 array_x
5 4 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
5 array_x 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_3D0 ,
kkk kkk 1
- ats(kkk, array_x, array_tmp2, 2)
array_tmp2 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp3, 2)
array_tmp3 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp4, 2)
array_tmp4 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp5, 2)
array_tmp5 : ----------------------------------,
kkk array_x
1
array_tmp6 : array_tmp5 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp6 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
array_tmp1
1
temp2], array_tmp1 : array_m1 array_const_3D0 , array_tmp2 : -----------,
1 1 1 1 array_x
1
array_tmp2 array_tmp3
1 1
array_tmp3 : -----------, array_tmp4 : -----------,
1 array_x 1 array_x
1 1
array_tmp4
1
array_tmp5 : -----------, array_tmp6 : array_tmp5 + array_const_0D0 ,
1 array_x 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_m1 array_const_3D0 ,
2 2 1
array_tmp1 - array_tmp2 array_x
2 1 2
array_tmp2 : ----------------------------------,
2 array_x
1
array_tmp2 - array_tmp3 array_x
2 1 2
array_tmp3 : ----------------------------------,
2 array_x
1
array_tmp3 - array_tmp4 array_x
2 1 2
array_tmp4 : ----------------------------------,
2 array_x
1
array_tmp4 - array_tmp5 array_x
2 1 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
2 array_x 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_3D0 ,
3 3 1
array_tmp1 - array_tmp2 array_x
3 2 2
array_tmp2 : ----------------------------------,
3 array_x
1
array_tmp2 - array_tmp3 array_x
3 2 2
array_tmp3 : ----------------------------------,
3 array_x
1
array_tmp3 - array_tmp4 array_x
3 2 2
array_tmp4 : ----------------------------------,
3 array_x
1
array_tmp4 - array_tmp5 array_x
3 2 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
3 array_x 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_m1 array_const_3D0 ,
4 4 1
array_tmp1 - array_tmp2 array_x
4 3 2
array_tmp2 : ----------------------------------,
4 array_x
1
array_tmp2 - array_tmp3 array_x
4 3 2
array_tmp3 : ----------------------------------,
4 array_x
1
array_tmp3 - array_tmp4 array_x
4 3 2
array_tmp4 : ----------------------------------,
4 array_x
1
array_tmp4 - array_tmp5 array_x
4 3 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
4 array_x 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_m1 array_const_3D0 ,
5 5 1
array_tmp1 - array_tmp2 array_x
5 4 2
array_tmp2 : ----------------------------------,
5 array_x
1
array_tmp2 - array_tmp3 array_x
5 4 2
array_tmp3 : ----------------------------------,
5 array_x
1
array_tmp3 - array_tmp4 array_x
5 4 2
array_tmp4 : ----------------------------------,
5 array_x
1
array_tmp4 - array_tmp5 array_x
5 4 2
array_tmp5 : ----------------------------------, array_tmp6 : array_tmp5 ,
5 array_x 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_3D0 ,
kkk kkk 1
- ats(kkk, array_x, array_tmp2, 2)
array_tmp2 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp3, 2)
array_tmp3 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp4, 2)
array_tmp4 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp5, 2)
array_tmp5 : ----------------------------------,
kkk array_x
1
array_tmp6 : array_tmp5 , order_d : 1,
kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp6 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) 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))
(%o17) 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))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
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,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
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,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i28) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o28) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o35) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o38) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) 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(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
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,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o55) 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(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
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,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
1.0
---
x
---
x
(%i56) exact_soln_y(x) := block(---)
x
1.0
---
x
---
x
(%o56) exact_soln_y(x) := block(---)
x
(%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-201, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, 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/sing5postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:-0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
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, " (1.0/x/x/x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, if glob_max_h < glob_h
then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
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, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no 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_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(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(),
glob_current_iter : 1 + glob_current_iter, atomall(),
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 : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(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 ) = m1 * 3.0 / x / x / x / x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T19:14:31-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing5"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "sing5 diffeq.max"),
logitem_str(html_log_file, "sing5 maxima results"
), logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-201, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, 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/sing5postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:-0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
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, " (1.0/x/x/x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 30, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms),
array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_tmp6, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term),
term
array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, if glob_max_h < glob_h
then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
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, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/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,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no 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_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(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(),
glob_current_iter : 1 + glob_current_iter, atomall(),
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 : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(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 ) = m1 * 3.0 / x / x / x / x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T19:14:31-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing5"),
logitem_str(html_log_file,
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "sing5 diffeq.max"),
logitem_str(html_log_file, "sing5 maxima results"
), logitem_str(html_log_file, "All Tests - All Languages"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i58) main()
"##############ECHO OF PROBLEM#################"
"##############temp/sing5postode.ode#################"
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-1.0,"
"x_end:-0.7,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (1.0/x/x/x) "
"));"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 0.30000000000000004 ""
estimated_steps = 300.00000000000006 ""
step_error = 3.3333333333333330000000000000E-13 ""
est_needed_step_err = 3.3333333333333330000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 4.0404069204059845000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 ""
max_value3 = 4.0404069204059845000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 ""
value3 = 4.0404069204059845000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -1. " "
y[1] (analytic) = -1. " "
y[1] (numeric) = -1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9985775248933194 " "
Order of pole = 625.0355618776704 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.999 " "
y[1] (analytic) = -1.003006010015021 " "
y[1] (numeric) = -1.003006010015021 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9975789473684217 " "
Order of pole = 625.0355618776675 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.998 " "
y[1] (analytic) = -1.0060240802406737 " "
y[1] (numeric) = -1.006024080240674 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.20715000054383400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9965803698435306 " "
Order of pole = 625.0355618776688 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.997 " "
y[1] (analytic) = -1.0090542712201236 " "
