(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 then (ind_var : array_x ,
1
omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20,
" "), analytic_val_y : exact_soln_y(ind_var),
omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y,
20, " "), term_no : 1, numeric_val : array_y ,
term_no
abserr : omniabs(numeric_val - analytic_val_y),
omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val,
20, " "), if omniabs(analytic_val_y) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"absolute error ", 4, abserr, 20, " "),
omniout_float(ALWAYS, "relative error ", 4, relerr, 20,
"%"), omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " "), omniout_float(ALWAYS,
"h ", 4, glob_h, 20, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
1 10.0
if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param,
12, "due to singularity."), omniout_str(INFO, "Reached Optimal"),
return(hnew))), if not glob_reached_optimal_h
then (glob_reached_optimal_h : true, glob_curr_iter_when_opt :
glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(),
glob_optimal_start : array_x ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
clock_sec1 : elapsed_time_seconds(), total_clock_sec :
convfloat(clock_sec1) - convfloat(glob_orig_start_sec),
glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec),
left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
convfloat(clock_sec1) - convfloat(glob_orig_start_sec)),
opt_clock_sec : convfloat(clock_sec1)
- convfloat(glob_optimal_clock_start_sec),
glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
omniout_str_noeol(INFO, "Total Elapsed Time "),
omniout_timestr(convfloat(total_clock_sec)),
omniout_str_noeol(INFO, "Elapsed Time(since restart) "),
omniout_timestr(convfloat(glob_clock_sec)),
if convfloat(percent_done) < convfloat(100.0)
then (omniout_str_noeol(INFO, "Expected Time Remaining "),
omniout_timestr(convfloat(expect_sec)),
omniout_str_noeol(INFO, "Optimized Time Remaining "),
omniout_timestr(convfloat(glob_optimal_expect_sec)),
omniout_str_noeol(INFO, "Expected Total Time "),
omniout_timestr(convfloat(glob_total_exp_sec))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m,
n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new,
ratio, term], n : glob_max_terms, m : - 1 - 1 + n,
while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m
1, m - 2
array_y_higher
1, m
: m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1,
array_y_higher
1, m - 2
if omniabs(hdrc) > glob_small_float glob_small_float
glob_h
then (rcs : ------, ord_no :
hdrc
rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3)
-----------------------------------------------------,
hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found_sing : 1,
1, 2 1, 2
array_type_pole : 2, if glob_display_flag
1
then (if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1"))),
if (1 # found_sing) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > - 1.0 glob_smallish_float)
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0)))
1, 1 1, 2 1, 1 1, 2
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found_sing : 1, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE for equation 1")),
if (1 # found_sing) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole > - 1.0
1, 1 1, 2
glob_smallish_float))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found_sing : 1, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))),
if (1 # found_sing) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2,
1, 2 1, 2 1
found_sing : 1, if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))),
if 1 # found_sing then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
array_tmp1
1
temp2], array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : -----------,
1 1 1 1 array_x
1
array_tmp2 array_tmp3
1 1
array_tmp3 : -----------, array_tmp4 : -----------,
1 array_x 1 array_x
1 1
array_tmp5 : array_tmp4 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_m1 array_const_2D0 ,
2 2 1
array_tmp1 - array_tmp2 array_x
2 1 2
array_tmp2 : ----------------------------------,
2 array_x
1
array_tmp2 - array_tmp3 array_x
2 1 2
array_tmp3 : ----------------------------------,
2 array_x
1
array_tmp3 - array_tmp4 array_x
2 1 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
2 array_x 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_2D0 ,
3 3 1
array_tmp1 - array_tmp2 array_x
3 2 2
array_tmp2 : ----------------------------------,
3 array_x
1
array_tmp2 - array_tmp3 array_x
3 2 2
array_tmp3 : ----------------------------------,
3 array_x
1
array_tmp3 - array_tmp4 array_x
3 2 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
3 array_x 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_m1 array_const_2D0 ,
4 4 1
array_tmp1 - array_tmp2 array_x
4 3 2
array_tmp2 : ----------------------------------,
4 array_x
1
array_tmp2 - array_tmp3 array_x
4 3 2
array_tmp3 : ----------------------------------,
4 array_x
1
array_tmp3 - array_tmp4 array_x
4 3 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
4 array_x 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_m1 array_const_2D0 ,
5 5 1
array_tmp1 - array_tmp2 array_x
5 4 2
array_tmp2 : ----------------------------------,
5 array_x
1
array_tmp2 - array_tmp3 array_x
5 4 2
array_tmp3 : ----------------------------------,
5 array_x
1
array_tmp3 - array_tmp4 array_x
5 4 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
5 array_x 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 ,
kkk kkk 1
- ats(kkk, array_x, array_tmp2, 2)
array_tmp2 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp3, 2)
array_tmp3 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp4, 2)
array_tmp4 : ----------------------------------,
kkk array_x
1
array_tmp5 : array_tmp4 , 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_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
array_tmp1
1
temp2], array_tmp1 : array_m1 array_const_2D0 , array_tmp2 : -----------,
1 1 1 1 array_x
1
array_tmp2 array_tmp3
1 1
array_tmp3 : -----------, array_tmp4 : -----------,
1 array_x 1 array_x
1 1
array_tmp5 : array_tmp4 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_m1 array_const_2D0 ,
2 2 1
array_tmp1 - array_tmp2 array_x
2 1 2
array_tmp2 : ----------------------------------,
2 array_x
1
array_tmp2 - array_tmp3 array_x
2 1 2
array_tmp3 : ----------------------------------,
2 array_x
1
array_tmp3 - array_tmp4 array_x
2 1 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
2 array_x 2 2
1
if not array_y_set_initial then (if 2 <= glob_max_terms
1, 3
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2),
2
array_y : temporary, array_y_higher : temporary,
3 1, 3
temporary 2.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 3,
glob_h 2, 2
array_tmp1 : array_m1 array_const_2D0 ,
3 3 1
array_tmp1 - array_tmp2 array_x
3 2 2
array_tmp2 : ----------------------------------,
3 array_x
1
array_tmp2 - array_tmp3 array_x
3 2 2
array_tmp3 : ----------------------------------,
3 array_x
1
array_tmp3 - array_tmp4 array_x
3 2 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
3 array_x 3 3
1
if not array_y_set_initial then (if 3 <= glob_max_terms
1, 4
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3),
3
array_y : temporary, array_y_higher : temporary,
4 1, 4
temporary 3.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 4,
glob_h 2, 3
array_tmp1 : array_m1 array_const_2D0 ,
4 4 1
array_tmp1 - array_tmp2 array_x
4 3 2
array_tmp2 : ----------------------------------,
4 array_x
1
array_tmp2 - array_tmp3 array_x
4 3 2
array_tmp3 : ----------------------------------,
4 array_x
1
array_tmp3 - array_tmp4 array_x
4 3 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
4 array_x 4 4
1
if not array_y_set_initial then (if 4 <= glob_max_terms
1, 5
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4),
4
array_y : temporary, array_y_higher : temporary,
5 1, 5
temporary 4.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 5,
glob_h 2, 4
array_tmp1 : array_m1 array_const_2D0 ,
5 5 1
array_tmp1 - array_tmp2 array_x
5 4 2
array_tmp2 : ----------------------------------,
5 array_x
1
array_tmp2 - array_tmp3 array_x
5 4 2
array_tmp3 : ----------------------------------,
5 array_x
1
array_tmp3 - array_tmp4 array_x
5 4 2
array_tmp4 : ----------------------------------, array_tmp5 : array_tmp4 ,
5 array_x 5 5
1
if not array_y_set_initial then (if 5 <= glob_max_terms
1, 6
then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5),
5
array_y : temporary, array_y_higher : temporary,
6 1, 6
temporary 5.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 6,
glob_h 2, 5
while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 ,
kkk kkk 1
- ats(kkk, array_x, array_tmp2, 2)
array_tmp2 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp3, 2)
array_tmp3 : ----------------------------------,
kkk array_x
1
- ats(kkk, array_x, array_tmp4, 2)
array_tmp4 : ----------------------------------,
kkk array_x
1
array_tmp5 : array_tmp4 , 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_tmp5 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "
~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att,
while iii_att <= mmm_att do (lll_att : ma_att - iii_att,
al_att : lll_att - 1, if lll_att <= glob_max_terms
then ret_att : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%o27) display_pole_debug(typ, radius, order2) :=
(if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS,
"DBG Radius of convergence ", 4, radius, 4, " "),
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " "))
(%i28) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o28) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o30) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o32) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i33) log_revs(file, revs) := printf(file, revs)
(%o33) log_revs(file, revs) := printf(file, revs)
(%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i35) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o35) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i36) logstart(file) := printf(file, "")
(%o36) logstart(file) := printf(file, "
")
(%i37) logend(file) := printf(file, "
~%")
(%o37) logend(file) := printf(file, "~%")
(%i38) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o38) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o40) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i41) factorial_2(nnn) := nnn!
