(%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,
temp2], array_tmp1 : array_const_3D0 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 ,
1 1 1
array_tmp3_a1 : sinh(array_tmp2 ), array_tmp3_a2 : cosh(array_tmp2 ),
1 1 1 1
array_tmp3_a1
1
array_tmp3 : --------------, array_tmp4 : array_tmp3 + array_const_0D0 ,
1 array_tmp3_a2 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 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_const_3D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3_a2 array_tmp2
1 2
array_tmp3_a1 : --------------------------,
2 1
array_tmp3_a1 array_tmp2
1 2
array_tmp3_a2 : --------------------------,
2 1
array_tmp3_a1 - ats(2, array_tmp3_a2, array_tmp3, 2)
2
array_tmp3 : -----------------------------------------------------,
2 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp3_a2 array_tmp2
2 2
array_tmp3_a1 : --------------------------,
3 2
array_tmp3_a1 array_tmp2
2 2
array_tmp3_a2 : --------------------------,
3 2
array_tmp3_a1 - ats(3, array_tmp3_a2, array_tmp3, 2)
3
array_tmp3 : -----------------------------------------------------,
3 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp3_a2 array_tmp2
3 2
array_tmp3_a1 : --------------------------,
4 3
array_tmp3_a1 array_tmp2
3 2
array_tmp3_a2 : --------------------------,
4 3
array_tmp3_a1 - ats(4, array_tmp3_a2, array_tmp3, 2)
4
array_tmp3 : -----------------------------------------------------,
4 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp3_a2 array_tmp2
4 2
array_tmp3_a1 : --------------------------,
5 4
array_tmp3_a1 array_tmp2
4 2
array_tmp3_a2 : --------------------------,
5 4
array_tmp3_a1 - ats(5, array_tmp3_a2, array_tmp3, 2)
5
array_tmp3 : -----------------------------------------------------,
5 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3_a1 :
kkk
array_tmp3_a2 array_tmp2
kkk - 1 2
--------------------------------, array_tmp3_a2 :
kkk - 1 kkk
array_tmp3_a1 array_tmp2
kkk - 1 2
--------------------------------, array_tmp3 :
kkk - 1 kkk
array_tmp3_a1 - ats(kkk, array_tmp3_a2, array_tmp3, 2)
kkk
---------------------------------------------------------,
array_tmp3_a2
1
array_tmp4 : array_tmp3 , 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_tmp4 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,
temp2], array_tmp1 : array_const_3D0 array_x ,
1 1 1
array_tmp2 : array_const_1D0 + array_tmp1 ,
1 1 1
array_tmp3_a1 : sinh(array_tmp2 ), array_tmp3_a2 : cosh(array_tmp2 ),
1 1 1 1
array_tmp3_a1
1
array_tmp3 : --------------, array_tmp4 : array_tmp3 + array_const_0D0 ,
1 array_tmp3_a2 1 1 1
1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 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_const_3D0 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
array_tmp3_a2 array_tmp2
1 2
array_tmp3_a1 : --------------------------,
2 1
array_tmp3_a1 array_tmp2
1 2
array_tmp3_a2 : --------------------------,
2 1
array_tmp3_a1 - ats(2, array_tmp3_a2, array_tmp3, 2)
2
array_tmp3 : -----------------------------------------------------,
2 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
array_tmp3_a2 array_tmp2
2 2
array_tmp3_a1 : --------------------------,
3 2
array_tmp3_a1 array_tmp2
2 2
array_tmp3_a2 : --------------------------,
3 2
array_tmp3_a1 - ats(3, array_tmp3_a2, array_tmp3, 2)
3
array_tmp3 : -----------------------------------------------------,
3 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
array_tmp3_a2 array_tmp2
3 2
array_tmp3_a1 : --------------------------,
4 3
array_tmp3_a1 array_tmp2
3 2
array_tmp3_a2 : --------------------------,
4 3
array_tmp3_a1 - ats(4, array_tmp3_a2, array_tmp3, 2)
4
array_tmp3 : -----------------------------------------------------,
4 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
array_tmp3_a2 array_tmp2
4 2
array_tmp3_a1 : --------------------------,
5 4
array_tmp3_a1 array_tmp2
4 2
array_tmp3_a2 : --------------------------,
5 4
array_tmp3_a1 - ats(5, array_tmp3_a2, array_tmp3, 2)
5
array_tmp3 : -----------------------------------------------------,
5 array_tmp3_a2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3_a1 :
kkk
array_tmp3_a2 array_tmp2
kkk - 1 2
--------------------------------, array_tmp3_a2 :
kkk - 1 kkk
array_tmp3_a1 array_tmp2
kkk - 1 2
--------------------------------, array_tmp3 :
kkk - 1 kkk
array_tmp3_a1 - ats(kkk, array_tmp3_a2, array_tmp3, 2)
kkk
---------------------------------------------------------,
array_tmp3_a2
1
array_tmp4 : array_tmp3 , 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_tmp4 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)
ln(cosh(1.0 + 3.0 x))
(%i56) exact_soln_y(x) := block(---------------------)
3.0
ln(cosh(1.0 + 3.0 x))
(%o56) exact_soln_y(x) := block(---------------------)
3.0
(%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/lin_tanhpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"),
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:1.1,"), omniout_str(ALWAYS, "x_end:2.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10,"),
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, " (ln(cosh(3.0*x + 1.0))/3.0) "),
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_g, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms),
array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 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_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp3_a2 : 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_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_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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
array(array_tmp3_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a2 : 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 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_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, 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), x_start : 1.1,
iiif, jjjf
x_end : 2.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 10, 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 ) = tanh (3.0 * x + 1.0 ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T15:59:26-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_tanh"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"),
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, "lin_tanh diffeq.max"),
logitem_str(html_log_file,
"lin_tanh 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/lin_tanhpostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"),
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:1.1,"), omniout_str(ALWAYS, "x_end:2.0,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10,"),
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, " (ln(cosh(3.0*x + 1.0))/3.0) "),
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_g, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms),
array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 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_g : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_tmp3_a2 : 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_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_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_g, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term),
term
array(array_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
array(array_tmp3_a2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a2 : 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_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 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_const_1D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term),
term
array_const_1D0 : 1.0, 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), x_start : 1.1,
iiif, jjjf
x_end : 2.0, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 10, 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 ) = tanh (3.0 * x + 1.0 ) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T15:59:26-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_tanh"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"),
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, "lin_tanh diffeq.max"),
logitem_str(html_log_file,
"lin_tanh 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/lin_tanhpostode.ode#################"
"diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:30,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:1.1,"
"x_end:2.0,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:10,"
"/* 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("
" (ln(cosh(3.0*x + 1.0))/3.0) "
"));"
""
"/* 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 = 0.8999999999999999 ""
estimated_steps = 899.9999999999999 ""
step_error = 1.11111111111111120000000000000E-13 ""
est_needed_step_err = 1.11111111111111120000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 4.1135837558932980000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 ""
max_value3 = 4.1135837558932980000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 ""
value3 = 4.1135837558932980000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1 " "
y[1] (analytic) = 1.2023456360961104 " "
y[1] (numeric) = 1.2023456360961104 " "
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 = 1.5274316090036404 " "
Order of pole = 3.16433092264194470E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.101 " "
y[1] (analytic) = 1.203345269054324 " "
y[1] (numeric) = 1.2033452690543243 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.845227721712240400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5284837627226338 " "
Order of pole = 3.318824382308349600E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1019999999999999 " "
y[1] (analytic) = 1.2043449042077943 " "