y[1] (numeric) = -1.0090542712201236 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9955817923186331 " "
Order of pole = 625.0355618776664 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.996 " "
y[1] (analytic) = -1.0120966438616192 " "
y[1] (numeric) = -1.0120966438616195 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.193907135961126500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9945832147937446 " "
Order of pole = 625.0355618776694 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.995 " "
y[1] (analytic) = -1.0151512594410652 " "
y[1] (numeric) = -1.0151512594410654 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.187305614409496300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9935846372688499 " "
Order of pole = 625.0355618776684 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.994 " "
y[1] (analytic) = -1.0182181796046124 " "
y[1] (numeric) = -1.0182181796046126 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.1807173489207800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9925860597439539 " "
Order of pole = 625.0355618776666 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.993 " "
y[1] (analytic) = -1.021297466371271 " "
y[1] (numeric) = -1.021297466371271 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9915874822190683 " "
Order of pole = 625.0355618776717 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.992 " "
y[1] (analytic) = -1.0243891821355442 " "
y[1] (numeric) = -1.0243891821355442 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.8779087045642053 " "
Order of pole = 2.157385381451604200000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.991 " "
y[1] (analytic) = -1.0274933896700835 " "
y[1] (numeric) = -1.0274933896700833 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.161031955605352600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9895903271692725 " "
Order of pole = 625.0355618776659 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.99 " "
y[1] (analytic) = -1.0306101521283648 " "
y[1] (numeric) = -1.0306101521283644 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.30899316228305800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9885917496443778 " "
Order of pole = 625.0355618776649 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.989 " "
y[1] (analytic) = -1.0337395330473862 " "
y[1] (numeric) = -1.0337395330473858 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.295948792254477600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9875931721194896 " "
Order of pole = 625.0355618776682 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.988 " "
y[1] (analytic) = -1.036881596350389 " "
y[1] (numeric) = -1.0368815963503888 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.141465387239805000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9865945945945982 " "
Order of pole = 625.0355618776695 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.987 " "
y[1] (analytic) = -1.0400364063496002 " "
y[1] (numeric) = -1.0400364063495995 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.4049086234696500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.985596017069705 " "
Order of pole = 625.0355618776696 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.986 " "
y[1] (analytic) = -1.0432040277489936 " "
y[1] (numeric) = -1.0432040277489931 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.256973689109599400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9845974395448097 " "
Order of pole = 625.0355618776681 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.985 " "
y[1] (analytic) = -1.046384525647081 " "
y[1] (numeric) = -1.0463845256470805 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.24403456822375350000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9835988620199213 " "
Order of pole = 625.0355618776715 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.984 " "
y[1] (analytic) = -1.0495779655397188 " "
y[1] (numeric) = -1.0495779655397184 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.23112169301020900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9826002844950267 " "
Order of pole = 625.0355618776706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.983 " "
y[1] (analytic) = -1.0527844133229418 " "
y[1] (numeric) = -1.0527844133229411 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.3273525552354200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9816017069701236 " "
Order of pole = 625.0355618776642 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.982 " "
y[1] (analytic) = -1.056003935295817 " "
y[1] (numeric) = -1.0560039352958166 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.20537457301861700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9806031294452271 " "
Order of pole = 625.0355618776622 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.981 " "
y[1] (analytic) = -1.0592365981633254 " "
y[1] (numeric) = -1.0592365981633247 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.28881041242479500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9796045519203406 " "
Order of pole = 625.0355618776667 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.98 " "
y[1] (analytic) = -1.062482469039261 " "
y[1] (numeric) = -1.06248246903926 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.35946423194400200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9786059743954543 " "
Order of pole = 625.0355618776712 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.979 " "
y[1] (analytic) = -1.0657416154491584 " "
y[1] (numeric) = -1.0657416154491577 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.25042510415951800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.977607396870561 " "
Order of pole = 625.0355618776712 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.978 " "
y[1] (analytic) = -1.0690141053332438 " "
y[1] (numeric) = -1.0690141053332431 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.23129116306131500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9766088193456626 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.977 " "
y[1] (analytic) = -1.0723000070494075 " "
y[1] (numeric) = -1.0723000070494069 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.21219631069536000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9756102418207742 " "
Order of pole = 625.0355618776711 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.976 " "
y[1] (analytic) = -1.0755993893762033 " "
y[1] (numeric) = -1.0755993893762026 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.1931405070936310000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9746116642958691 " "
Order of pole = 625.0355618776633 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.975 " "
y[1] (analytic) = -1.078912321515872 " "
y[1] (numeric) = -1.0789123215158711 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.23216494971745500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9736130867709873 " "
Order of pole = 625.0355618776711 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.974 " "
y[1] (analytic) = -1.0822388730973884 " "
y[1] (numeric) = -1.0822388730973878 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.1551458863107200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9726145092460965 " "
Order of pole = 625.0355618776725 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.973 " "
y[1] (analytic) = -1.0855791141795361 " "
y[1] (numeric) = -1.0855791141795357 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.090804659462321500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9716159317211981 " "
Order of pole = 625.0355618776691 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.972 " "
y[1] (analytic) = -1.088933115254005 " "
y[1] (numeric) = -1.0889331152540045 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.07820465397890130000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.970617354196296 " "
Order of pole = 625.0355618776634 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.971 " "
y[1] (analytic) = -1.0923009472485155 " "
y[1] (numeric) = -1.0923009472485148 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.09844582166729700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9696187766714119 " "
Order of pole = 625.0355618776695 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.97 " "
y[1] (analytic) = -1.0956826815299676 " "
y[1] (numeric) = -1.095682681529967 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 6.07962347132229300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9686201991465162 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.969 " "
y[1] (analytic) = -1.0990783899076189 " "
y[1] (numeric) = -1.099078389907618 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.08111985328707500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9676216216216171 " "
Order of pole = 625.0355618776642 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.968 " "
y[1] (analytic) = -1.1024881446362844 " "
y[1] (numeric) = -1.1024881446362833 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.00701583960471880000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9666230440967262 " "