(%o41) factorial_2(nnn) := nnn!
(%i42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o42) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o43) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i44) convfp(mmm) := mmm
(%o44) convfp(mmm) := mmm
(%i45) convfloat(mmm) := mmm
(%o45) convfloat(mmm) := mmm
(%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i47) Si(x) := 0.0
(%o47) Si(x) := 0.0
(%i48) Ci(x) := 0.0
(%o48) Ci(x) := 0.0
(%i49) ln(x) := log(x)
(%o49) ln(x) := log(x)
(%i50) arcsin(x) := asin(x)
(%o50) arcsin(x) := asin(x)
(%i51) arccos(x) := acos(x)
(%o51) arccos(x) := acos(x)
(%i52) arctan(x) := atan(x)
(%o52) arctan(x) := atan(x)
(%i53) omniabs(x) := abs(x)
(%o53) omniabs(x) := abs(x)
(%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i55) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o55) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, ""), desired_abs_gbl_error :
expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer),
omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32,
""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
1.0
---
x
(%i56) exact_soln_y(x) := block(---)
x
1.0
---
x
(%o56) exact_soln_y(x) := block(---)
x
(%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord,
order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter,
calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms,
opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer,
best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-201, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10,
glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1,
glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0,
glob_max_minutes : 15.0, omniout_str(ALWAYS,
"##############ECHO OF PROBLEM#################"),
omniout_str(ALWAYS, "##############temp/sing3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:-0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (1.0/x/x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 20, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 20
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, if glob_max_h < glob_h
then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T19:06:56-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing3"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "sing3 diffeq.max"),
logitem_str(html_log_file, "sing3 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/sing3postode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"),
omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-1.0,"), omniout_str(ALWAYS, "x_end:-0.7,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("),
omniout_str(ALWAYS, " (1.0/x/x) "), omniout_str(ALWAYS, "));"),
omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32,
max_terms : 20, glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms),
array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1,
term
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_tmp5, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term),
term
array(array_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_2D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term),
term
array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 1.0, x_end : - 0.7, array_y_init : exact_soln_y(x_start),
1 + 0
glob_look_poles : true, glob_max_iter : 100, glob_desired_digits_correct : 10,
glob_display_interval : 0.001, glob_look_poles : true,
glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3,
glob_last_good_h : glob_h, glob_max_terms : max_terms,
glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 20
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, if glob_max_h < glob_h
then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0,
omniout_str(DEBUGL, " "), glob_reached_optimal_h : true,
glob_optimal_clock_start_sec : elapsed_time_seconds(),
while (glob_current_iter < glob_max_iter)
and (glob_check_sign array_x < glob_check_sign x_end)
1
and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval
() then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-28T19:06:56-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "sing3"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
logitem_time(html_log_file, convfloat(glob_clock_sec)),
if glob_percent_done < 100.0 then (logitem_time(html_log_file,
convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"),
0), log_revs(html_log_file, " 165 | "), logitem_str(html_log_file, "sing3 diffeq.max"),
logitem_str(html_log_file, "sing3 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/sing3postode.ode#################"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"Digits:32,"
"max_terms:20,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-1.0,"
"x_end:-0.7,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (1.0/x/x) "
"));"
""
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 0.30000000000000004 ""
estimated_steps = 300.00000000000006 ""
step_error = 3.3333333333333330000000000000E-13 ""
est_needed_step_err = 3.3333333333333330000000000000E-13 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 1.8758827696078434000000000000000000000000000000000000000000000000E-48 ""
max_value3 = 1.8758827696078434000000000000000000000000000000000000000000000000E-48 ""
value3 = 1.8758827696078434000000000000000000000000000000000000000000000000E-48 ""
best_h = 1.000E-3 ""
"START of Soultion"
" "
"TOP MAIN SOLVE Loop"
x[1] = -1. " "
y[1] (analytic) = 1. " "
y[1] (numeric) = 1. " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9963369963369947 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.999 " "
y[1] (analytic) = 1.002003004005006 " "
y[1] (numeric) = 1.002003004005006 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9953406593406595 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.998 " "
y[1] (analytic) = 1.0040120320801924 " "
y[1] (numeric) = 1.0040120320801926 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.21157314683750900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9943443223443221 " "
Order of pole = 225.05494505494505 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.997 " "
y[1] (analytic) = 1.0060271084064631 " "
y[1] (numeric) = 1.0060271084064634 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.207143356969254200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.993347985347987 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.996 " "
y[1] (analytic) = 1.0080482572861729 " "
y[1] (numeric) = 1.008048257286173 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.202718007993098600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9923516483516507 " "
Order of pole = 225.0549450549456 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.995 " "
y[1] (analytic) = 1.01007550314386 " "
y[1] (numeric) = 1.0100755031438602 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.19829709990904120000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9913553113553109 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.994 " "
y[1] (analytic) = 1.0121088705269847 " "
y[1] (numeric) = 1.012108870526985 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.193880632717082600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9903589743589732 " "
Order of pole = 225.05494505494482 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.993 " "
y[1] (analytic) = 1.014148384106672 " "
y[1] (numeric) = 1.0141483841066723 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.189468606417222200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9893626373626379 " "
Order of pole = 225.05494505494514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.992 " "
y[1] (analytic) = 1.0161940686784598 " "
y[1] (numeric) = 1.01619406867846 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.185061021009460000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9883663003663046 " "
Order of pole = 225.05494505494602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.991 " "
y[1] (analytic) = 1.0182459491630527 " "
y[1] (numeric) = 1.0182459491630529 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.180657876493796700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9873699633699674 " "
Order of pole = 225.05494505494602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.99 " "
y[1] (analytic) = 1.020304050607081 " "
y[1] (numeric) = 1.020304050607081 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5910017974415938 " "
Order of pole = 1.0444978215673473000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.989 " "
y[1] (analytic) = 1.022368398183865 " "
y[1] (numeric) = 1.022368398183865 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5908023484188833 " "
Order of pole = 1.0462741784067475000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.988 " "
y[1] (analytic) = 1.0244390171941844 " "
y[1] (numeric) = 1.0244390171941846 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.167475088299397600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9843809523809511 " "
Order of pole = 225.05494505494477 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.987 " "
y[1] (analytic) = 1.0265159330670552 " "
y[1] (numeric) = 1.0265159330670552 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9833846153846183 " "
Order of pole = 225.05494505494573 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.986 " "
y[1] (analytic) = 1.0285991713605076 " "
y[1] (numeric) = 1.0285991713605076 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.24132965006399087 " "
Order of pole = 7.6916251146030850000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.985 " "
y[1] (analytic) = 1.0306887577623747 " "
y[1] (numeric) = 1.0306887577623747 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9813919413919426 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.984 " "
y[1] (analytic) = 1.0327847180910834 " "
y[1] (numeric) = 1.0327847180910834 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9803956043956024 " "
Order of pole = 225.0549450549446 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.983 " "
y[1] (analytic) = 1.0348870782964519 " "
y[1] (numeric) = 1.0348870782964517 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.145592592484035500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9793992673992634 " "
Order of pole = 225.05494505494414 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.982 " "
y[1] (analytic) = 1.0369958644604924 " "
y[1] (numeric) = 1.0369958644604924 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9784029304029327 " "
Order of pole = 225.05494505494556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.981 " "
y[1] (analytic) = 1.0391111027982223 " "
y[1] (numeric) = 1.0391111027982223 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9774065934065953 " "
Order of pole = 225.0549450549455 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.98 " "
y[1] (analytic) = 1.0412328196584757 " "
y[1] (numeric) = 1.0412328196584757 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.9656263696246429 " "
Order of pole = 1.1262102361797588000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.979 " "
y[1] (analytic) = 1.043361041524726 " "
y[1] (numeric) = 1.043361041524726 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9754139194139217 " "
Order of pole = 225.05494505494562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.978 " "
y[1] (analytic) = 1.0454957950159125 " "
y[1] (numeric) = 1.0454957950159125 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9744175824175857 " "
Order of pole = 225.0549450549458 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.977 " "
y[1] (analytic) = 1.0476371068872712 " "
y[1] (numeric) = 1.0476371068872712 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.973421245421248 " "
Order of pole = 225.05494505494562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.976 " "
y[1] (analytic) = 1.0497850040311743 " "
y[1] (numeric) = 1.0497850040311745 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.115143615810666500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9724249084249073 " "
Order of pole = 225.05494505494477 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.975 " "
y[1] (analytic) = 1.0519395134779752 " "
y[1] (numeric) = 1.051939513477975 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.110811525568578600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.861675886475732 " "
Order of pole = 3.3946179200938786000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.974 " "
y[1] (analytic) = 1.0541006623968563 " "
y[1] (numeric) = 1.0541006623968563 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.970432234432239 " "
Order of pole = 225.05494505494613 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.973 " "
y[1] (analytic) = 1.0562684780966887 " "
y[1] (numeric) = 1.0562684780966887 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9694358974358914 " "
Order of pole = 225.0549450549436 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.972 " "
y[1] (analytic) = 1.0584429880268929 " "
y[1] (numeric) = 1.0584429880268929 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9684395604395621 " "
Order of pole = 225.05494505494545 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.971 " "
y[1] (analytic) = 1.0606242197783085 " "