y[1] (numeric) = 1.2043449042077947 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.68739227690077660000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5295392324768 " "
Order of pole = 3.477937366910488500E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1029999999999998 " "
y[1] (analytic) = 1.205344541543394 " "
y[1] (numeric) = 1.2053445415433945 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.684334184493212600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5305980549378 " "
Order of pole = 3.641724304361204600E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1039999999999996 " "
y[1] (analytic) = 1.2063441810480742 " "
y[1] (numeric) = 1.2063441810480748 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.52192173046630500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5316602665679084 " "
Order of pole = 3.81023934306998770E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1049999999999995 " "
y[1] (analytic) = 1.2073438227088638 " "
y[1] (numeric) = 1.2073438227088646 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.35646634367465200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5327259036303695 " "
Order of pole = 3.98353636683452800E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1059999999999994 " "
y[1] (analytic) = 1.2083434665128696 " "
y[1] (numeric) = 1.2083434665128707 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.1879755664928900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5337950021541171 " "
Order of pole = 4.16166894597829200E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1069999999999993 " "
y[1] (analytic) = 1.2093431124472758 " "
y[1] (numeric) = 1.2093431124472769 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.18038076372274700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5348675979421174 " "
Order of pole = 4.34469035060658370E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1079999999999992 " "
y[1] (analytic) = 1.2103427604993422 " "
y[1] (numeric) = 1.2103427604993433 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 9.1727984902980710000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.535943726560557 " "
Order of pole = 4.532653534114139400E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.108999999999999 " "
y[1] (analytic) = 1.2113424106564052 " "
y[1] (numeric) = 1.2113424106564068 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.28313202014694150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5370234233187965 " "
Order of pole = 4.725611106932703400E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.109999999999999 " "
y[1] (analytic) = 1.2123420629058776 " "
y[1] (numeric) = 1.2123420629058794 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.46522742528827130000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5381067232719867 " "
Order of pole = 4.923615341032494500E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1109999999999989 " "
y[1] (analytic) = 1.2133417172352468 " "
y[1] (numeric) = 1.2133417172352485 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.4640202460423970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.539193661206581 " "
Order of pole = 5.12671814851017900E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1119999999999988 " "
y[1] (analytic) = 1.214341373632075 " "
y[1] (numeric) = 1.2143413736320765 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.27996317034500500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5402842716327803 " "
Order of pole = 5.33497107390861200E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1129999999999987 " "
y[1] (analytic) = 1.2153410320839981 " "
y[1] (numeric) = 1.2153410320840001 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.6443133174715050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5413785887641425 " "
Order of pole = 5.54842526383350100E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1139999999999985 " "
y[1] (analytic) = 1.2163406925787275 " "
y[1] (numeric) = 1.2163406925787297 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.825513248712260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5424766465338642 " "
Order of pole = 5.76713149172185500E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1149999999999984 " "
y[1] (analytic) = 1.2173403551040471 " "
y[1] (numeric) = 1.2173403551040494 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.82401416328675760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5435784785526727 " "
Order of pole = 5.9911400993149400E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1159999999999983 " "
y[1] (analytic) = 1.2183400196478138 " "
y[1] (numeric) = 1.218340019647816 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.82251753487682240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5446841181275703 " "
Order of pole = 6.220501023072345000E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1169999999999982 " "
y[1] (analytic) = 1.2193396861979569 " "
y[1] (numeric) = 1.2193396861979593 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 2.00312569321131100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5457935982395477 " "
Order of pole = 6.45526376330316500E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.117999999999998 " "
y[1] (analytic) = 1.2203393547424783 " "
y[1] (numeric) = 1.220339354742481 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.18343795006320870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5469069515283547 " "
Order of pole = 6.69547736461382200E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.118999999999998 " "
y[1] (analytic) = 1.2213390252694523 " "
y[1] (numeric) = 1.2213390252694547 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.99984656482787900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.548024210300398 " "
Order of pole = 6.94119042594536500E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1199999999999979 " "
y[1] (analytic) = 1.2223386977670228 " "
y[1] (numeric) = 1.2223386977670252 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.99821101846591630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.54914540650461 " "
Order of pole = 7.1924510674712390E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1209999999999978 " "
y[1] (analytic) = 1.2233383722234055 " "
y[1] (numeric) = 1.2233383722234081 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 2.1780852457506170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.550270571727666 " "
Order of pole = 7.44930692631076100E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1219999999999977 " "
y[1] (analytic) = 1.2243380486268867 " "
y[1] (numeric) = 1.2243380486268896 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.35766573395538050000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.55139973718793 " "
Order of pole = 7.71180514617029200E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1229999999999976 " "
y[1] (analytic) = 1.2253377269658228 " "
y[1] (numeric) = 1.2253377269658257 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.3557422582369570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.552532933724637 " "
Order of pole = 7.97999236429642900E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1239999999999974 " "
y[1] (analytic) = 1.2263374072286393 " "
y[1] (numeric) = 1.2263374072286422 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 2.35382191476055270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5536701917814064 " "
Order of pole = 8.25391468817144900E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1249999999999973 " "
y[1] (analytic) = 1.227337089403831 " "
y[1] (numeric) = 1.227337089403834 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 2.53282044174223340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5548115414109112 " "
Order of pole = 8.5336177025123300E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1259999999999972 " "
y[1] (analytic) = 1.2283367734799617 " "
y[1] (numeric) = 1.228336773479965 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.7115276085396817000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5559570122534743 " "
Order of pole = 8.81914643967771600E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1269999999999971 " "
y[1] (analytic) = 1.229336459445664 " "
y[1] (numeric) = 1.2293364594456673 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.7093226173226370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5571066335370913 " "
Order of pole = 9.1105453818386200E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.127999999999997 " "
y[1] (analytic) = 1.2303361472896375 " "
y[1] (numeric) = 1.2303361472896408 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 2.7071212052191990000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5582604340633848 " "
Order of pole = 9.407858438840400E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.128999999999997 " "
y[1] (analytic) = 1.2313358370006495 " "
y[1] (numeric) = 1.231335837000653 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.88525158778321740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5594184421909505 " "
Order of pole = 9.71112892830721100E-2 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1299999999999968 " "
y[1] (analytic) = 1.2323355285675353 " "
y[1] (numeric) = 1.232335528567539 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.06309296147073250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5605806858460713 " "
Order of pole = 0.1002039958918779 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1309999999999967 " "
y[1] (analytic) = 1.2333352219791964 " "
y[1] (numeric) = 1.2333352219792002 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.06061013782447900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.561747192496718 " "