Order of pole = 625.0355618776657 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.967 " "
y[1] (analytic) = -1.1059120184195663 " "
y[1] (numeric) = -1.1059120184195654 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 8.03118516579104400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9656244665718473 " "
Order of pole = 625.0355618776754 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.966 " "
y[1] (analytic) = -1.1093500844131106 " "
y[1] (numeric) = -1.1093500844131094 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 1.00078689335703060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9646258890469448 " "
Order of pole = 625.0355618776692 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.965 " "
y[1] (analytic) = -1.1128024162278867 " "
y[1] (numeric) = -1.1128024162278853 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.19721849101139780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9636273115220475 " "
Order of pole = 625.0355618776666 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.964 " "
y[1] (analytic) = -1.1162690879334993 " "
y[1] (numeric) = -1.116269087933498 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.19350042382393410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9626287339971563 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.963 " "
y[1] (analytic) = -1.1197501740615254 " "
y[1] (numeric) = -1.1197501740615243 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.91491718727033300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9616301564722664 " "
Order of pole = 625.0355618776703 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.962 " "
y[1] (analytic) = -1.1232457496088792 " "
y[1] (numeric) = -1.1232457496088781 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.88406165802757400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9606315789473703 " "
Order of pole = 625.0355618776684 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.961 " "
y[1] (analytic) = -1.1267558900412045 " "
y[1] (numeric) = -1.1267558900412034 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.85327021085779900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9596330014224815 " "
Order of pole = 625.0355618776714 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.96 " "
y[1] (analytic) = -1.1302806712962965 " "
y[1] (numeric) = -1.1302806712962954 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.82254277914762400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.713732016703418 " "
Order of pole = 1.905320345940708600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.959 " "
y[1] (analytic) = -1.1338201697875523 " "
y[1] (numeric) = -1.1338201697875514 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.83350343702693400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9576358463726969 " "
Order of pole = 625.0355618776726 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.958 " "
y[1] (analytic) = -1.1373744624074493 " "
y[1] (numeric) = -1.1373744624074484 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.80902375652203700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9566372688478023 " "
Order of pole = 625.035561877672 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.957 " "
y[1] (analytic) = -1.1409436265310529 " "
y[1] (numeric) = -1.1409436265310517 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.73074391064088100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.7173575970119936 " "
Order of pole = 2.246558494789496800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.956 " "
y[1] (analytic) = -1.1445277400195533 " "
y[1] (numeric) = -1.1445277400195524 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.76021749970823400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9546401137980105 " "
Order of pole = 625.0355618776683 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.955 " "
y[1] (analytic) = -1.1481268812238343 " "
y[1] (numeric) = -1.1481268812238334 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.73589081681791400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9536415362731239 " "
Order of pole = 625.0355618776729 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.954 " "
y[1] (analytic) = -1.1517411289880684 " "
y[1] (numeric) = -1.1517411289880675 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.71161502655104400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9526429587482178 " "
Order of pole = 625.0355618776645 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.953 " "
y[1] (analytic) = -1.1553705626533444 " "
y[1] (numeric) = -1.1553705626533433 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.60923759452114500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9516443812233322 " "
Order of pole = 625.0355618776695 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.952 " "
y[1] (analytic) = -1.159015262061325 " "
y[1] (numeric) = -1.1590152620613239 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.57901988840603500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9506458036984303 " "
Order of pole = 625.0355618776638 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.951 " "
y[1] (analytic) = -1.1626753075579357 " "
y[1] (numeric) = -1.1626753075579348 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.63909247858407400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9496472261735496 " "
Order of pole = 625.0355618776722 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.95 " "
y[1] (analytic) = -1.1663507799970843 " "
y[1] (numeric) = -1.1663507799970834 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.61501972590394900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9486486486486492 " "
Order of pole = 625.0355618776675 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.949 " "
y[1] (analytic) = -1.170041760744411 " "
y[1] (numeric) = -1.17004176074441 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.59099759939374400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9476500711237656 " "
Order of pole = 625.0355618776741 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.948 " "
y[1] (analytic) = -1.1737483316810713 " "
y[1] (numeric) = -1.1737483316810706 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.675269534322069000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9466514935988692 " "
Order of pole = 625.0355618776721 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.947 " "
y[1] (analytic) = -1.177470575207552 " "
y[1] (numeric) = -1.1774705752075512 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.54310501172028500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5653393181719961 " "
Order of pole = 1.284661266254261000000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.946 " "
y[1] (analytic) = -1.1812085742475156 " "
y[1] (numeric) = -1.181208574247515 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.63942583298171500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9446543385490715 " "
Order of pole = 625.0355618776645 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.945 " "
y[1] (analytic) = -1.1849624122516822 " "
y[1] (numeric) = -1.184962412251681 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.36926786154756800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.6284605934032496 " "
Order of pole = 1.168842800325364800000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.944 " "
y[1] (analytic) = -1.1887321732017395 " "
y[1] (numeric) = -1.1887321732017384 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.33955561777110900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9426571834992894 " "
Order of pole = 625.0355618776676 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.943 " "
y[1] (analytic) = -1.1925179416142908 " "
y[1] (numeric) = -1.1925179416142897 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.30990625702676500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.941658605974399 " "
Order of pole = 625.0355618776696 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.942 " "
y[1] (analytic) = -1.1963198025448327 " "
y[1] (numeric) = -1.1963198025448316 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.28031971270115600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.940660028449502 " "
Order of pole = 625.0355618776671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.941 " "
y[1] (analytic) = -1.2001378415917687 " "
y[1] (numeric) = -1.2001378415917676 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.25079591818089600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9396614509246068 " "
Order of pole = 625.0355618776658 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.94 " "
y[1] (analytic) = -1.2039721449004557 " "
y[1] (numeric) = -1.2039721449004548 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.37706784548208700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9386628733997168 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.939 " "
y[1] (analytic) = -1.207822799167287 " "
y[1] (numeric) = -1.207822799167286 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.35354904968232900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.937664295874829 " "