y[1] (numeric) = 1.0606242197783082 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.093527573521214400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.967443223443224 " "
Order of pole = 225.0549450549452 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.97 " "
y[1] (analytic) = 1.0628122010840686 " "
y[1] (numeric) = 1.0628122010840684 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.089217687739619300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9664468864468867 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.969 " "
y[1] (analytic) = 1.0650069598204825 " "
y[1] (numeric) = 1.0650069598204823 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.08491224285012300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.965450549450549 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.968 " "
y[1] (analytic) = 1.0672085240079232 " "
y[1] (numeric) = 1.0672085240079228 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.1612224777054500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9644542124542166 " "
Order of pole = 225.05494505494605 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.967 " "
y[1] (analytic) = 1.0694169218117207 " "
y[1] (numeric) = 1.0694169218117204 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.07631467574742600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9634578754578788 " "
Order of pole = 225.05494505494585 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.966 " "
y[1] (analytic) = 1.0716321815430647 " "
y[1] (numeric) = 1.0716321815430645 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.07202255353422500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.962461538461538 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.965 " "
y[1] (analytic) = 1.0738543316599105 " "
y[1] (numeric) = 1.0738543316599103 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.067734872213122500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9614652014652042 " "
Order of pole = 225.0549450549457 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.964 " "
y[1] (analytic) = 1.0760834007678932 " "
y[1] (numeric) = 1.076083400767893 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.063451631784118700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9604688644688647 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.963 " "
y[1] (analytic) = 1.078319417621249 " "
y[1] (numeric) = 1.0783194176212487 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.059172832247213600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9594725274725285 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.962 " "
y[1] (analytic) = 1.0805624111237417 " "
y[1] (numeric) = 1.0805624111237415 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 2.054898473602406700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9584761904761917 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.961 " "
y[1] (analytic) = 1.0828124103295975 " "
y[1] (numeric) = 1.082812410329597 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.10125711169939570000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.7617319659364342 " "
Order of pole = 1.106670310946356000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.96 " "
y[1] (analytic) = 1.0850694444444446 " "
y[1] (numeric) = 1.0850694444444442 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.09272615797817650000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9564835164835199 " "
Order of pole = 225.0549450549459 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.959 " "
y[1] (analytic) = 1.0873335428262627 " "
y[1] (numeric) = 1.0873335428262623 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.08420408604115400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.459082932253201 " "
Order of pole = 2.2026824808563106000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.958 " "
y[1] (analytic) = 1.0896047349863365 " "
y[1] (numeric) = 1.089604734986336 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.075690895888328700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9544908424908466 " "
Order of pole = 225.05494505494607 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.957 " "
y[1] (analytic) = 1.0918830505902175 " "
y[1] (numeric) = 1.091883050590217 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.067186587519699400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.953494505494507 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.956 " "
y[1] (analytic) = 1.094168519458693 " "
y[1] (numeric) = 1.0941685194586925 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.05869116093526770000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9524981684981696 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.955 " "
y[1] (analytic) = 1.0964611715687618 " "
y[1] (numeric) = 1.0964611715687613 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.050204616135033600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.7859895686930835 " "
Order of pole = 5.5777604757167860000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.954 " "
y[1] (analytic) = 1.0987610370546173 " "
y[1] (numeric) = 1.0987610370546168 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.04172695311899600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.950505494505494 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.953 " "
y[1] (analytic) = 1.1010681462086371 " "
y[1] (numeric) = 1.1010681462086367 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.03325817188715500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9495091575091587 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.952 " "
y[1] (analytic) = 1.1033825294823814 " "
y[1] (numeric) = 1.103382529482381 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.024798272439510400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.94851282051282 " "
Order of pole = 225.054945054945 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.951 " "
y[1] (analytic) = 1.1057042174875968 " "
y[1] (numeric) = 1.1057042174875964 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.01634725477606400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9475164835164858 " "
Order of pole = 225.05494505494562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.95 " "
y[1] (analytic) = 1.10803324099723 " "
y[1] (numeric) = 1.1080332409972296 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 4.00790511889681500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9465201465201476 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.949 " "
y[1] (analytic) = 1.110369630946446 " "
y[1] (numeric) = 1.1103696309464455 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.99947186480176200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.945523809523812 " "
Order of pole = 225.05494505494565 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.948 " "
y[1] (analytic) = 1.1127134184336556 " "
y[1] (numeric) = 1.1127134184336553 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.995523746245453400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9445274725274726 " "
Order of pole = 225.05494505494508 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.947 " "
y[1] (analytic) = 1.1150646347215518 " "
y[1] (numeric) = 1.1150646347215514 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.98263200196424700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.6869570936925448 " "
Order of pole = 1.31450406115618530000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.946 " "
y[1] (analytic) = 1.1174233112381498 " "
y[1] (numeric) = 1.1174233112381495 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.98711269661089300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9425347985347993 " "
Order of pole = 225.05494505494522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.945 " "
y[1] (analytic) = 1.1197894795778396 " "
y[1] (numeric) = 1.1197894795778391 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.96582766626352060000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9415384615384619 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.944 " "
y[1] (analytic) = 1.122163171502442 " "
y[1] (numeric) = 1.1221631715024416 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.95743882108945300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9405421245421267 " "
Order of pole = 225.05494505494562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.943 " "
y[1] (analytic) = 1.1245444189422762 " "
y[1] (numeric) = 1.1245444189422757 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.949058857699582000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9395457875457869 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.942 " "
y[1] (analytic) = 1.1269332539972323 " "
y[1] (numeric) = 1.1269332539972319 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.94068777609390900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9385494505494527 " "
Order of pole = 225.05494505494556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.941 " "
y[1] (analytic) = 1.1293297089378542 " "
y[1] (numeric) = 1.1293297089378538 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.932325576272432400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9375531135531155 " "
Order of pole = 225.05494505494556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.94 " "
y[1] (analytic) = 1.1317338162064283 " "
y[1] (numeric) = 1.1317338162064279 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.92397225823515300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9365567765567738 " "
Order of pole = 225.05494505494437 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.939 " "
y[1] (analytic) = 1.1341456084180823 " "
y[1] (numeric) = 1.134145608418082 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.957813910991035300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9355604395604362 " "
Order of pole = 225.05494505494423 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.938 " "
y[1] (analytic) = 1.1365651183618914 " "
y[1] (numeric) = 1.1365651183618912 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.953646133756592200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9345641025641027 " "
Order of pole = 225.05494505494508 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9369999999999999 " "
y[1] (analytic) = 1.1389923790019922 " "
y[1] (numeric) = 1.1389923790019918 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.89896559482849570000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9335677655677673 " "
Order of pole = 225.05494505494553 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9359999999999999 " "
y[1] (analytic) = 1.1414274234787056 " "
y[1] (numeric) = 1.1414274234787052 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.89064780392800400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9325714285714258 " "
Order of pole = 225.05494505494437 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9349999999999999 " "
y[1] (analytic) = 1.1438702851096687 " "
y[1] (numeric) = 1.1438702851096683 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.88233889481170940000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9315750915750886 " "
Order of pole = 225.05494505494428 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9339999999999999 " "
y[1] (analytic) = 1.1463209973909736 " "
y[1] (numeric) = 1.1463209973909732 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.87403886747961170000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9305787545787573 " "
Order of pole = 225.05494505494576 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9329999999999999 " "
y[1] (analytic) = 1.148779593998316 " "
y[1] (numeric) = 1.1487795939983156 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.86574772193171100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9295824175824191 " "
Order of pole = 225.05494505494548 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9319999999999999 " "
y[1] (analytic) = 1.1512461087881525 " "
y[1] (numeric) = 1.151246108788152 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.85746545816800700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9285860805860826 " "
Order of pole = 225.05494505494556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9309999999999999 " "
y[1] (analytic) = 1.1537205757988651 " "
y[1] (numeric) = 1.1537205757988647 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.84919207618850070000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9275897435897431 " "
Order of pole = 225.05494505494488 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9299999999999999 " "
y[1] (analytic) = 1.156203029251937 " "
y[1] (numeric) = 1.1562030292519363 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.76139136398978500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9265934065934064 " "
Order of pole = 225.05494505494505 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9289999999999999 " "
y[1] (analytic) = 1.1586935035531336 " "
y[1] (numeric) = 1.1586935035531334 " "
absolute error = 2.2204460492503130000000000000000E-16 " "
relative error = 1.916335978791039500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9255970695970706 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9279999999999999 " "