Order of pole = 0.10335712545387388 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1319999999999966 " "
y[1] (analytic) = 1.2343349172246005 " "
y[1] (numeric) = 1.2343349172246043 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 3.05813133133515160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5629179891492544 " "
Order of pole = 0.10657109303564738 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1329999999999965 " "
y[1] (analytic) = 1.2353346142927812 " "
y[1] (numeric) = 1.2353346142927852 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 3.2354010341875670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5640931023395797 " "
Order of pole = 0.10984630739761769 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1339999999999963 " "
y[1] (analytic) = 1.236334313172838 " "
y[1] (numeric) = 1.2363343131728424 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.59198321294168900000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5652725581284679 " "
Order of pole = 0.11318317093347652 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1349999999999962 " "
y[1] (analytic) = 1.2373340138539357 " "
y[1] (numeric) = 1.2373340138539402 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.58908107978745200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5664563820752926 " "
Order of pole = 0.11658207930511644 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1359999999999961 " "
y[1] (analytic) = 1.2383337163253036 " "
y[1] (numeric) = 1.238333716325308 " "
absolute error = 4.440892098500626000000000000000E-15 " "
relative error = 3.5861836272041125000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5676445992575168 " "
Order of pole = 0.12004342172343385 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.136999999999996 " "
y[1] (analytic) = 1.2393334205762352 " "
y[1] (numeric) = 1.2393334205762399 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.7624553861039250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5688372342429104 " "
Order of pole = 0.12356758055689099 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.137999999999996 " "
y[1] (analytic) = 1.2403331265960882 " "
y[1] (numeric) = 1.240333126596093 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.9384429905188467000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5700343110747907 " "
Order of pole = 0.12715493113855736 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1389999999999958 " "
y[1] (analytic) = 1.2413328343742842 " "
y[1] (numeric) = 1.241332834374289 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.9352711642506820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.571235853290182 " "
Order of pole = 0.13080584200569234 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1399999999999957 " "
y[1] (analytic) = 1.242332543900308 " "
y[1] (numeric) = 1.2423325439003126 " "
absolute error = 4.6629367034256575000000000000000E-15 " "
relative error = 3.75337241732905840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5724418838789669 " "
Order of pole = 0.13452067433972204 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1409999999999956 " "
y[1] (analytic) = 1.243332255163706 " "
y[1] (numeric) = 1.243332255163711 " "
absolute error = 4.884981308350689000000000000000E-15 " "
relative error = 3.92894279711861640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5736524253043438 " "
Order of pole = 0.13829978225833983 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1419999999999955 " "
y[1] (analytic) = 1.244331968154089 " "
y[1] (numeric) = 1.2443319681540943 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.28267588922125850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5748674994629126 " "
Order of pole = 0.14214351225650645 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1429999999999954 " "
y[1] (analytic) = 1.2453316828611292 " "
y[1] (numeric) = 1.2453316828611345 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.2792378862130120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5760871277031536 " "
Order of pole = 0.14605220345101522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1439999999999952 " "
y[1] (analytic) = 1.2463313992745602 " "
y[1] (numeric) = 1.2463313992745655 " "
absolute error = 5.329070518200751000000000000000E-15 " "
relative error = 4.2758053927732150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5773113308244793 " "
Order of pole = 0.1500261876062563 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1449999999999951 " "
y[1] (analytic) = 1.2473311173841768 " "
y[1] (numeric) = 1.2473311173841823 " "
absolute error = 5.551115123125783000000000000000E-15 " "
relative error = 4.45039416219105250000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5785401290208598 " "
Order of pole = 0.1540657882961174 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.145999999999995 " "
y[1] (analytic) = 1.2483308371798356 " "
y[1] (numeric) = 1.2483308371798414 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.624703288667639000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5797735419246206 " "
Order of pole = 0.1581713215549172 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.146999999999995 " "
y[1] (analytic) = 1.2493305586514536 " "
y[1] (numeric) = 1.2493305586514594 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.6210025745967910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5810115885757097 " "
Order of pole = 0.16234309543805026 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1479999999999948 " "
y[1] (analytic) = 1.2503302817890078 " "
y[1] (numeric) = 1.2503302817890136 " "
absolute error = 5.773159728050814000000000000000E-15 " "
relative error = 4.6173077723035016000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5822542874115313 " "
Order of pole = 0.16658140987013859 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1489999999999947 " "
y[1] (analytic) = 1.251330006582535 " "
y[1] (numeric) = 1.251330006582541 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 4.7910657471957740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5835016562570863 " "
Order of pole = 0.17088655651821583 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1499999999999946 " "
y[1] (analytic) = 1.2523297330221321 " "
y[1] (numeric) = 1.2523297330221383 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.9645462963634673000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5847537123333257 " "
Order of pole = 0.1752588189089863 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1509999999999945 " "
y[1] (analytic) = 1.253329461097955 " "
y[1] (numeric) = 1.2533294610979613 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.9605862870680273000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.586010472232364 " "
Order of pole = 0.17969847205891654 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1519999999999944 " "
y[1] (analytic) = 1.2543291908002183 " "
y[1] (numeric) = 1.2543291908002245 " "
absolute error = 6.217248937900877000000000000000E-15 " "
relative error = 4.9566325837753070000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5872719519165297 " "
Order of pole = 0.18420578249215325 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1529999999999943 " "
y[1] (analytic) = 1.2553289221191948 " "
y[1] (numeric) = 1.2553289221192014 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.3064483980067490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.588538166708287 " "
Order of pole = 0.18878100806523435 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1539999999999941 " "
y[1] (analytic) = 1.2563286550452164 " "
y[1] (numeric) = 1.256328655045223 " "
absolute error = 6.661338147750939000000000000000E-15 " "
relative error = 5.3022257519957560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5898091312866967 " "
Order of pole = 0.19342439795089028 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.154999999999994 " "
y[1] (analytic) = 1.257328389568672 " "
y[1] (numeric) = 1.2573283895686789 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 5.474610141458209000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5910848596731622 " "
Order of pole = 0.1981361923973992 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.155999999999994 " "
y[1] (analytic) = 1.2583281256800085 " "
y[1] (numeric) = 1.2583281256800154 " "
absolute error = 6.8833827526759700000000000000000E-15 " "
relative error = 5.4702605879973850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5923653652225238 " "
Order of pole = 0.202916622627761 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1569999999999938 " "
y[1] (analytic) = 1.2593278633697291 " "
y[1] (numeric) = 1.2593278633697362 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.6422378669429170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.593650660631642 " "
Order of pole = 0.2077659109517498 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1579999999999937 " "
y[1] (analytic) = 1.2603276026283947 " "
y[1] (numeric) = 1.260327602628402 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 5.8139423013863210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5949407579247021 " "
Order of pole = 0.2126842705498042 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1589999999999936 " "
y[1] (analytic) = 1.2613273434466226 " "
y[1] (numeric) = 1.26132734344663 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 5.8093341118757090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5962356684113983 " "
Order of pole = 0.21767190487801358 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1599999999999935 " "
y[1] (analytic) = 1.2623270858150855 " "