Order of pole = 625.0355618776719 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.938 " "
y[1] (analytic) = -1.2116898916438077 " "
y[1] (numeric) = -1.2116898916438066 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.16260036731841800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9366657183499294 " "
Order of pole = 625.0355618776674 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9369999999999999 " "
y[1] (analytic) = -1.215573510140867 " "
y[1] (numeric) = -1.2155735101408658 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.1333269058857500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9356671408250354 " "
Order of pole = 625.0355618776671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9359999999999999 " "
y[1] (analytic) = -1.2194737430328053 " "
y[1] (numeric) = -1.2194737430328042 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.10411586119153000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9346685633001441 " "
Order of pole = 625.0355618776684 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9349999999999999 " "
y[1] (analytic) = -1.2233906792616778 " "
y[1] (numeric) = -1.2233906792616767 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.07496716662237100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9336699857752502 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9339999999999999 " "
y[1] (analytic) = -1.2273244083415136 " "
y[1] (numeric) = -1.2273244083415122 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.08550569066778710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5177136997230768 " "
Order of pole = 1.374012015276093700000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9329999999999999 " "
y[1] (analytic) = -1.231275020362611 " "
y[1] (numeric) = -1.2312750203626097 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.08202278736868590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9316728307254671 " "
Order of pole = 625.0355618776704 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9319999999999999 " "
y[1] (analytic) = -1.2352426059958719 " "
y[1] (numeric) = -1.2352426059958705 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.07854734210377470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.930674253200567 " "
Order of pole = 625.0355618776657 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9309999999999999 " "
y[1] (analytic) = -1.2392272564971698 " "
y[1] (numeric) = -1.2392272564971687 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.95899455732873700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.22336111321316826 " "
Order of pole = 2.9682922786378185000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9299999999999999 " "
y[1] (analytic) = -1.2432290637117602 " "
y[1] (numeric) = -1.243229063711759 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.07161879370210020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9286770981507878 " "
Order of pole = 625.035561877671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9289999999999999 " "
y[1] (analytic) = -1.247248120078723 " "
y[1] (numeric) = -1.247248120078722 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.90138062148437700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9276785206258896 " "
Order of pole = 625.0355618776675 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9279999999999999 " "
y[1] (analytic) = -1.2512845186354509 " "
y[1] (numeric) = -1.2512845186354493 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.24217331176623660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.2742587221253 " "
Order of pole = 4.352074256530613600000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9269999999999999 " "
y[1] (analytic) = -1.2553383530221671 " "
y[1] (numeric) = -1.2553383530221656 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.23816199093518240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9256813655760995 " "
Order of pole = 625.0355618776653 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9259999999999999 " "
y[1] (analytic) = -1.259409717486492 " "
y[1] (numeric) = -1.2594097174864907 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.05785084159037960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9246827880512085 " "
Order of pole = 625.0355618776667 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9249999999999999 " "
y[1] (analytic) = -1.2634987068880423 " "
y[1] (numeric) = -1.263498706888041 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 1.05442737874383840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9236842105263189 " "
Order of pole = 625.0355618776692 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9239999999999999 " "
y[1] (analytic) = -1.2676054167030726 " "
y[1] (numeric) = -1.267605416703071 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.22617986164641440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9226856330014197 " "
Order of pole = 625.0355618776651 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9229999999999999 " "
y[1] (analytic) = -1.2717299430291567 " "
y[1] (numeric) = -1.271729943029155 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.22220306519871240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9216870554765285 " "
Order of pole = 625.0355618776669 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9219999999999999 " "
y[1] (analytic) = -1.275872382589911 " "
y[1] (numeric) = -1.2758723825899094 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.21823487653216480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.6404061466367182 " "
Order of pole = 9.166001291305292000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9209999999999999 " "
y[1] (analytic) = -1.2800328327397572 " "
y[1] (numeric) = -1.2800328327397557 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.21427528632089820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9196899004267483 " "
Order of pole = 625.0355618776711 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9199999999999999 " "
y[1] (analytic) = -1.2842113914687272 " "
y[1] (numeric) = -1.2842113914687254 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.38322775455890200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9186913229018489 " "
Order of pole = 625.0355618776669 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9189999999999999 " "
y[1] (analytic) = -1.288408157407309 " "
y[1] (numeric) = -1.2884081574073072 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.37872213024081650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9176927453769569 " "
Order of pole = 625.0355618776678 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9179999999999999 " "
y[1] (analytic) = -1.292623229831337 " "
y[1] (numeric) = -1.2926232298313354 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.2024480131600510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9166941678520661 " "
Order of pole = 625.0355618776696 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9169999999999999 " "
y[1] (analytic) = -1.2968567086669234 " "
y[1] (numeric) = -1.2968567086669216 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.36974025544134260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9156955903271763 " "
Order of pole = 625.0355618776721 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9159999999999999 " "
y[1] (analytic) = -1.301108694495432 " "
y[1] (numeric) = -1.3011086944954302 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.36526398364367170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9146970128022833 " "
Order of pole = 625.0355618776723 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9149999999999999 " "
y[1] (analytic) = -1.3053792885584978 " "
y[1] (numeric) = -1.3053792885584958 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.53089715904108860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9136984352773887 " "
Order of pole = 625.0355618776714 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9139999999999999 " "
y[1] (analytic) = -1.309668592763088 " "
y[1] (numeric) = -1.3096685927630862 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.35634071796175680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9126998577524883 " "
Order of pole = 625.0355618776663 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9129999999999999 " "
y[1] (analytic) = -1.3139767096866104 " "
y[1] (numeric) = -1.3139767096866086 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.35189370276123070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9117012802276016 " "
Order of pole = 625.035561877671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9119999999999999 " "
y[1] (analytic) = -1.3183037425820634 " "
y[1] (numeric) = -1.3183037425820614 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.51588847074890450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.8890324279211224 " "
Order of pole = 8.705924869900628000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9109999999999999 " "
y[1] (analytic) = -1.3226497953832332 " "