y[1] (analytic) = 1.1611920332936982 " "
y[1] (numeric) = 1.1611920332936978 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.824425220955162000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9246007326007284 " "
Order of pole = 225.054945054944 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9269999999999999 " "
y[1] (analytic) = 1.1636986532515488 " "
y[1] (numeric) = 1.1636986532515483 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.81618736611244400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9236043956043929 " "
Order of pole = 225.05494505494434 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9259999999999999 " "
y[1] (analytic) = 1.1662133983924916 " "
y[1] (numeric) = 1.1662133983924912 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.807958393053922400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9226080586080562 " "
Order of pole = 225.05494505494448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9249999999999999 " "
y[1] (analytic) = 1.1687363038714391 " "
y[1] (numeric) = 1.1687363038714387 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.799738301779597700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9216117216117183 " "
Order of pole = 225.05494505494426 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9239999999999999 " "
y[1] (analytic) = 1.171267405033639 " "
y[1] (numeric) = 1.1712674050336385 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.7915270922894700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9206153846153898 " "
Order of pole = 225.0549450549464 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9229999999999999 " "
y[1] (analytic) = 1.1738067374159116 " "
y[1] (numeric) = 1.1738067374159111 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.7833247645835400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9196190476190502 " "
Order of pole = 225.05494505494573 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9219999999999999 " "
y[1] (analytic) = 1.176354336747898 " "
y[1] (numeric) = 1.1763543367478975 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.77513131866180630000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.24089637379326878 " "
Order of pole = 2.447819724693545100000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9209999999999999 " "
y[1] (analytic) = 1.1789102389533164 " "
y[1] (numeric) = 1.178910238953316 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.7669467545242696000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9176263736263744 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9199999999999999 " "
y[1] (analytic) = 1.181474480151229 " "
y[1] (numeric) = 1.1814744801512282 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.63815660825639400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9166300366300356 " "
Order of pole = 225.05494505494477 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9189999999999999 " "
y[1] (analytic) = 1.1840470966573169 " "
y[1] (numeric) = 1.1840470966573162 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.6259064074026800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9156336996337013 " "
Order of pole = 225.05494505494548 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9179999999999999 " "
y[1] (analytic) = 1.1866281249851671 " "
y[1] (numeric) = 1.1866281249851667 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.74244635281684170000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.91463736263736 " "
Order of pole = 225.0549450549444 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9169999999999999 " "
y[1] (analytic) = 1.1892176018475686 " "
y[1] (numeric) = 1.189217601847568 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.601445973724138000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9136410256410284 " "
Order of pole = 225.05494505494573 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9159999999999999 " "
y[1] (analytic) = 1.1918155641578156 " "
y[1] (numeric) = 1.191815564157815 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.58923574089931100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9126446886446876 " "
Order of pole = 225.05494505494485 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9149999999999999 " "
y[1] (analytic) = 1.1944220490310253 " "
y[1] (numeric) = 1.1944220490310247 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.57703883075077900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9116483516483528 " "
Order of pole = 225.0549450549454 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9139999999999999 " "
y[1] (analytic) = 1.1970370937854624 " "
y[1] (numeric) = 1.1970370937854617 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.56485524327854300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9106520146520171 " "
Order of pole = 225.05494505494568 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9129999999999999 " "
y[1] (analytic) = 1.1996607359438751 " "
y[1] (numeric) = 1.1996607359438747 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.70178998565506840000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9096556776556803 " "
Order of pole = 225.05494505494576 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9119999999999999 " "
y[1] (analytic) = 1.2022930132348417 " "
y[1] (numeric) = 1.202293013234841 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.54052803636295600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.8721057396055435 " "
Order of pole = 2.1795898419441073000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9109999999999999 " "
y[1] (analytic) = 1.2049339635941254 " "
y[1] (numeric) = 1.2049339635941247 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.52838441691960600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.907663003663007 " "
Order of pole = 225.05494505494593 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9099999999999999 " "
y[1] (analytic) = 1.207583625166043 " "
y[1] (numeric) = 1.2075836251660423 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.516254120152552000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9066666666666671 " "
Order of pole = 225.05494505494516 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9089999999999999 " "
y[1] (analytic) = 1.2102420363048407 " "
y[1] (numeric) = 1.2102420363048403 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.669424764041195300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9056703296703296 " "
Order of pole = 225.05494505494505 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9079999999999999 " "
y[1] (analytic) = 1.2129092355760835 " "
y[1] (numeric) = 1.212909235576083 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.661355663098219700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9046739926739885 " "
Order of pole = 225.054945054944 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9069999999999999 " "
y[1] (analytic) = 1.2155852617580525 " "
y[1] (numeric) = 1.215585261758052 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.653295443939441600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9036776556776528 " "
Order of pole = 225.05494505494437 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9059999999999999 " "
y[1] (analytic) = 1.2182701538431553 " "
y[1] (numeric) = 1.2182701538431546 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.467866159847289000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5748831351339536 " "
Order of pole = 2.666311615939776000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9049999999999999 " "
y[1] (analytic) = 1.2209639510393457 " "
y[1] (numeric) = 1.220963951039345 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.45580247646171200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9016849816849845 " "
Order of pole = 225.0549450549458 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9039999999999999 " "
y[1] (analytic) = 1.2236666927715565 " "
y[1] (numeric) = 1.2236666927715556 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.25833615433657300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.9006886446886461 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9029999999999999 " "
y[1] (analytic) = 1.2263784186831395 " "
y[1] (numeric) = 1.2263784186831388 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.43171507771944600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8996923076923112 " "
Order of pole = 225.05494505494596 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9019999999999999 " "
y[1] (analytic) = 1.2290991686373227 " "
y[1] (numeric) = 1.2290991686373218 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.22625514981700500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8986959706959671 " "
Order of pole = 225.05494505494414 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.9009999999999999 " "
y[1] (analytic) = 1.2318289827186715 " "
y[1] (numeric) = 1.2318289827186706 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.21024129290981300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8976996336996342 " "
Order of pole = 225.05494505494516 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8999999999999999 " "
y[1] (analytic) = 1.234567901234568 " "
y[1] (numeric) = 1.2345679012345674 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.3956838996782600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.33045868336932477 " "
Order of pole = 2.9878322038712213000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8989999999999999 " "
y[1] (analytic) = 1.2373159647166982 " "
y[1] (numeric) = 1.2373159647166974 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.17826686980060800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8957069597069619 " "
Order of pole = 225.05494505494565 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8979999999999999 " "
y[1] (analytic) = 1.2400732139225503 " "
y[1] (numeric) = 1.2400732139225494 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.16230630359859600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8947106227106257 " "
Order of pole = 225.05494505494582 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8969999999999999 " "
y[1] (analytic) = 1.2428396898369274 " "
y[1] (numeric) = 1.2428396898369265 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.14636350096497800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8937142857142842 " "
Order of pole = 225.05494505494468 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8959999999999999 " "
y[1] (analytic) = 1.2456154336734695 " "
y[1] (numeric) = 1.2456154336734688 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.34782884642481800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5580311371242235 " "
Order of pole = 3.204547738278052000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8949999999999999 " "
y[1] (analytic) = 1.2484004868761902 " "
y[1] (numeric) = 1.2484004868761893 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.11453118640292600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8917216117216128 " "
Order of pole = 225.0549450549454 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8939999999999999 " "
y[1] (analytic) = 1.2511948911210207 " "
y[1] (numeric) = 1.25119489112102 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.32398125585587000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8907252747252783 " "
Order of pole = 225.05494505494602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8929999999999999 " "
y[1] (analytic) = 1.2539986883173724 " "
y[1] (numeric) = 1.2539986883173715 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.08276992611444900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8897289377289407 " "
Order of pole = 225.05494505494585 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8919999999999999 " "
y[1] (analytic) = 1.2568119206097048 " "
y[1] (numeric) = 1.2568119206097041 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.300186955992102000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8887326007325992 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8909999999999999 " "
y[1] (analytic) = 1.2596346303791126 " "
y[1] (numeric) = 1.2596346303791117 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 7.0510797200995490000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8877362637362616 " "
Order of pole = 225.05494505494448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8899999999999999 " "
y[1] (analytic) = 1.2624668602449187 " "
y[1] (numeric) = 1.262466860244918 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.27644594683351800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8867399267399242 " "
Order of pole = 225.05494505494448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8889999999999999 " "
y[1] (analytic) = 1.2653086530662858 " "
y[1] (numeric) = 1.2653086530662851 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.2645954262686700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8857435897435946 " "
Order of pole = 225.0549450549463 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8879999999999999 " "