y[1] (numeric) = 1.2623270858150926 " "
absolute error = 7.105427357601002000000000000000E-15 " "
relative error = 5.6288322079479280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5975354027373159 " "
Order of pole = 0.22272900838598275 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1609999999999934 " "
y[1] (analytic) = 1.2633268297245117 " "
y[1] (numeric) = 1.263326829724519 " "
absolute error = 7.327471962526033000000000000000E-15 " "
relative error = 5.8001395918456860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.5988399708369951 " "
Order of pole = 0.22785576584555045 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1619999999999933 " "
y[1] (analytic) = 1.264326575165686 " "
y[1] (numeric) = 1.2643265751656936 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 5.9711760519324090000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6001493819526549 " "
Order of pole = 0.2330523526027939 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1629999999999932 " "
y[1] (analytic) = 1.2653263221294477 " "
y[1] (numeric) = 1.2653263221294555 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.1419422298092650000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.601463644590359 " "
Order of pole = 0.23831893396578074 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.163999999999993 " "
y[1] (analytic) = 1.2663260706066912 " "
y[1] (numeric) = 1.266326070606699 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.1370932438062940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6027827665522463 " "
Order of pole = 0.24365566564109464 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.164999999999993 " "
y[1] (analytic) = 1.2673258205883646 " "
y[1] (numeric) = 1.2673258205883724 " "
absolute error = 7.771561172376096000000000000000E-15 " "
relative error = 6.1322519009106080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6041067549078405 " "
Order of pole = 0.2490626933402691 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1659999999999928 " "
y[1] (analytic) = 1.2683255720654707 " "
y[1] (numeric) = 1.2683255720654787 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.3024872740549780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6054356159924859 " "
Order of pole = 0.2545401527341138 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1669999999999927 " "
y[1] (analytic) = 1.2693253250290661 " "
y[1] (numeric) = 1.2693253250290741 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.2975232745144220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.606769355399838 " "
Order of pole = 0.2600881693434616 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1679999999999926 " "
y[1] (analytic) = 1.270325079470261 " "
y[1] (numeric) = 1.270325079470269 " "
absolute error = 7.993605777301127000000000000000E-15 " "
relative error = 6.2925670810455430000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6081079779704828 " "
Order of pole = 0.2657068583724769 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1689999999999925 " "
y[1] (analytic) = 1.2713248353802178 " "
y[1] (numeric) = 1.271324835380226 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 6.4622747496072360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6094514877956991 " "
Order of pole = 0.27139632475709696 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1699999999999924 " "
y[1] (analytic) = 1.2723245927501527 " "
y[1] (numeric) = 1.2723245927501614 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 6.8062345422075320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6107998882032881 " "
Order of pole = 0.2771566629578004 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1709999999999923 " "
y[1] (analytic) = 1.2733243515713348 " "
y[1] (numeric) = 1.2733243515713435 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 6.8008905832906940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6121531817620254 " "
Order of pole = 0.28298795700101564 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1719999999999922 " "
y[1] (analytic) = 1.2743241118350843 " "
y[1] (numeric) = 1.274324111835093 " "
absolute error = 8.659739592076221000000000000000E-15 " "
relative error = 6.7955550017850670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6135113702459498 " "
Order of pole = 0.28889027997091254 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.172999999999992 " "
y[1] (analytic) = 1.2753238735327737 " "
y[1] (numeric) = 1.2753238735327825 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.9643361826183260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6148744546695766 " "
Order of pole = 0.2948636945065406 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.173999999999992 " "
y[1] (analytic) = 1.276323636655827 " "
y[1] (numeric) = 1.2763236366558361 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 7.1328529382874850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6162424352429188 " "
Order of pole = 0.30090825214708694 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1749999999999918 " "
y[1] (analytic) = 1.2773234011957204 " "
y[1] (numeric) = 1.2773234011957293 " "
absolute error = 8.881784197001252000000000000000E-15 " "
relative error = 6.9534341801668150000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6176153114006937 " "
Order of pole = 0.30702399373076616 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1759999999999917 " "
y[1] (analytic) = 1.2783231671439794 " "
y[1] (numeric) = 1.2783231671439885 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 7.1216958558812580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6189930817627558 " "
Order of pole = 0.3132109488159802 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1769999999999916 " "
y[1] (analytic) = 1.2793229344921815 " "
y[1] (numeric) = 1.2793229344921908 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 7.2896945371757570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6203757441509845 " "
Order of pole = 0.3194691359348152 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1779999999999915 " "
y[1] (analytic) = 1.280322703231954 " "
y[1] (numeric) = 1.2803227032319635 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 7.4574308396424380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6217632955743095 " "
Order of pole = 0.325798562341582 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1789999999999914 " "
y[1] (analytic) = 1.2813224733549748 " "
y[1] (numeric) = 1.2813224733549842 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 7.2783187689143850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6231557322250503 " "
Order of pole = 0.33219922397166 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1799999999999913 " "
y[1] (analytic) = 1.2823222448529707 " "
y[1] (numeric) = 1.28232224485298 " "
absolute error = 9.325873406851315000000000000000E-15 " "
relative error = 7.2726441768313910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6245530494757816 " "
Order of pole = 0.3386711053465188 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1809999999999912 " "
y[1] (analytic) = 1.2833220177177185 " "
y[1] (numeric) = 1.283322017717728 " "
absolute error = 9.547918011776346000000000000000E-15 " "
relative error = 7.4400017142669500000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6259552418723844 " "
Order of pole = 0.34521417950535316 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.181999999999991 " "
y[1] (analytic) = 1.284321791941044 " "
y[1] (numeric) = 1.284321791941054 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 7.7799872931573580000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6273623031219095 " "
Order of pole = 0.3518284077855274 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.182999999999991 " "
y[1] (analytic) = 1.2853215675148224 " "
y[1] (numeric) = 1.2853215675148324 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 7.7739357015116620000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6287742260909996 " "
Order of pole = 0.3585137398039393 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1839999999999908 " "
y[1] (analytic) = 1.286321344430977 " "
y[1] (numeric) = 1.286321344430987 " "
absolute error = 9.992007221626409000000000000000E-15 " "
relative error = 7.767893508792330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.630191002807852 " "
Order of pole = 0.3652701134433318 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1849999999999907 " "
y[1] (analytic) = 1.2873211226814785 " "
y[1] (numeric) = 1.287321122681489 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 8.1068322795311360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6316126244622657 " "
Order of pole = 0.3720974548799525 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1859999999999906 " "
y[1] (analytic) = 1.2883209022583475 " "
y[1] (numeric) = 1.2883209022583582 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 8.2728930484000030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.633039081354331 " "
Order of pole = 0.3789956777905896 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1869999999999905 " "
y[1] (analytic) = 1.2893206831536517 " "
y[1] (numeric) = 1.289320683153662 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 8.0942596887145210000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6344703629596868 " "
Order of pole = 0.3859646842956863 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1879999999999904 " "
y[1] (analytic) = 1.290320465359505 " "
y[1] (numeric) = 1.2903204653595155 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 8.0879879934081320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6359064578853955 " "