y[1] (numeric) = -1.3226497953832312 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.51090746114412800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9097041251778136 " "
Order of pole = 625.0355618776701 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9099999999999999 " "
y[1] (analytic) = -1.3270149727099374 " "
y[1] (numeric) = -1.3270149727099354 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.50593737480164660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9087055476529172 " "
Order of pole = 625.0355618776679 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9089999999999999 " "
y[1] (analytic) = -1.3313993798733124 " "
y[1] (numeric) = -1.3313993798733104 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.50097819973105060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9077069701280217 " "
Order of pole = 625.0355618776665 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9079999999999999 " "
y[1] (analytic) = -1.3358031228811493 " "
y[1] (numeric) = -1.3358031228811473 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.49602992394193250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9067083926031332 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9069999999999999 " "
y[1] (analytic) = -1.3402263084432773 " "
y[1] (numeric) = -1.3402263084432753 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.4910925354438830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9057098150782356 " "
Order of pole = 625.0355618776667 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9059999999999999 " "
y[1] (analytic) = -1.3446690439769928 " "
y[1] (numeric) = -1.3446690439769904 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.8164251383012692000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9047112375533408 " "
Order of pole = 625.0355618776658 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9049999999999999 " "
y[1] (analytic) = -1.349131437612537 " "
y[1] (numeric) = -1.3491314376125345 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.81041712177254450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.903712660028455 " "
Order of pole = 625.0355618776711 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9039999999999999 " "
y[1] (analytic) = -1.3536135981986246 " "
y[1] (numeric) = -1.353613598198622 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.96846076505607840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9027140825035564 " "
Order of pole = 625.0355618776674 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9029999999999999 " "
y[1] (analytic) = -1.3581156353080173 " "
y[1] (numeric) = -1.3581156353080148 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.7984408622329082000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.27163830700354874 " "
Order of pole = 1.50954804212233280000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9019999999999999 " "
y[1] (analytic) = -1.3626376592431517 " "
y[1] (numeric) = -1.3626376592431488 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.11837669716885450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9007169274537714 " "
Order of pole = 625.0355618776683 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9009999999999999 " "
y[1] (analytic) = -1.367179781041811 " "
y[1] (numeric) = -1.367179781041808 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.11133890659631560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.762594405895857 " "
Order of pole = 3.514699642437335600000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8999999999999999 " "
y[1] (analytic) = -1.3717421124828535 " "
y[1] (numeric) = -1.3717421124828508 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.94244620388417360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8987197724039871 " "
Order of pole = 625.0355618776701 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8989999999999999 " "
y[1] (analytic) = -1.3763247660919893 " "
y[1] (numeric) = -1.3763247660919864 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.09731012268399240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8977211948790955 " "
Order of pole = 625.0355618776713 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8979999999999999 " "
y[1] (analytic) = -1.3809278551476063 " "
y[1] (numeric) = -1.3809278551476034 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.090319094705250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8967226173542 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8969999999999999 " "
y[1] (analytic) = -1.3855514936866526 " "
y[1] (numeric) = -1.3855514936866498 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.08334361961881510000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.895724039829305 " "
Order of pole = 625.0355618776687 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8959999999999999 " "
y[1] (analytic) = -1.3901957965105687 " "
y[1] (numeric) = -1.390195796510566 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.91666185855865480000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.894725462304412 " "
Order of pole = 625.0355618776687 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8949999999999999 " "
y[1] (analytic) = -1.3948608791912742 " "
y[1] (numeric) = -1.394860879191271 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.22862689414071640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8937268847795223 " "
Order of pole = 625.0355618776715 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8939999999999999 " "
y[1] (analytic) = -1.3995468580772046 " "
y[1] (numeric) = -1.3995468580772017 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.06251033851856340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.892728307254621 " "
Order of pole = 625.0355618776657 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8929999999999999 " "
y[1] (analytic) = -1.4042538502994093 " "
y[1] (numeric) = -1.4042538502994062 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.2137197404070710000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8917297297297344 " "
Order of pole = 625.0355618776706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8919999999999999 " "
y[1] (analytic) = -1.408981973777696 " "
y[1] (numeric) = -1.4089819737776932 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.04869893138948040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8907311522048326 " "
Order of pole = 625.0355618776645 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8909999999999999 " "
y[1] (analytic) = -1.413731347226838 " "
y[1] (numeric) = -1.413731347226835 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.19887921071304420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.889732574679951 " "
Order of pole = 625.0355618776728 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8899999999999999 " "
y[1] (analytic) = -1.4185020901628302 " "
y[1] (numeric) = -1.4185020901628271 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.1914838832515210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8887339971550573 " "
Order of pole = 625.0355618776726 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8889999999999999 " "
y[1] (analytic) = -1.423294322909208 " "
y[1] (numeric) = -1.423294322909205 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.18410515584466170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.7303624429616864 " "
Order of pole = 2.87290191636202500000000000E-11 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8879999999999999 " "
y[1] (analytic) = -1.428108166603419 " "
y[1] (numeric) = -1.4281081666034159 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.17674300984071980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8867368421052652 " "
Order of pole = 625.0355618776686 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8869999999999999 " "
y[1] (analytic) = -1.4329437432032528 " "
y[1] (numeric) = -1.4329437432032495 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.32435438562994450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8857382645803719 " "
Order of pole = 625.0355618776687 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8859999999999999 " "
y[1] (analytic) = -1.4378011754933304 " "
y[1] (numeric) = -1.437801175493327 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.31650184367992920000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8847396870554756 " "
Order of pole = 625.0355618776665 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8849999999999999 " "
y[1] (analytic) = -1.442680587091652 " "
y[1] (numeric) = -1.4426805870916486 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.3086670075667110000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8837411095305945 " "
Order of pole = 625.0355618776753 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8839999999999999 " "
y[1] (analytic) = -1.4475821024562023 " "
y[1] (numeric) = -1.4475821024561988 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.45423984779335900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8827425320056963 " "