y[1] (analytic) = 1.2681600519438359 " "
y[1] (numeric) = 1.2681600519438352 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.25275822838011600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8847472527472516 " "
Order of pole = 225.0549450549448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8869999999999999 " "
y[1] (analytic) = 1.271021100221285 " "
y[1] (numeric) = 1.2710211002212843 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.24093435316785800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8837509157509145 " "
Order of pole = 225.05494505494477 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8859999999999999 " "
y[1] (analytic) = 1.2738918414870906 " "
y[1] (numeric) = 1.27389184148709 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.229123800631895000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8827545787545811 " "
Order of pole = 225.05494505494573 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8849999999999999 " "
y[1] (analytic) = 1.2767723195761118 " "
y[1] (numeric) = 1.2767723195761111 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.21732657077222800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8817582417582424 " "
Order of pole = 225.05494505494522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8839999999999999 " "
y[1] (analytic) = 1.2796625785712827 " "
y[1] (numeric) = 1.2796625785712819 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.94072355145180800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8807619047619074 " "
Order of pole = 225.0549450549458 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8829999999999999 " "
y[1] (analytic) = 1.2825626628052982 " "
y[1] (numeric) = 1.2825626628052975 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.193772079081781000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8797655677655689 " "
Order of pole = 225.0549450549454 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8819999999999999 " "
y[1] (analytic) = 1.285472616862316 " "
y[1] (numeric) = 1.2854726168623152 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.90935308966800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8787692307692339 " "
Order of pole = 225.0549450549459 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8809999999999999 " "
y[1] (analytic) = 1.2883924855796676 " "
y[1] (numeric) = 1.2883924855796667 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.89369450412868700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.877772893772894 " "
Order of pole = 225.05494505494514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8799999999999999 " "
y[1] (analytic) = 1.291322314049587 " "
y[1] (numeric) = 1.2913223140495864 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.15854026161832600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8767765567765567 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8789999999999999 " "
y[1] (analytic) = 1.2942621476209524 " "
y[1] (numeric) = 1.2942621476209517 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.14682296781643200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.8036218355716963 " "
Order of pole = 1.2096990076315706000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8779999999999999 " "
y[1] (analytic) = 1.2972120319010387 " "
y[1] (numeric) = 1.297212031901038 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.13511899669083300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.874783882783886 " "
Order of pole = 225.05494505494593 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8769999999999999 " "
y[1] (analytic) = 1.3001720127572882 " "
y[1] (numeric) = 1.3001720127572876 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.12342834824153100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8737875457875421 " "
Order of pole = 225.0549450549441 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8759999999999999 " "
y[1] (analytic) = 1.303142136319093 " "
y[1] (numeric) = 1.3031421363190923 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.11175102246852400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.872791208791208 " "
Order of pole = 225.05494505494485 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8749999999999999 " "
y[1] (analytic) = 1.3061224489795922 " "
y[1] (numeric) = 1.3061224489795915 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.100087019371812000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8717948717948726 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8739999999999999 " "
y[1] (analytic) = 1.3091129973974835 " "
y[1] (numeric) = 1.309112997397483 " "
absolute error = 4.4408920985006260000000000000000E-16 " "
relative error = 3.39229089263426400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8707985347985344 " "
Order of pole = 225.05494505494497 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8729999999999999 " "
y[1] (analytic) = 1.3121138284988503 " "
y[1] (numeric) = 1.3121138284988496 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.07679898120727400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8698021978021957 " "
Order of pole = 225.0549450549445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8719999999999999 " "
y[1] (analytic) = 1.3151249894790005 " "
y[1] (numeric) = 1.3151249894789998 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.065174946139449000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8688058608058565 " "
Order of pole = 225.05494505494394 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8709999999999999 " "
y[1] (analytic) = 1.318146527804324 " "
y[1] (numeric) = 1.3181465278043234 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.05356423374791900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.576879924907525 " "
Order of pole = 2.3572255258841324000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8699999999999999 " "
y[1] (analytic) = 1.3211784912141633 " "
y[1] (numeric) = 1.3211784912141626 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.04196684403268500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8668131868131859 " "
Order of pole = 225.05494505494485 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8689999999999999 " "
y[1] (analytic) = 1.324220927722698 " "
y[1] (numeric) = 1.324220927722697 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.70717703599166000000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.8357899868906106 " "
Order of pole = 1.545430450278218000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8679999999999999 " "
y[1] (analytic) = 1.327273885620846 " "
y[1] (numeric) = 1.3272738856208453 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.01881203263110300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8648205128205158 " "
Order of pole = 225.05494505494588 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8669999999999999 " "
y[1] (analytic) = 1.3303374134781807 " "
y[1] (numeric) = 1.33033741347818 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 5.00725461094475500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8638241758241737 " "
Order of pole = 225.05494505494457 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8659999999999999 " "
y[1] (analytic) = 1.3334115601448622 " "
y[1] (numeric) = 1.3334115601448613 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.6609473492462700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8628278388278385 " "
Order of pole = 225.054945054945 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8649999999999999 " "
y[1] (analytic) = 1.3364963747535838 " "
y[1] (numeric) = 1.336496374753583 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.6455729808012600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8618315018315019 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8639999999999999 " "
y[1] (analytic) = 1.339591906721537 " "
y[1] (numeric) = 1.3395919067215358 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.28777046990580400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8608351648351628 " "
Order of pole = 225.0549450549445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8629999999999999 " "
y[1] (analytic) = 1.3426982057523882 " "
y[1] (numeric) = 1.342698205752387 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.26859691827052900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8598388278388281 " "
Order of pole = 225.05494505494514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8619999999999999 " "
y[1] (analytic) = 1.3458153218382765 " "
y[1] (numeric) = 1.3458153218382756 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.59955645687659600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8588424908424962 " "
Order of pole = 225.05494505494653 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8609999999999999 " "
y[1] (analytic) = 1.3489433052618236 " "
y[1] (numeric) = 1.3489433052618227 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.58425314270516300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8578461538461554 " "
Order of pole = 225.05494505494553 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8599999999999999 " "
y[1] (analytic) = 1.3520822065981615 " "
y[1] (numeric) = 1.3520822065981608 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.92672569407659360000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8568498168498183 " "
Order of pole = 225.05494505494548 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8589999999999999 " "
y[1] (analytic) = 1.3552320767169777 " "
y[1] (numeric) = 1.355232076716977 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.9152748538006097000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.855853479853481 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8579999999999999 " "
y[1] (analytic) = 1.3583929667845758 " "
y[1] (numeric) = 1.3583929667845747 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.17306222700153300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.854857142857142 " "
Order of pole = 225.05494505494482 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8569999999999999 " "
y[1] (analytic) = 1.3615649282659523 " "
y[1] (numeric) = 1.3615649282659512 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.15402190212921300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8538608058608047 " "
Order of pole = 225.0549450549448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8559999999999999 " "
y[1] (analytic) = 1.3647480129268936 " "
y[1] (numeric) = 1.3647480129268927 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.50800302537390700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8528644688644723 " "
Order of pole = 225.05494505494605 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8549999999999999 " "
y[1] (analytic) = 1.3679422728360866 " "
y[1] (numeric) = 1.367942272836086 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.86960471945962900000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8518681318681303 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8539999999999999 " "
y[1] (analytic) = 1.3711477603672486 " "
y[1] (numeric) = 1.3711477603672477 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.47762732342016300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8508717948717945 " "
Order of pole = 225.05494505494505 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8529999999999999 " "
y[1] (analytic) = 1.3743645282012735 " "
y[1] (numeric) = 1.3743645282012724 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.07808264724485200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8498754578754573 " "
Order of pole = 225.0549450549449 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8519999999999999 " "
y[1] (analytic) = 1.3775926293283967 " "
y[1] (numeric) = 1.3775926293283955 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.05915334467499300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8488791208791174 " "
Order of pole = 225.05494505494414 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8509999999999999 " "
y[1] (analytic) = 1.3808321170503772 " "
y[1] (numeric) = 1.3808321170503763 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.43219699725250200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8478827838827832 " "
Order of pole = 225.0549450549449 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8499999999999999 " "
y[1] (analytic) = 1.3840830449826995 " "
y[1] (numeric) = 1.3840830449826984 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 8.02136135291675300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8468864468864473 " "
Order of pole = 225.05494505494525 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8489999999999999 " "
y[1] (analytic) = 1.3873454670567886 " "
y[1] (numeric) = 1.3873454670567877 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.40199893098269700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8458901098901106 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8479999999999999 " "
y[1] (analytic) = 1.3906194375222505 " "
y[1] (numeric) = 1.3906194375222494 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.98365817900048200000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8448937728937705 " "