Order of pole = 0.3930043642942245 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1889999999999903 " "
y[1] (analytic) = 1.2913202488680695 " "
y[1] (numeric) = 1.2913202488680802 " "
absolute error = 1.065814103640150300000000000000E-14 " "
relative error = 8.253677618502531000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6373473538507377 " "
Order of pole = 0.40011459517417336 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1899999999999902 " "
y[1] (analytic) = 1.2923200336715541 " "
y[1] (numeric) = 1.2923200336715652 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 8.5909294578599870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.638793037717229 " "
Order of pole = 0.40729524224870595 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.19099999999999 " "
y[1] (analytic) = 1.2933198197622147 " "
y[1] (numeric) = 1.2933198197622258 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 8.5842883381256640000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6402434954664187 " "
Order of pole = 0.4145461583800376 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.19199999999999 " "
y[1] (analytic) = 1.2943196071323526 " "
y[1] (numeric) = 1.2943196071323637 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 8.5776574696641300000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6416987121907674 " "
Order of pole = 0.42186718384832567 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1929999999999898 " "
y[1] (analytic) = 1.2953193957743154 " "
y[1] (numeric) = 1.2953193957743265 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 8.5710368288084490000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6431586721125855 " "
Order of pole = 0.4292581465961316 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1939999999999897 " "
y[1] (analytic) = 1.2963191856804965 " "
y[1] (numeric) = 1.296319185680508 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 8.9070034476427520000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6446233585396046 " "
Order of pole = 0.43671886158249507 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1949999999999896 " "
y[1] (analytic) = 1.2973189768433355 " "
y[1] (numeric) = 1.297318976843347 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 8.9001391810334730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6460927539022325 " "
Order of pole = 0.4442491312853125 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1959999999999895 " "
y[1] (analytic) = 1.2983187692553164 " "
y[1] (numeric) = 1.2983187692553277 " "
absolute error = 1.132427485117659700000000000000E-14 " "
relative error = 8.7222607570188030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6475668397334036 " "
Order of pole = 0.4518487453930735 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1969999999999894 " "
y[1] (analytic) = 1.2993185629089679 " "
y[1] (numeric) = 1.2993185629089794 " "
absolute error = 1.154631945610162800000000000000E-14 " "
relative error = 8.8864423134625680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6490455966478552 " "
Order of pole = 0.4595174804825639 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1979999999999893 " "
y[1] (analytic) = 1.3003183577968638 " "
y[1] (numeric) = 1.3003183577968758 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 9.2211331125610680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6505290043578456 " "
Order of pole = 0.4672551002220633 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.1989999999999892 " "
y[1] (analytic) = 1.3013181539116232 " "
y[1] (numeric) = 1.301318153911635 " "
absolute error = 1.17683640610266600000000000000E-14 " "
relative error = 9.0434180339774840000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6520170416935829 " "
Order of pole = 0.47506135564884566 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.199999999999989 " "
y[1] (analytic) = 1.3023179512459075 " "
y[1] (numeric) = 1.3023179512459195 " "
absolute error = 1.19904086659516900000000000000E-14 " "
relative error = 9.206974882347780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.653509686533083 " "
Order of pole = 0.48293598412363714 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.200999999999989 " "
y[1] (analytic) = 1.3033177497924233 " "
y[1] (numeric) = 1.3033177497924355 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 9.3702807874915960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6550069158697756 " "
Order of pole = 0.49087871028414654 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2019999999999889 " "
y[1] (analytic) = 1.3043175495439203 " "
y[1] (numeric) = 1.3043175495439328 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.5333363260731350000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.656508705752891 " "
Order of pole = 0.49888924516909583 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2029999999999887 " "
y[1] (analytic) = 1.305317350493192 " "
y[1] (numeric) = 1.3053173504932045 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.5260343173279570000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.658015031314746 " "
Order of pole = 0.5069672865799735 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2039999999999886 " "
y[1] (analytic) = 1.3063171526330748 " "
y[1] (numeric) = 1.306317152633087 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 9.3487659151230780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6595258667788118 " "
Order of pole = 0.5151125191451147 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2049999999999885 " "
y[1] (analytic) = 1.307316955956447 " "
y[1] (numeric) = 1.3073169559564595 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.5114637801852280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6610411854280271 " "
Order of pole = 0.5233246139001491 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2059999999999884 " "
y[1] (analytic) = 1.308316760456231 " "
y[1] (numeric) = 1.3083167604562436 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 9.6739129722019670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6625609596049646 " "
Order of pole = 0.5316032281926653 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2069999999999883 " "
y[1] (analytic) = 1.309316566125391 " "
y[1] (numeric) = 1.3093165661254034 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.4969377135421670000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6640851607408358 " "
Order of pole = 0.5399480061126276 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2079999999999882 " "
y[1] (analytic) = 1.3103163729569325 " "
y[1] (numeric) = 1.310316372956945 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.4896912932114060000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.665613759309192 " "
Order of pole = 0.5483585777894628 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.208999999999988 " "
y[1] (analytic) = 1.3113161809439038 " "
y[1] (numeric) = 1.3113161809439162 " "
absolute error = 1.243449787580175300000000000000E-14 " "
relative error = 9.4824559145233970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6671467247058285 " "
Order of pole = 0.5568345576192915 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.209999999999988 " "
y[1] (analytic) = 1.3123159900793941 " "
y[1] (numeric) = 1.3123159900794068 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 9.6444321157445270000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6686840260033298 " "
Order of pole = 0.5653755551636337 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2109999999999879 " "
y[1] (analytic) = 1.3133158003565348 " "
y[1] (numeric) = 1.3133158003565475 " "
absolute error = 1.265654248072678500000000000000E-14 " "
relative error = 9.6370899347215850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6702256303988372 " "
Order of pole = 0.5739811526374723 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2119999999999878 " "
y[1] (analytic) = 1.3143156117684973 " "
y[1] (numeric) = 1.3143156117685102 " "
absolute error = 1.287858708565181600000000000000E-14 " "
relative error = 9.7987020547696590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6717715047628012 " "
Order of pole = 0.5826509273204721 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2129999999999876 " "
y[1] (analytic) = 1.3153154243084944 " "
y[1] (numeric) = 1.3153154243085075 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 9.9600684736623470000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6733216148768577 " "
Order of pole = 0.5913844404748545 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2139999999999875 " "
y[1] (analytic) = 1.3163152379697793 " "
y[1] (numeric) = 1.3163152379697927 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.0121189750906574000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6748759255603594 " "
Order of pole = 0.6001812391367078 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2149999999999874 " "
y[1] (analytic) = 1.3173150527456463 " "
y[1] (numeric) = 1.3173150527456596 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.0113507978014646000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6764344006997611 " "
Order of pole = 0.609040856562105 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2159999999999873 " "
y[1] (analytic) = 1.3183148686294288 " "
y[1] (numeric) = 1.318314868629442 " "
absolute error = 1.310063169057684700000000000000E-14 " "
relative error = 9.9374072175919340000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6779970032209983 " "
Order of pole = 0.6179628117224407 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2169999999999872 " "
y[1] (analytic) = 1.3193146856145 " "