Order of pole = 625.0355618776719 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8829999999999999 " "
y[1] (analytic) = -1.4525058468916177 " "
y[1] (numeric) = -1.4525058468916143 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.2930503729146060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8817439544808061 " "
Order of pole = 625.0355618776741 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8819999999999999 " "
y[1] (analytic) = -1.4574519465559141 " "
y[1] (numeric) = -1.4574519465559104 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.58997100566204950000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.880745376955907 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8809999999999999 " "
y[1] (analytic) = -1.4624205284672733 " "
y[1] (numeric) = -1.4624205284672696 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.5811715647083827000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.4107985716468478 " "
Order of pole = 2.291500322826323000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799999999999999 " "
y[1] (analytic) = -1.4674117205108945 " "
y[1] (numeric) = -1.467411720510891 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.42107489611953440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.878748221906119 " "
Order of pole = 625.0355618776688 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8789999999999999 " "
y[1] (analytic) = -1.4724256514459073 " "
y[1] (numeric) = -1.4724256514459035 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.56363252026936440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8777496443812348 " "
Order of pole = 625.0355618776755 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8779999999999999 " "
y[1] (analytic) = -1.477462450912345 " "
y[1] (numeric) = -1.477462450912341 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.70518068745673000000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8767510668563356 " "
Order of pole = 625.0355618776714 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8769999999999999 " "
y[1] (analytic) = -1.4825222494381851 " "
y[1] (numeric) = -1.4825222494381813 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.5461731081310990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8757524893314363 " "
Order of pole = 625.0355618776671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8759999999999999 " "
y[1] (analytic) = -1.4876051784464532 " "
y[1] (numeric) = -1.4876051784464495 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.5374732075533750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8747539118065438 " "
Order of pole = 625.0355618776675 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8749999999999999 " "
y[1] (analytic) = -1.4927113702623913 " "
y[1] (numeric) = -1.4927113702623873 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.67754568517020060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.873755334281659 " "
Order of pole = 625.0355618776737 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8739999999999999 " "
y[1] (analytic) = -1.4978409581206908 " "
y[1] (numeric) = -1.4978409581206868 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.66837601614611200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8727567567567622 " "
Order of pole = 625.0355618776712 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8729999999999999 " "
y[1] (analytic) = -1.5029940761727956 " "
y[1] (numeric) = -1.5029940761727913 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.8069621567095010000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.871758179231861 " "
Order of pole = 625.0355618776654 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8719999999999999 " "
y[1] (analytic) = -1.5081708594942669 " "
y[1] (numeric) = -1.5081708594942627 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.79732728358794540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8707596017069776 " "
Order of pole = 625.0355618776725 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8709999999999999 " "
y[1] (analytic) = -1.5133714440922208 " "
y[1] (numeric) = -1.5133714440922166 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.78771448347647670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8697610241820827 " "
Order of pole = 625.0355618776715 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8699999999999999 " "
y[1] (analytic) = -1.5185959669128315 " "
y[1] (numeric) = -1.5185959669128275 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.63190669258506150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8687624466571845 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8689999999999999 " "
y[1] (analytic) = -1.5238445658489046 " "
y[1] (numeric) = -1.5238445658489004 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.7685550010314570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.867763869132294 " "
Order of pole = 625.0355618776699 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8679999999999999 " "
y[1] (analytic) = -1.5291173797475186 " "
y[1] (numeric) = -1.5291173797475144 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.75900826807173760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8667652916074057 " "
Order of pole = 625.0355618776737 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8669999999999999 " "
y[1] (analytic) = -1.5344145484177403 " "
y[1] (numeric) = -1.5344145484177363 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.6047738486134614000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8657667140825116 " "
Order of pole = 625.0355618776731 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8659999999999999 " "
y[1] (analytic) = -1.539736212638409 " "
y[1] (numeric) = -1.5397362126384049 " "
absolute error = 4.218847493575595000000000000000E-15 " "
relative error = 2.73998069211245250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8647681365576182 " "
Order of pole = 625.0355618776731 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8649999999999999 " "
y[1] (analytic) = -1.5450825141659932 " "
y[1] (numeric) = -1.5450825141659887 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.87421031419654470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8637695590327211 " "
Order of pole = 625.0355618776701 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8639999999999999 " "
y[1] (analytic) = -1.5504535957425198 " "
y[1] (numeric) = -1.5504535957425152 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.0074661481194180000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8627709815078206 " "
Order of pole = 625.035561877665 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8629999999999999 " "
y[1] (analytic) = -1.5558496011035787 " "
y[1] (numeric) = -1.555849601103574 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 2.99703563899633540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8617724039829329 " "
Order of pole = 625.035561877669 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8619999999999999 " "
y[1] (analytic) = -1.5612706749863998 " "
y[1] (numeric) = -1.5612706749863954 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.8444088329138130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8607738264580403 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8609999999999999 " "
y[1] (analytic) = -1.5667169631380067 " "
y[1] (numeric) = -1.5667169631380022 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.83452097793457260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8597752489331484 " "
Order of pole = 625.0355618776706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8599999999999999 " "
y[1] (analytic) = -1.5721886123234439 " "
y[1] (numeric) = -1.5721886123234394 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.8246560646039130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.858776671408251 " "
Order of pole = 625.0355618776676 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8589999999999999 " "
y[1] (analytic) = -1.5776857703340836 " "
y[1] (numeric) = -1.5776857703340792 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 2.8148140662764820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8577780938833617 " "
Order of pole = 625.0355618776707 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8579999999999999 " "
y[1] (analytic) = -1.5832085859960092 " "
y[1] (numeric) = -1.5832085859960043 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.0854944519376190000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8567795163584578 " "
Order of pole = 625.0355618776629 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8569999999999999 " "
y[1] (analytic) = -1.5887572091784743 " "
y[1] (numeric) = -1.5887572091784694 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.0747185788548830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8557809388335721 " "
Order of pole = 625.0355618776686 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8559999999999999 " "
y[1] (analytic) = -1.5943317908024461 " "
y[1] (numeric) = -1.5943317908024413 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.0639678243460350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8547823613086768 " "