Order of pole = 225.05494505494445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8469999999999999 " "
y[1] (analytic) = 1.3939050109491242 " "
y[1] (numeric) = 1.3939050109491233 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.3718719189864700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8438974358974353 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8459999999999999 " "
y[1] (analytic) = 1.3972022422301587 " "
y[1] (numeric) = 1.3972022422301578 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.35683505834094700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.18493865606284507 " "
Order of pole = 2.120970066243899000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8449999999999999 " "
y[1] (analytic) = 1.4005111865831035 " "
y[1] (numeric) = 1.4005111865831024 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.9272699515797700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8419047619047575 " "
Order of pole = 225.05494505494394 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8439999999999999 " "
y[1] (analytic) = 1.4038318995530203 " "
y[1] (numeric) = 1.4038318995530195 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.32681462775508300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.840908424908427 " "
Order of pole = 225.05494505494565 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8429999999999999 " "
y[1] (analytic) = 1.4071644370146166 " "
y[1] (numeric) = 1.4071644370146157 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.31183105781474100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8399120879120887 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8419999999999999 " "
y[1] (analytic) = 1.4105088551745932 " "
y[1] (numeric) = 1.4105088551745923 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.29686525144279400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8389157509157544 " "
Order of pole = 225.05494505494605 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8409999999999999 " "
y[1] (analytic) = 1.4138652105740157 " "
y[1] (numeric) = 1.4138652105740146 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.8523965107990500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8379194139194145 " "
Order of pole = 225.05494505494528 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8399999999999999 " "
y[1] (analytic) = 1.4172335600907033 " "
y[1] (numeric) = 1.4172335600907024 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.26698692940408100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8369230769230774 " "
Order of pole = 225.05494505494525 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8389999999999999 " "
y[1] (analytic) = 1.4206139609416402 " "
y[1] (numeric) = 1.4206139609416393 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.25207441373731700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8359267399267353 " "
Order of pole = 225.0549450549438 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8379999999999999 " "
y[1] (analytic) = 1.4240064706854032 " "
y[1] (numeric) = 1.4240064706854023 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.23717966163894500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8349304029303986 " "
Order of pole = 225.05494505494394 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8369999999999999 " "
y[1] (analytic) = 1.4274111472246136 " "
y[1] (numeric) = 1.4274111472246127 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.22230267310896800000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.83393406593407 " "
Order of pole = 225.05494505494622 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8359999999999999 " "
y[1] (analytic) = 1.4308280488084069 " "
y[1] (numeric) = 1.430828048808406 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.20744344814738500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8329377289377301 " "
Order of pole = 225.0549450549454 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8349999999999999 " "
y[1] (analytic) = 1.4342572340349244 " "
y[1] (numeric) = 1.4342572340349238 " "
absolute error = 6.6613381477509390000000000000000E-16 " "
relative error = 4.64445149006564750000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.42164434313274807 " "
Order of pole = 1.3784529073745944000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8339999999999999 " "
y[1] (analytic) = 1.4376987618538268 " "
y[1] (numeric) = 1.437698761853826 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.177778288929401000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.830945054945051 " "
Order of pole = 225.05494505494397 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8329999999999999 " "
y[1] (analytic) = 1.4411526915688249 " "
y[1] (numeric) = 1.441152691568824 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.16297235467300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8299487179487175 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8319999999999999 " "
y[1] (analytic) = 1.4446190828402372 " "
y[1] (numeric) = 1.4446190828402363 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.14818418398499300000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8289523809523791 " "
Order of pole = 225.05494505494462 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8309999999999998 " "
y[1] (analytic) = 1.4480979956875648 " "
y[1] (numeric) = 1.4480979956875637 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.66676722108172400000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8279560439560432 " "
Order of pole = 225.05494505494485 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8299999999999998 " "
y[1] (analytic) = 1.4515894904920894 " "
y[1] (numeric) = 1.4515894904920883 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 7.648326416642700000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.826959706959708 " "
Order of pole = 225.05494505494536 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8289999999999998 " "
y[1] (analytic) = 1.455093627999494 " "
y[1] (numeric) = 1.455093627999493 " "
absolute error = 8.8817841970012520000000000000000E-16 " "
relative error = 6.10392625333133500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8259633699633707 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8279999999999998 " "
y[1] (analytic) = 1.4586104693225053 " "
y[1] (numeric) = 1.458610469322504 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.13381370537535500000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.824967032967031 " "
Order of pole = 225.0549450549445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8269999999999998 " "
y[1] (analytic) = 1.462140075943556 " "
y[1] (numeric) = 1.4621400759435548 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.11176467610630100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8239706959706974 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8259999999999998 " "
y[1] (analytic) = 1.4656825097174755 " "
y[1] (numeric) = 1.4656825097174742 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.08974229218983600000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8229743589743596 " "
Order of pole = 225.05494505494522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8249999999999998 " "
y[1] (analytic) = 1.469237832874197 " "
y[1] (numeric) = 1.4692378328741955 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.05790376458969560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8219780219780218 " "
Order of pole = 225.05494505494505 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8239999999999998 " "
y[1] (analytic) = 1.4728061080214916 " "
y[1] (numeric) = 1.4728061080214903 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 9.04577746041468100000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8209816849816863 " "
Order of pole = 225.0549450549455 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8229999999999998 " "
y[1] (analytic) = 1.4763873981477251 " "
y[1] (numeric) = 1.4763873981477234 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.20317800167413170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.42860254426192207 " "
Order of pole = 1.2825296380469808000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8219999999999998 " "
y[1] (analytic) = 1.4799817666246358 " "
y[1] (numeric) = 1.4799817666246342 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.05022390783915360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.818989010989013 " "
Order of pole = 225.05494505494568 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8209999999999998 " "
y[1] (analytic) = 1.4835892772101407 " "
y[1] (numeric) = 1.4835892772101391 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.04767017283791080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8179926739926765 " "
Order of pole = 225.05494505494582 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8199999999999998 " "
y[1] (analytic) = 1.4872099940511605 " "
y[1] (numeric) = 1.4872099940511592 " "
absolute error = 1.3322676295501878000000000000000E-15 " "
relative error = 8.9581675410954610000000000000E-14 "%"
Correct digits = 16
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.816996336996339 " "
Order of pole = 225.05494505494568 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8189999999999998 " "
y[1] (analytic) = 1.4908439816864731 " "
y[1] (numeric) = 1.4908439816864716 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.0425720287088320000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8159999999999983 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8179999999999998 " "
y[1] (analytic) = 1.4944913050495878 " "
y[1] (numeric) = 1.4944913050495863 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.04002761958099610000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8150036630036647 " "
Order of pole = 225.05494505494556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8169999999999998 " "
y[1] (analytic) = 1.4981520294716473 " "
y[1] (numeric) = 1.4981520294716457 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.03748631907762910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8140073260073254 " "
Order of pole = 225.0549450549449 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8159999999999998 " "
y[1] (analytic) = 1.501826220684353 " "
y[1] (numeric) = 1.5018262206843511 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.18279785965569260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.5724289835225 " "
Order of pole = 2.6627589022609754000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8149999999999998 " "
y[1] (analytic) = 1.5055139448229145 " "
y[1] (numeric) = 1.505513944822913 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.0324130439443020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8120146520146506 " "
Order of pole = 225.05494505494468 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8139999999999998 " "
y[1] (analytic) = 1.509215268429028 " "
y[1] (numeric) = 1.5092152684290265 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.0298810693143419000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8110183150183169 " "
Order of pole = 225.0549450549456 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8129999999999998 " "
y[1] (analytic) = 1.5129302584538766 " "
y[1] (numeric) = 1.5129302584538749 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.17411680378154370000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8100219780219788 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8119999999999998 " "
y[1] (analytic) = 1.5166589822611571 " "
y[1] (numeric) = 1.5166589822611554 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.17123022391751820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8090256410256407 " "
Order of pole = 225.05494505494502 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8109999999999998 " "
y[1] (analytic) = 1.5204015076301356 " "
y[1] (numeric) = 1.5204015076301338 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.16834719676717160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8080293040293055 " "
Order of pole = 225.0549450549455 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8099999999999998 " "
y[1] (analytic) = 1.5241579027587262 " "
y[1] (numeric) = 1.5241579027587246 " "
absolute error = 1.5543122344752192000000000000000E-15 " "
relative error = 1.0197842570391910000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.22880404036838264 " "
Order of pole = 1.52766688188421540000000000000E-13 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8089999999999998 " "
y[1] (analytic) = 1.5279282362665998 " "
y[1] (numeric) = 1.5279282362665978 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.3079157756834542000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8060366300366264 " "
Order of pole = 225.05494505494406 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8079999999999998 " "
y[1] (analytic) = 1.5317125771983144 " "
y[1] (numeric) = 1.5317125771983127 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.15971943159820460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8050402930402956 " "
Order of pole = 225.0549450549458 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8069999999999998 " "