y[1] (numeric) = 1.3193146856145133 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 1.0098179335657548000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.679563695102282 " "
Order of pole = 0.626946609515528 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.217999999999987 " "
y[1] (analytic) = 1.3203145036942734 " "
y[1] (numeric) = 1.320314503694287 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.0258707953694698000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6811344373866617 " "
Order of pole = 0.6359917408819467 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.218999999999987 " "
y[1] (analytic) = 1.321314322862202 " "
y[1] (numeric) = 1.3213143228622155 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.0250945339854209000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6827091901314348 " "
Order of pole = 0.6450976820471279 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2199999999999869 " "
y[1] (analytic) = 1.3223141431117773 " "
y[1] (numeric) = 1.3223141431117909 " "
absolute error = 1.35447209004269100000000000000E-14 " "
relative error = 1.0243194456464308000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6842879124685646 " "
Order of pole = 0.6542638953844708 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2209999999999868 " "
y[1] (analytic) = 1.32331396443653 " "
y[1] (numeric) = 1.3233139644365437 " "
absolute error = 1.376676550535194000000000000000E-14 " "
relative error = 1.040324962580884000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.68587056257195 " "
Order of pole = 0.6634898288584878 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2219999999999867 " "
y[1] (analytic) = 1.3243137868300294 " "
y[1] (numeric) = 1.3243137868300434 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.056306311192423000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6874570976496452 " "
Order of pole = 0.6727749159454053 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2229999999999865 " "
y[1] (analytic) = 1.3253136102858836 " "
y[1] (numeric) = 1.3253136102858978 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.0722635461456234000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6890474739746866 " "
Order of pole = 0.682118575965216 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2239999999999864 " "
y[1] (analytic) = 1.3263134347977388 " "
y[1] (numeric) = 1.3263134347977528 " "
absolute error = 1.398881011027697200000000000000E-14 " "
relative error = 1.0547137458809086000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6906416468535992 " "
Order of pole = 0.6915202136666991 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2249999999999863 " "
y[1] (analytic) = 1.3273132603592785 " "
y[1] (numeric) = 1.3273132603592928 " "
absolute error = 1.421085471520200400000000000000E-14 " "
relative error = 1.0706481385830044000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6922395706515956 " "
Order of pole = 0.7009792195050171 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2259999999999862 " "
y[1] (analytic) = 1.3283130869642248 " "
y[1] (numeric) = 1.3283130869642394 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.1032748279658232000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6938411987687598 " "
Order of pole = 0.7104949692853122 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.226999999999986 " "
y[1] (analytic) = 1.3293129146063374 " "
y[1] (numeric) = 1.329312914606352 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.1024450123086317000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6954464836646932 " "
Order of pole = 0.7200668244823127 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.227999999999986 " "
y[1] (analytic) = 1.3303127432794128 " "
y[1] (numeric) = 1.3303127432794275 " "
absolute error = 1.465494392505206600000000000000E-14 " "
relative error = 1.1016164431324257000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6970553768316134 " "
Order of pole = 0.72969413180701 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2289999999999859 " "
y[1] (analytic) = 1.3313125729772846 " "
y[1] (numeric) = 1.3313125729772994 " "
absolute error = 1.487698852997709800000000000000E-14 " "
relative error = 1.1174677406303542000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.6986678288311303 " "
Order of pole = 0.7393762236958263 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2299999999999858 " "
y[1] (analytic) = 1.3323124036938234 " "
y[1] (numeric) = 1.3323124036938385 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.1332952461479909000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7002837892635498 " "
Order of pole = 0.749112417851201 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2309999999999857 " "
y[1] (analytic) = 1.3333122354229372 " "
y[1] (numeric) = 1.3333122354229523 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.1324454042914109000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.701903206788809 " "
Order of pole = 0.7589020175015424 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2319999999999856 " "
y[1] (analytic) = 1.3343120681585692 " "
y[1] (numeric) = 1.3343120681585843 " "
absolute error = 1.50990331349021300000000000000E-14 " "
relative error = 1.131596835194611000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.703526029107744 " "
Order of pole = 0.7687443110786969 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2329999999999854 " "
y[1] (analytic) = 1.3353119018946993 " "
y[1] (numeric) = 1.3353119018947146 " "
absolute error = 1.53210777398271600000000000000E-14 " "
relative error = 1.1473782056527614000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7051522030057364 " "
Order of pole = 0.7786385728329197 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2339999999999853 " "
y[1] (analytic) = 1.3363117366253434 " "
y[1] (numeric) = 1.3363117366253592 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.1797521878756978000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7067816742901893 " "
Order of pole = 0.7885840618620801 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2349999999999852 " "
y[1] (analytic) = 1.337311572344554 " "
y[1] (numeric) = 1.3373115723445697 " "
absolute error = 1.576516694967722300000000000000E-14 " "
relative error = 1.1788701508084595000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7084143878503522 " "
Order of pole = 0.798580022969956 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.235999999999985 " "
y[1] (analytic) = 1.338311409046418 " "
y[1] (numeric) = 1.3383114090464336 " "
absolute error = 1.55431223447521920000000000000E-14 " "
relative error = 1.1613980303602935000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7100502876296857 " "
Order of pole = 0.8086256862244152 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.236999999999985 " "
y[1] (analytic) = 1.3393112467250576 " "
y[1] (numeric) = 1.3393112467250736 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.193689039324868100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7116893166346578 " "
Order of pole = 0.8187202670455438 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.237999999999985 " "
y[1] (analytic) = 1.3403110853746314 " "
y[1] (numeric) = 1.3403110853746474 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.192798577065686000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7133314169455554 " "
Order of pole = 0.8288629662823492 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2389999999999848 " "
y[1] (analytic) = 1.3413109249893316 " "
y[1] (numeric) = 1.3413109249893478 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.2084637392822406000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7149765297058737 " "
Order of pole = 0.8390529701011413 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2399999999999847 " "
y[1] (analytic) = 1.3423107655633864 " "
y[1] (numeric) = 1.3423107655634023 " "
absolute error = 1.598721155460225400000000000000E-14 " "
relative error = 1.191021629621826100000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7166245951395762 " "
Order of pole = 0.8492894501254238 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2409999999999846 " "
y[1] (analytic) = 1.343310607091057 " "
y[1] (numeric) = 1.3433106070910732 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.2066647932326297000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7182755525364108 " "
Order of pole = 0.8595715632451686 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2419999999999844 " "
y[1] (analytic) = 1.34431044956664 " "
y[1] (numeric) = 1.3443104495666565 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.2222846865282651000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7199293402684732 " "
Order of pole = 0.8698984517654598 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2429999999999843 " "
y[1] (analytic) = 1.3453102929844662 " "
y[1] (numeric) = 1.3453102929844827 " "
absolute error = 1.643130076445231700000000000000E-14 " "
relative error = 1.2213762765466361000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7215858957988623 " "
Order of pole = 0.8802692435180468 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2439999999999842 " "
y[1] (analytic) = 1.3463101373389 " "
y[1] (numeric) = 1.3463101373389161 " "
absolute error = 1.620925615952728500000000000000E-14 " "
relative error = 1.2039763877561156000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.723245155671108 " "
Order of pole = 0.890683051692843 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2449999999999841 " "
y[1] (analytic) = 1.3473099826243384 " "
y[1] (numeric) = 1.347309982624355 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.2360440866725687000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.72490705552708 " "