Order of pole = 625.0355618776671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8549999999999999 " "
y[1] (analytic) = -1.5999324828492243 " "
y[1] (numeric) = -1.5999324828492196 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 2.9144584245965877000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8537837837837884 " "
Order of pole = 625.0355618776706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8539999999999999 " "
y[1] (analytic) = -1.6055594383691438 " "
y[1] (numeric) = -1.605559438369139 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.042541553810450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8527852062588909 " "
Order of pole = 625.0355618776675 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8529999999999999 " "
y[1] (analytic) = -1.6112128114903561 " "
y[1] (numeric) = -1.611212811490351 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.16967806912593460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8517866287339996 " "
Order of pole = 625.035561877669 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8519999999999999 " "
y[1] (analytic) = -1.616892757427696 " "
y[1] (numeric) = -1.6168927574276908 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.15854337884502230000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8507880512091083 " "
Order of pole = 625.0355618776706 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8509999999999999 " "
y[1] (analytic) = -1.6225994324916304 " "
y[1] (numeric) = -1.6225994324916255 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.0105898045640330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8497894736842112 " "
Order of pole = 625.0355618776678 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8499999999999999 " "
y[1] (analytic) = -1.6283329940972937 " "
y[1] (numeric) = -1.6283329940972886 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.136352288990450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8487908961593156 " "
Order of pole = 625.0355618776659 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8489999999999999 " "
y[1] (analytic) = -1.6340936007736029 " "
y[1] (numeric) = -1.6340936007735978 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.1252958281324783000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8477923186344266 " "
Order of pole = 625.0355618776694 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8479999999999999 " "
y[1] (analytic) = -1.6398814121724654 " "
y[1] (numeric) = -1.63988141217246 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.2496682251803560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8467937411095362 " "
Order of pole = 625.0355618776714 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8469999999999999 " "
y[1] (analytic) = -1.645696589078069 " "
y[1] (numeric) = -1.645696589078064 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.1032609213443846000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.845795163584641 " "
Order of pole = 625.03556187767 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8459999999999999 " "
y[1] (analytic) = -1.6515392934162634 " "
y[1] (numeric) = -1.6515392934162583 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 3.09228241412995300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8447965860597492 " "
Order of pole = 625.0355618776712 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8449999999999999 " "
y[1] (analytic) = -1.6574096882640281 " "
y[1] (numeric) = -1.6574096882640224 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.48324241672415050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8437980085348519 " "
Order of pole = 625.0355618776681 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8439999999999999 " "
y[1] (analytic) = -1.6633079378590292 " "
y[1] (numeric) = -1.6633079378590236 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.3373947161408050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8427994310099657 " "
Order of pole = 625.0355618776733 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8429999999999999 " "
y[1] (analytic) = -1.6692342076092725 " "
y[1] (numeric) = -1.6692342076092672 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 3.19252414904269600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8418008534850703 " "
Order of pole = 625.0355618776722 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8419999999999999 " "
y[1] (analytic) = -1.6751886641028426 " "
y[1] (numeric) = -1.675188664102837 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.313725338571769700000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8408022759601792 " "
Order of pole = 625.0355618776738 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8409999999999999 " "
y[1] (analytic) = -1.681171475117736 " "
y[1] (numeric) = -1.6811714751177302 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.434010042102640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8398036984352854 " "
Order of pole = 625.0355618776733 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8399999999999999 " "
y[1] (analytic) = -1.68718280963179 " "
y[1] (numeric) = -1.6871828096317845 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.29016813793714200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8388051209103833 " "
Order of pole = 625.0355618776666 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8389999999999999 " "
y[1] (analytic) = -1.693222837832706 " "
y[1] (numeric) = -1.6932228378327006 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.27843152070350500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8378065433854948 " "
Order of pole = 625.0355618776704 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8379999999999999 " "
y[1] (analytic) = -1.6992917311281663 " "
y[1] (numeric) = -1.6992917311281608 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 3.26672284778339700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8368079658605988 " "
Order of pole = 625.0355618776682 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8369999999999999 " "
y[1] (analytic) = -1.70538966215605 " "
y[1] (numeric) = -1.7053896621560443 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.38524376930493360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8358093883357091 " "
Order of pole = 625.035561877671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8359999999999999 " "
y[1] (analytic) = -1.7115168047947453 " "
y[1] (numeric) = -1.7115168047947396 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.37312476972328860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8348108108108079 " "
Order of pole = 625.035561877665 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8349999999999999 " "
y[1] (analytic) = -1.7176733341735626 " "
y[1] (numeric) = -1.7176733341735568 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 3.36103472831083940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5888924531332838 " "
Order of pole = 4.305888978706207000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8339999999999999 " "
y[1] (analytic) = -1.7238594266832459 " "
y[1] (numeric) = -1.7238594266832399 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.47778028775280600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8328136557610245 " "
Order of pole = 625.0355618776674 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8329999999999999 " "
y[1] (analytic) = -1.7300752599865847 " "
y[1] (numeric) = -1.7300752599865787 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.46528528072376050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8318150782361361 " "
Order of pole = 625.0355618776713 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8319999999999999 " "
y[1] (analytic) = -1.7363210130291316 " "
y[1] (numeric) = -1.7363210130291253 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 3.5807024687528590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8308165007112447 " "
Order of pole = 625.0355618776726 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8309999999999998 " "
y[1] (analytic) = -1.7425968660500182 " "
y[1] (numeric) = -1.7425968660500117 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.69522846521696870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8298179231863453 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8299999999999998 " "
y[1] (analytic) = -1.7489030005928792 " "
y[1] (numeric) = -1.7489030005928727 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.68190433697179500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8288193456614577 " "
Order of pole = 625.0355618776723 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8289999999999998 " "
y[1] (analytic) = -1.7552395995168808 " "
y[1] (numeric) = -1.7552395995168748 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.4156045332078816000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8278207681365656 " "
Order of pole = 625.0355618776734 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8279999999999998 " "
y[1] (analytic) = -1.761606847007857 " "