y[1] (analytic) = 1.5355109950264807 " "
y[1] (numeric) = 1.5355109950264787 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.30145694221539460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8040439560439527 " "
Order of pole = 225.05494505494417 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8059999999999998 " "
y[1] (analytic) = 1.5393235596549457 " "
y[1] (numeric) = 1.539323559654944 " "
absolute error = 1.7763568394002505000000000000000E-15 " "
relative error = 1.15398535172062080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8030476190476222 " "
Order of pole = 225.05494505494602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8049999999999998 " "
y[1] (analytic) = 1.5431503414220138 " "
y[1] (numeric) = 1.5431503414220118 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.29501409595889020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8020512820512798 " "
Order of pole = 225.05494505494448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8039999999999998 " "
y[1] (analytic) = 1.5469914111036862 " "
y[1] (numeric) = 1.5469914111036842 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.29179866803497080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8010549450549467 " "
Order of pole = 225.05494505494556 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8029999999999998 " "
y[1] (analytic) = 1.5508468399169373 " "
y[1] (numeric) = 1.5508468399169353 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.288587236913940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.8000586080586071 " "
Order of pole = 225.05494505494482 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8019999999999998 " "
y[1] (analytic) = 1.5547166995230135 " "
y[1] (numeric) = 1.5547166995230115 " "
absolute error = 1.9984014443252818000000000000000E-15 " "
relative error = 1.2853798025957980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.799062271062269 " "
Order of pole = 225.0549450549445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.8009999999999998 " "
y[1] (analytic) = 1.5586010620307644 " "
y[1] (numeric) = 1.5586010620307622 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.42464040564504930000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7980659340659325 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7999999999999998 " "
y[1] (analytic) = 1.5625000000000007 " "
y[1] (numeric) = 1.5624999999999984 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.42108547152019980000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7970695970695947 " "
Order of pole = 225.0549450549444 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7989999999999998 " "
y[1] (analytic) = 1.566413586444884 " "
y[1] (numeric) = 1.5664135864448818 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.41753497828744860000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7960732600732555 " "
Order of pole = 225.05494505494377 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7979999999999998 " "
y[1] (analytic) = 1.5703418948373449 " "
y[1] (numeric) = 1.5703418948373424 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.5553878185414752000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7950769230769227 " "
Order of pole = 225.05494505494497 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7969999999999998 " "
y[1] (analytic) = 1.5742849991105297 " "
y[1] (numeric) = 1.5742849991105274 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.41044731449824160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7940805860805848 " "
Order of pole = 225.05494505494474 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7959999999999998 " "
y[1] (analytic) = 1.578242973662282 " "
y[1] (numeric) = 1.5782429736622796 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.5476011583359642000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.3909893648388873 " "
Order of pole = 1.55964130499342000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7949999999999998 " "
y[1] (analytic) = 1.5822158933586496 " "
y[1] (numeric) = 1.5822158933586472 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.54371515570517120000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7920879120879104 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7939999999999998 " "
y[1] (analytic) = 1.5862038335374258 " "
y[1] (numeric) = 1.5862038335374233 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.53983403805568660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7910915750915729 " "
Order of pole = 225.05494505494445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7929999999999998 " "
y[1] (analytic) = 1.5902068700117205 " "
y[1] (numeric) = 1.5902068700117182 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.39632527762500960000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.49189670739297403 " "
Order of pole = 1.113775738303957000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7919999999999998 " "
y[1] (analytic) = 1.5942250790735648 " "
y[1] (numeric) = 1.5942250790735624 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.53208645770064240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7890989010988994 " "
Order of pole = 225.05494505494462 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7909999999999998 " "
y[1] (analytic) = 1.5982585374975433 " "
y[1] (numeric) = 1.598258537497541 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.38929090454098460000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7881025641025625 " "
Order of pole = 225.05494505494462 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7899999999999998 " "
y[1] (analytic) = 1.6023073225444648 " "
y[1] (numeric) = 1.6023073225444624 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.52435841727083160000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7871062271062255 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7889999999999998 " "
y[1] (analytic) = 1.606371511965059 " "
y[1] (numeric) = 1.6063715119650566 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.52050172452788870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.786109890109888 " "
Order of pole = 225.05494505494445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7879999999999998 " "
y[1] (analytic) = 1.6104511840037112 " "
y[1] (numeric) = 1.6104511840037088 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.51664991676625420000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7851135531135558 " "
Order of pole = 225.05494505494585 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7869999999999998 " "
y[1] (analytic) = 1.6145464174022277 " "
y[1] (numeric) = 1.6145464174022255 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.37527544907811660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7841172161172157 " "
Order of pole = 225.054945054945 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7859999999999998 " "
y[1] (analytic) = 1.6186572914036357 " "
y[1] (numeric) = 1.6186572914036332 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.50896095618691020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7831208791208797 " "
Order of pole = 225.05494505494528 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7849999999999998 " "
y[1] (analytic) = 1.6227838857560153 " "
y[1] (numeric) = 1.6227838857560128 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.50512380336920080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7821245421245384 " "
Order of pole = 225.054945054944 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7839999999999998 " "
y[1] (analytic) = 1.6269262807163691 " "
y[1] (numeric) = 1.6269262807163665 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.63777258421759970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7811282051282079 " "
Order of pole = 225.05494505494593 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7829999999999998 " "
y[1] (analytic) = 1.631084557054523 " "
y[1] (numeric) = 1.6310845570545205 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.4974641526777072000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7801318681318694 " "
Order of pole = 225.05494505494548 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7819999999999998 " "
y[1] (analytic) = 1.6352587960570648 " "
y[1] (numeric) = 1.6352587960570621 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.62942725978609730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7791355311355308 " "
Order of pole = 225.05494505494502 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7809999999999998 " "
y[1] (analytic) = 1.6394490795313152 " "
y[1] (numeric) = 1.6394490795313124 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.76070114044080020000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7781391941391927 " "
Order of pole = 225.0549450549447 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7799999999999998 " "
y[1] (analytic) = 1.6436554898093367 " "
y[1] (numeric) = 1.643655489809334 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.6211032516366680000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7771428571428536 " "
Order of pole = 225.05494505494408 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7789999999999998 " "
y[1] (analytic) = 1.6478781097519786 " "
y[1] (numeric) = 1.647878109751976 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.61694924116773030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7761465201465185 " "
Order of pole = 225.05494505494465 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7779999999999998 " "
y[1] (analytic) = 1.6521170227529565 " "
y[1] (numeric) = 1.6521170227529536 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.74720060641675360000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7751501831501817 " "
Order of pole = 225.05494505494462 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7769999999999998 " "
y[1] (analytic) = 1.65637231274297 " "
y[1] (numeric) = 1.656372312742967 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.7427119747281940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7741538461538466 " "
Order of pole = 225.05494505494525 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7759999999999998 " "
y[1] (analytic) = 1.6606440641938578 " "
y[1] (numeric) = 1.660644064193855 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.73822911619936240000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7731575091575057 " "
Order of pole = 225.0549450549441 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7749999999999998 " "
y[1] (analytic) = 1.6649323621227896 " "
y[1] (numeric) = 1.6649323621227867 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.7337520308302590000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7721611721611732 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7739999999999998 " "
y[1] (analytic) = 1.6692372920964962 " "
y[1] (numeric) = 1.6692372920964933 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.72928071862088400000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7711648351648324 " "
Order of pole = 225.05494505494428 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7729999999999998 " "
y[1] (analytic) = 1.6735589402355375 " "
y[1] (numeric) = 1.6735589402355346 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.72481517957123660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7701684981684966 " "
Order of pole = 225.05494505494468 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7719999999999998 " "
y[1] (analytic) = 1.6778973932186108 " "
y[1] (numeric) = 1.6778973932186079 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.72035541368131730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7691721611721598 " "
Order of pole = 225.05494505494468 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7709999999999998 " "
y[1] (analytic) = 1.6822527382868955 " "
y[1] (numeric) = 1.6822527382868928 " "
absolute error = 2.6645352591003757000000000000000E-15 " "
relative error = 1.58390900395488560000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7681758241758249 " "
Order of pole = 225.05494505494536 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7699999999999998 " "
y[1] (analytic) = 1.686625063248441 " "
y[1] (numeric) = 1.6866250632484379 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.84310344764071380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7671794871794846 " "
Order of pole = 225.05494505494428 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7689999999999998 " "
y[1] (analytic) = 1.6910144564825893 " "
y[1] (numeric) = 1.6910144564825864 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.70701075496992800000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.6196113551812801 " "
Order of pole = 2.3643309532417334000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7679999999999998 " "
y[1] (analytic) = 1.6954210069444453 " "
y[1] (numeric) = 1.6954210069444424 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.70257408171892080000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7651868131868124 " "
Order of pole = 225.0549450549449 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7669999999999998 " "