Order of pole = 0.9011389750145913 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.245999999999984 " "
y[1] (analytic) = 1.348309828835214 " "
y[1] (numeric) = 1.3483098288352309 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2515958582665523000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7265715300897215 " "
Order of pole = 0.9116360975041573 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.246999999999984 " "
y[1] (analytic) = 1.3493096759659915 " "
y[1] (numeric) = 1.3493096759660084 " "
absolute error = 1.68753899743023800000000000000E-14 " "
relative error = 1.2506684177018912000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7282385131888793 " "
Order of pole = 0.9221734887639279 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2479999999999838 " "
y[1] (analytic) = 1.3503095240111689 " "
y[1] (numeric) = 1.3503095240111855 " "
absolute error = 1.665334536937734800000000000000E-14 " "
relative error = 1.2332983714658004000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7299079377679711 " "
Order of pole = 0.9327502040769797 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2489999999999837 " "
y[1] (analytic) = 1.3513093729652763 " "
y[1] (numeric) = 1.3513093729652934 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.2652494625793403000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7315797358756806 " "
Order of pole = 0.9433652842413736 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2499999999999836 " "
y[1] (analytic) = 1.3523092228228781 " "
y[1] (numeric) = 1.3523092228228952 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.2643139816452165000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7332538386685323 " "
Order of pole = 0.9540177555735596 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2509999999999835 " "
y[1] (analytic) = 1.3533090735785702 " "
y[1] (numeric) = 1.3533090735785873 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.263379882174031000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7349301764346508 " "
Order of pole = 0.9647066301911558 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2519999999999833 " "
y[1] (analytic) = 1.3543089252269809 " "
y[1] (numeric) = 1.354308925226998 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.2624471611129565000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7366086785709338 " "
Order of pole = 0.9754309056705548 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2529999999999832 " "
y[1] (analytic) = 1.3553087777627706 " "
y[1] (numeric) = 1.3553087777627877 " "
absolute error = 1.70974345792274100000000000000E-14 " "
relative error = 1.2615158154181227000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7382892736205486 " "
Order of pole = 0.9861895655637554 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2539999999999831 " "
y[1] (analytic) = 1.3563086311806316 " "
y[1] (numeric) = 1.3563086311806491 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.2933283314586025000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7399718892524276 " "
Order of pole = 0.9969815790277305 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.254999999999983 " "
y[1] (analytic) = 1.3573084854752888 " "
y[1] (numeric) = 1.3573084854753064 " "
absolute error = 1.754152378907747300000000000000E-14 " "
relative error = 1.292375607814384000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7416564522999396 " "
Order of pole = 1.0078059014013547 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.255999999999983 " "
y[1] (analytic) = 1.3583083406414975 " "
y[1] (numeric) = 1.3583083406415148 " "
absolute error = 1.731947918415244200000000000000E-14 " "
relative error = 1.275077143086146000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7433428887292803 " "
Order of pole = 1.018661473654804 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2569999999999828 " "
y[1] (analytic) = 1.3593081966740443 " "
y[1] (numeric) = 1.359308196674062 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3068094812836714000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7450311236747655 " "
Order of pole = 1.0295472229219413 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2579999999999827 " "
y[1] (analytic) = 1.360308053567748 " "
y[1] (numeric) = 1.360308053567766 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.322172058877088000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7467210814141827 " "
Order of pole = 1.0404620620608416 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2589999999999826 " "
y[1] (analytic) = 1.3613079113174582 " "
y[1] (numeric) = 1.3613079113174762 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.3212009457523290000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7484126854265418 " "
Order of pole = 1.0514048905110656 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2599999999999825 " "
y[1] (analytic) = 1.3623077699180548 " "
y[1] (numeric) = 1.3623077699180726 " "
absolute error = 1.776356839400250500000000000000E-14 " "
relative error = 1.3039321059639125000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7501058583426516 " "
Order of pole = 1.0623745934679363 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2609999999999824 " "
y[1] (analytic) = 1.3633076293644477 " "
y[1] (numeric) = 1.3633076293644657 " "
absolute error = 1.798561299892753600000000000000E-14 " "
relative error = 1.3192629903576600000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7518005220029484 " "
Order of pole = 1.073370042789282 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2619999999999822 " "
y[1] (analytic) = 1.3643074896515788 " "
y[1] (numeric) = 1.364307489651597 " "
absolute error = 1.820765760385256700000000000000E-14 " "
relative error = 1.3345714028516031000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.753496597428777 " "
Order of pole = 1.0843900964438369 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2629999999999821 " "
y[1] (analytic) = 1.3653073507744191 " "
y[1] (numeric) = 1.3653073507744375 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.3498573927932084000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7551940048526096 " "
Order of pole = 1.0954335989998487 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.263999999999982 " "
y[1] (analytic) = 1.3663072127279705 " "
y[1] (numeric) = 1.366307212727989 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.3488695687978428000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7568926637062015 " "
Order of pole = 1.1064993813695985 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.264999999999982 " "
y[1] (analytic) = 1.3673070755072638 " "
y[1] (numeric) = 1.3673070755072825 " "
absolute error = 1.86517468137026300000000000000E-14 " "
relative error = 1.3641227451984720000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7585924926467331 " "
Order of pole = 1.1175862611708158 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2659999999999818 " "
y[1] (analytic) = 1.3683069391073603 " "
y[1] (numeric) = 1.3683069391073792 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.379353628867826800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7602934095716847 " "
Order of pole = 1.128693042956609 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2669999999999817 " "
y[1] (analytic) = 1.3693068035233509 " "
y[1] (numeric) = 1.3693068035233698 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.3783464282850040000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7619953316018024 " "
Order of pole = 1.1398185178662317 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2679999999999816 " "
y[1] (analytic) = 1.3703066687503556 " "
y[1] (numeric) = 1.370306668750374 " "
absolute error = 1.8429702208777599000000000000E-14 " "
relative error = 1.3449326803309272000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7636981751081928 " "
Order of pole = 1.1509614640270982 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2689999999999815 " "
y[1] (analytic) = 1.3713065347835223 " "
y[1] (numeric) = 1.3713065347835411 " "
absolute error = 1.88737914186276600000000000000E-14 " "
relative error = 1.3763364309794618000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7654018557085394 " "
Order of pole = 1.1621206465029612 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2699999999999814 " "
y[1] (analytic) = 1.3723064016180304 " "
y[1] (numeric) = 1.3723064016180495 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.391514023474463800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7671062883328659 " "
Order of pole = 1.1732948181515983 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2709999999999813 " "
y[1] (analytic) = 1.3733062692490867 " "
y[1] (numeric) = 1.3733062692491058 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.3905008992636542000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7688113871283118 " "
Order of pole = 1.184482718274026 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2719999999999811 " "
y[1] (analytic) = 1.3743061376719268 " "
y[1] (numeric) = 1.3743061376719459 " "
absolute error = 1.909583602355269200000000000000E-14 " "
relative error = 1.3894892484363797000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7705170655737694 " "
Order of pole = 1.1956830742251743 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.272999999999981 " "
y[1] (analytic) = 1.3753060068818144 " "
y[1] (numeric) = 1.3753060068818337 " "
absolute error = 1.931788062847772400000000000000E-14 " "
relative error = 1.4046241732250200000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7722232364168093 " "