y[1] (numeric) = -1.7616068470078505 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.65535224489121700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8268221906116618 " "
Order of pole = 625.0355618776654 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8269999999999998 " "
y[1] (analytic) = -1.7680049285895483 " "
y[1] (numeric) = -1.7680049285895418 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.64212420378428940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8258236130867743 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8259999999999998 " "
y[1] (analytic) = -1.7744340311349585 " "
y[1] (numeric) = -1.7744340311349522 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 3.5037926622294420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8248250355618789 " "
Order of pole = 625.0355618776682 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8249999999999998 " "
y[1] (analytic) = -1.780894342877815 " "
y[1] (numeric) = -1.7808943428778086 " "
absolute error = 6.439293542825908000000000000000E-15 " "
relative error = 3.6157639382583523000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8238264580369891 " "
Order of pole = 625.035561877671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8239999999999998 " "
y[1] (analytic) = -1.7873860534241406 " "
y[1] (numeric) = -1.7873860534241344 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 3.47840295944479100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8228278805120961 " "
Order of pole = 625.0355618776711 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8229999999999998 " "
y[1] (analytic) = -1.7939093537639434 " "
y[1] (numeric) = -1.7939093537639366 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 3.8370850445890140000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8218293029872008 " "
Order of pole = 625.0355618776697 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8219999999999998 " "
y[1] (analytic) = -1.8004644362830122 " "
y[1] (numeric) = -1.8004644362830056 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 3.69978879533050360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8208307254623093 " "
Order of pole = 625.035561877671 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8209999999999998 " "
y[1] (analytic) = -1.8070514947748366 " "
y[1] (numeric) = -1.80705149477483 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 3.68630233671396250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8198321479374168 " "
Order of pole = 625.0355618776716 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8199999999999998 " "
y[1] (analytic) = -1.813670724452635 " "
y[1] (numeric) = -1.8136707244526284 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 3.6728486918491380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8188335704125259 " "
Order of pole = 625.0355618776736 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8189999999999998 " "
y[1] (analytic) = -1.8203223219615061 " "
y[1] (numeric) = -1.8203223219614992 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 3.7814087481269330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8178349928876301 " "
Order of pole = 625.0355618776717 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8179999999999998 " "
y[1] (analytic) = -1.8270064853906944 " "
y[1] (numeric) = -1.8270064853906878 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 3.646039683502520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8168364153627351 " "
Order of pole = 625.0355618776704 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8169999999999998 " "
y[1] (analytic) = -1.8337234142859824 " "
y[1] (numeric) = -1.8337234142859755 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 3.75377371475415830000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8158378378378416 " "
Order of pole = 625.0355618776701 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8159999999999998 " "
y[1] (analytic) = -1.8404733096621975 " "
y[1] (numeric) = -1.8404733096621904 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.860652213916180300000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.814839260312948 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8149999999999998 " "
y[1] (analytic) = -1.8472563740158463 " "
y[1] (numeric) = -1.8472563740158394 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 3.7262736507503980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8138406827880549 " "
Order of pole = 625.0355618776701 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8139999999999998 " "
y[1] (analytic) = -1.8540728113378728 " "
y[1] (numeric) = -1.854072811337866 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 3.7125741290111570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.3228188955313651 " "
Order of pole = 7.709388682997087000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8129999999999998 " "
y[1] (analytic) = -1.86092282712654 " "
y[1] (numeric) = -1.8609228271265328 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.81822784589757940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.811843527738263 " "
Order of pole = 625.035561877666 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8119999999999998 " "
y[1] (analytic) = -1.8678066284004402 " "
y[1] (numeric) = -1.867806628400433 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.80415576728409870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8108449502133734 " "
Order of pole = 625.035561877669 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8109999999999998 " "
y[1] (analytic) = -1.874724423711635 " "
y[1] (numeric) = -1.8747244237116276 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 3.9085595033849760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.809846372688481 " "
Order of pole = 625.0355618776698 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8099999999999998 " "
y[1] (analytic) = -1.8816764231589216 " "
y[1] (numeric) = -1.8816764231589145 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 3.7761154203508324000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.808847795163591 " "
Order of pole = 625.0355618776722 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8089999999999998 " "
y[1] (analytic) = -1.8886628384012363 " "
y[1] (numeric) = -1.8886628384012285 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.11484835427522100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8078492176386889 " "
Order of pole = 625.0355618776654 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8079999999999998 " "
y[1] (analytic) = -1.8956838826711817 " "
y[1] (numeric) = -1.8956838826711742 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 3.9824765281082336000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.806850640113801 " "
Order of pole = 625.0355618776697 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8069999999999998 " "
y[1] (analytic) = -1.9027397707887002 " "
y[1] (numeric) = -1.9027397707886924 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.0844057036526460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8058520625889097 " "
Order of pole = 625.0355618776712 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8059999999999998 " "
y[1] (analytic) = -1.9098307191748711 " "
y[1] (numeric) = -1.9098307191748636 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 3.95297682231898540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8048534850640175 " "
Order of pole = 625.0355618776721 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8049999999999998 " "
y[1] (analytic) = -1.916956945865856 " "
y[1] (numeric) = -1.9169569458658482 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.0541135726268585000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.803854907539126 " "
Order of pole = 625.0355618776737 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8039999999999998 " "
y[1] (analytic) = -1.9241186705269733 " "
y[1] (numeric) = -1.9241186705269655 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.0390238353893410000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.802856330014223 " "
Order of pole = 625.0355618776657 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8029999999999998 " "
y[1] (analytic) = -1.931316114466921 " "
y[1] (numeric) = -1.9313161144669133 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.02397158816291960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8018577524893323 " "
Order of pole = 625.035561877668 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8019999999999998 " "
y[1] (analytic) = -1.938549500652137 " "
y[1] (numeric) = -1.9385495006521292 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 4.00895678431822700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8008591749644429 " "
Order of pole = 625.0355618776711 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ;"
Iterations = 199
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 1 Minutes 30 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 1 Minutes 30 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 4 Minutes 32 Seconds
"Time to Timeout " Unknown
Percent Done = 66.66666666666671 "%"
(%o58) true
(%o58) diffeq.max