Order of pole = 1.2068946004906174 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.273999999999981 " "
y[1] (analytic) = 1.3763058768740422 " "
y[1] (numeric) = 1.376305876874062 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.43587048274563000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7739298117381062 " "
Order of pole = 1.2181159996001032 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2749999999999808 " "
y[1] (analytic) = 1.3773057476439312 " "
y[1] (numeric) = 1.377305747643951 " "
absolute error = 1.976196983832778600000000000000E-14 " "
relative error = 1.43482809624031000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.775636702932559 " "
Order of pole = 1.2293459617822293 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2759999999999807 " "
y[1] (analytic) = 1.37830561918683 " "
y[1] (numeric) = 1.3783056191868495 " "
absolute error = 1.953992523340275500000000000000E-14 " "
relative error = 1.4176772525189937000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7773438207132288 " "
Order of pole = 1.2405831650855834 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2769999999999806 " "
y[1] (analytic) = 1.379305491498114 " "
y[1] (numeric) = 1.379305491498134 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.4488461451384096000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7790510751423056 " "
Order of pole = 1.2518262757054686 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2779999999999805 " "
y[1] (analytic) = 1.3803053645731884 " "
y[1] (numeric) = 1.3803053645732084 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.4477966221215247000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7807583758149885 " "
Order of pole = 1.2630739507997006 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2789999999999804 " "
y[1] (analytic) = 1.3813052384074844 " "
y[1] (numeric) = 1.3813052384075044 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.4467486177271371000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7824656310471847 " "
Order of pole = 1.2743248262783986 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2799999999999803 " "
y[1] (analytic) = 1.382305112996461 " "
y[1] (numeric) = 1.382305112996481 " "
absolute error = 1.998401444325281800000000000000E-14 " "
relative error = 1.4457021286662913000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7841727494748685 " "
Order of pole = 1.2855775406965027 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2809999999999802 " "
y[1] (analytic) = 1.3833049883356037 " "
y[1] (numeric) = 1.3833049883356239 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.4607088977890434000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7858796385205675 " "
Order of pole = 1.2968307122664875 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.28199999999998 " "
y[1] (analytic) = 1.384304864420426 " "
y[1] (numeric) = 1.3843048644204463 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.4596538354748628000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7875862051448526 " "
Order of pole = 1.3080829501869182 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.28299999999998 " "
y[1] (analytic) = 1.385304741246468 " "
y[1] (numeric) = 1.3853047412464883 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.4586002954120306000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7892923557367133 " "
Order of pole = 1.31933285282798 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2839999999999798 " "
y[1] (analytic) = 1.386304618809296 " "
y[1] (numeric) = 1.3863046188093162 " "
absolute error = 2.02060590481778500000000000000E-14 " "
relative error = 1.4575482743131113000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.790997996132686 " "
Order of pole = 1.3305790081146558 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2849999999999797 " "
y[1] (analytic) = 1.3873044971045025 " "
y[1] (numeric) = 1.387304497104523 " "
absolute error = 2.04281036531028800000000000000E-14 " "
relative error = 1.4725032388880144000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7927030315825785 " "
Order of pole = 1.3418199929371646 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2859999999999796 " "
y[1] (analytic) = 1.3883043761277074 " "
y[1] (numeric) = 1.3883043761277283 " "
absolute error = 2.087219286295294300000000000000E-14 " "
relative error = 1.5034306036814618000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7944073668534348 " "
Order of pole = 1.3530543747455592 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2869999999999795 " "
y[1] (analytic) = 1.389304255874557 " "
y[1] (numeric) = 1.3893042558745776 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.4863661556286525000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.796110906124419 " "
Order of pole = 1.3642807098581695 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2879999999999794 " "
y[1] (analytic) = 1.390304136340722 " "
y[1] (numeric) = 1.3903041363407427 " "
absolute error = 2.065014825802791200000000000000E-14 " "
relative error = 1.4852971891732310000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7978135531181463 " "
Order of pole = 1.3754975455234284 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2889999999999793 " "
y[1] (analytic) = 1.3913040175218996 " "
y[1] (numeric) = 1.391304017521921 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.5321081377145868000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.7995152110195165 " "
Order of pole = 1.3867034185927771 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2899999999999792 " "
y[1] (analytic) = 1.3923038994138144 " "
y[1] (numeric) = 1.3923038994138355 " "
absolute error = 2.109423746787797400000000000000E-14 " "
relative error = 1.5150598570297072000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8012157825683546 " "
Order of pole = 1.3978968569757395 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.290999999999979 " "
y[1] (analytic) = 1.3933037820122143 " "
y[1] (numeric) = 1.3933037820122356 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.5299091517585600000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8029151700166661 " "
Order of pole = 1.4090763789507452 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.291999999999979 " "
y[1] (analytic) = 1.394303665312874 " "
y[1] (numeric) = 1.3943036653128953 " "
absolute error = 2.131628207280300600000000000000E-14 " "
relative error = 1.5288120230265442000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8046132751791897 " "
Order of pole = 1.420240493904343 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2929999999999788 " "
y[1] (analytic) = 1.3953035493115922 " "
y[1] (numeric) = 1.3953035493116142 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.5754576055098313000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.806309999443223 " "
Order of pole = 1.4313877024448285 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2939999999999787 " "
y[1] (analytic) = 1.3963034340041949 " "
y[1] (numeric) = 1.3963034340042169 " "
absolute error = 2.1982415887578100000000000000E-14 " "
relative error = 1.5743294295666724000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8080052437620615 " "
Order of pole = 1.4425164963738144 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2949999999999786 " "
y[1] (analytic) = 1.3973033193865307 " "
y[1] (numeric) = 1.397303319386553 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.589093805506146800000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8096989087028446 " "
Order of pole = 1.4536253592819115 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2959999999999785 " "
y[1] (analytic) = 1.3983032054544748 " "
y[1] (numeric) = 1.398303205454497 " "
absolute error = 2.22044604925031300000000000000E-14 " "
relative error = 1.5879574906135085000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8113908944527877 " "
Order of pole = 1.4647127667548752 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2969999999999784 " "
y[1] (analytic) = 1.3993030922039258 " "
y[1] (numeric) = 1.3993030922039482 " "
absolute error = 2.242650509742816200000000000000E-14 " "
relative error = 1.6026910268672415000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8130811008152132 " "
Order of pole = 1.4757771862154794 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2979999999999783 " "
y[1] (analytic) = 1.4003029796308073 " "
y[1] (numeric) = 1.40030297963083 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 1.6174035213668210000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8147694272547914 " "
Order of pole = 1.4868170776356724 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.2989999999999782 " "
y[1] (analytic) = 1.4013028677310677 " "
y[1] (numeric) = 1.4013028677310906 " "
absolute error = 2.287059430727822500000000000000E-14 " "
relative error = 1.6320950191381078000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8164557729232371 " "
Order of pole = 1.4978308939005949 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = 1.299999999999978 " "
y[1] (analytic) = 1.4023027565006796 " "
y[1] (numeric) = 1.4023027565007022 " "
absolute error = 2.264854970235319300000000000000E-14 " "
relative error = 1.61509699651954000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.8181400366132836 " "
Order of pole = 1.5088170801578773 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ;"
Iterations = 201
"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 10 Minutes 27 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 10 Minutes 22 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 13 Minutes 23 Seconds
"Time to Timeout " Unknown
Percent Done = 22.444444444441974 "%"
(%o58) true
(%o58) diffeq.max