y[1] (analytic) = 1.6998448041693803 " "
y[1] (numeric) = 1.6998448041693772 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.82876958021438330000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7641904761904772 " "
Order of pole = 225.05494505494542 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7659999999999998 " "
y[1] (analytic) = 1.7042859382775812 " "
y[1] (numeric) = 1.7042859382775783 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.69371805469609100000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7631941391941355 " "
Order of pole = 225.054945054944 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7649999999999998 " "
y[1] (analytic) = 1.7087444999786419 " "
y[1] (numeric) = 1.7087444999786385 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.94919080875877030000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7621978021978 " "
Order of pole = 225.05494505494443 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7639999999999998 " "
y[1] (analytic) = 1.7132205805761913 " "
y[1] (numeric) = 1.7132205805761882 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.8144916680284940000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7612014652014651 " "
Order of pole = 225.0549450549451 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7629999999999998 " "
y[1] (analytic) = 1.7177142719725724 " "
y[1] (numeric) = 1.7177142719725693 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.80974479846440700000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.4589986251361418 " "
Order of pole = 1.5116796703296131000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7619999999999998 " "
y[1] (analytic) = 1.7222256666735565 " "
y[1] (numeric) = 1.7222256666735534 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.80500414614925750000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.759208791208792 " "
Order of pole = 225.05494505494536 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7609999999999998 " "
y[1] (analytic) = 1.7267548577931047 " "
y[1] (numeric) = 1.7267548577931016 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.80026971108304600000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7582124542124522 " "
Order of pole = 225.0549450549445 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7599999999999998 " "
y[1] (analytic) = 1.7313019390581728 " "
y[1] (numeric) = 1.7313019390581696 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.79554149326577200000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.757216117216116 " "
Order of pole = 225.05494505494477 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7589999999999998 " "
y[1] (analytic) = 1.7358670048135603 " "
y[1] (numeric) = 1.7358670048135572 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.79081949269743630000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7562197802197808 " "
Order of pole = 225.0549450549453 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7579999999999998 " "
y[1] (analytic) = 1.740450150026804 " "
y[1] (numeric) = 1.7404501500268008 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.78610370937803850000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7552234432234434 " "
Order of pole = 225.05494505494516 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7569999999999998 " "
y[1] (analytic) = 1.7450514702931175 " "
y[1] (numeric) = 1.7450514702931141 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.90863658211526260000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7542271062271068 " "
Order of pole = 225.05494505494522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7559999999999998 " "
y[1] (analytic) = 1.7496710618403752 " "
y[1] (numeric) = 1.749671061840372 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.9035972798064890000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7532307692307699 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7549999999999998 " "
y[1] (analytic) = 1.7543090215341441 " "
y[1] (numeric) = 1.754309021534141 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.77199366291347280000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7522344322344336 " "
Order of pole = 225.05494505494553 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7539999999999998 " "
y[1] (analytic) = 1.7589654468827625 " "
y[1] (numeric) = 1.7589654468827591 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.89353865920338540000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7512380952380969 " "
Order of pole = 225.05494505494562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7529999999999998 " "
y[1] (analytic) = 1.7636404360424625 " "
y[1] (numeric) = 1.7636404360424591 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.8885193409090550000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7502417582417584 " "
Order of pole = 225.0549450549452 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7519999999999998 " "
y[1] (analytic) = 1.7683340878225453 " "
y[1] (numeric) = 1.7683340878225418 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 2.0090737962163970000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7492454212454225 " "
Order of pole = 225.05494505494553 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7509999999999998 " "
y[1] (analytic) = 1.7730465016906007 " "
y[1] (numeric) = 1.7730465016905974 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.8785006883348380000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7482490842490831 " "
Order of pole = 225.05494505494474 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7499999999999998 " "
y[1] (analytic) = 1.7777777777777788 " "
y[1] (numeric) = 1.7777777777777752 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.99840144432528040000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7472527472527473 " "
Order of pole = 225.05494505494514 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7489999999999998 " "
y[1] (analytic) = 1.7825280168841064 " "
y[1] (numeric) = 1.782528016884103 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.99307592652075870000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.746256410256408 " "
Order of pole = 225.05494505494443 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7479999999999998 " "
y[1] (analytic) = 1.7872973204838583 " "
y[1] (numeric) = 1.7872973204838547 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.98775751414359440000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7452600732600752 " "
Order of pole = 225.0549450549457 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7469999999999998 " "
y[1] (analytic) = 1.792085790730975 " "
y[1] (numeric) = 1.7920857907309715 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.98244620719378730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7442637362637387 " "
Order of pole = 225.05494505494585 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7459999999999998 " "
y[1] (analytic) = 1.7968935304645341 " "
y[1] (numeric) = 1.7968935304645306 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.97714200567133820000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7432673992673984 " "
Order of pole = 225.05494505494485 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7449999999999998 " "
y[1] (analytic) = 1.801720643214271 " "
y[1] (numeric) = 1.8017206432142674 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.97184490957624660000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7422710622710599 " "
Order of pole = 225.05494505494437 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7439999999999998 " "
y[1] (analytic) = 1.806567233206152 " "
y[1] (numeric) = 1.8065672332061486 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.8436452364767308000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7412747252747265 " "
Order of pole = 225.0549450549455 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7429999999999998 " "
y[1] (analytic) = 1.8114334053680028 " "
y[1] (numeric) = 1.8114334053679995 " "
absolute error = 3.3306690738754696000000000000000E-15 " "
relative error = 1.8386925315638780000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7402783882783879 " "
Order of pole = 225.05494505494502 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7419999999999998 " "
y[1] (analytic) = 1.8163192653351847 " "
y[1] (numeric) = 1.8163192653351812 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.95599625385511760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7392820512820504 " "
Order of pole = 225.05494505494482 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7409999999999998 " "
y[1] (analytic) = 1.8212249194563292 " "
y[1] (numeric) = 1.8212249194563255 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.07264805318629760000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7382857142857133 " "
Order of pole = 225.05494505494482 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7399999999999998 " "
y[1] (analytic) = 1.8261504747991246 " "
y[1] (numeric) = 1.826150474799121 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.9454660105111530000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.737289377289377 " "
Order of pole = 225.05494505494508 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7389999999999998 " "
y[1] (analytic) = 1.8310960391561588 " "
y[1] (numeric) = 1.8310960391561553 " "
absolute error = 3.552713678800501000000000000000E-15 " "
relative error = 1.94021154698020730000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7362930402930424 " "
Order of pole = 225.05494505494576 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7379999999999998 " "
y[1] (analytic) = 1.836061721050816 " "
y[1] (numeric) = 1.8360617210508123 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.05589945068140740000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7352967032967005 " "
Order of pole = 225.05494505494426 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7369999999999998 " "
y[1] (analytic) = 1.8410476297432303 " "
y[1] (numeric) = 1.8410476297432266 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.05033168221291220000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7343003663003693 " "
Order of pole = 225.05494505494613 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7359999999999998 " "
y[1] (analytic) = 1.846053875236296 " "
y[1] (numeric) = 1.8460538752362923 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.04477146326098450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7333040293040275 " "
Order of pole = 225.0549450549446 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7349999999999998 " "
y[1] (analytic) = 1.8510805682817355 " "
y[1] (numeric) = 1.8510805682817317 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.03921879382562450000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7323076923076949 " "
Order of pole = 225.05494505494596 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7339999999999998 " "
y[1] (analytic) = 1.8561278203862241 " "
y[1] (numeric) = 1.8561278203862204 " "
absolute error = 3.774758283725532000000000000000E-15 " "
relative error = 2.03367367390683170000000000000E-13 "%"
Correct digits = 15
h = 1.000E-3 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 1.2197288303630399E-2 " "
Order of pole = 1.2683187833317788000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7329022440526732 " "
y[1] (analytic) = 1.8616922768505362 " "
y[1] (numeric) = 1.8616922768505333 " "
absolute error = 2.886579864025407000000000000000E-15 " "
relative error = 1.55051395975531200000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7302176204480866 " "
Order of pole = 225.05494505494562 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.731926460988383 " "
y[1] (analytic) = 1.8666594936841705 " "
y[1] (numeric) = 1.8666594936841683 " "
absolute error = 2.220446049250313000000000000000E-15 " "
relative error = 1.18952924020860630000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7292454116807331 " "
Order of pole = 225.05494505494502 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7309506779240927 " "
y[1] (analytic) = 1.8716466167605696 " "
y[1] (numeric) = 1.8716466167605685 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.93179831429247700000000000000E-14 "%"
Correct digits = 16
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7282732029133793 " "
Order of pole = 225.05494505494423 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7299748948598025 " "
y[1] (analytic) = 1.8766537525883356 " "
y[1] (numeric) = 1.8766537525883356 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.72730099414603 " "
Order of pole = 225.05494505494494 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7289991117955122 " "
y[1] (analytic) = 1.881681008389368 " "
y[1] (numeric) = 1.8816810083893691 " "
absolute error = 1.1102230246251565000000000000000E-15 " "
relative error = 5.90016596689497500000000000000E-14 "%"
Correct digits = 16
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7263287853786802 " "
Order of pole = 225.05494505494548 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7279013558481857 " "
y[1] (analytic) = 1.887360855248356 " "
y[1] (numeric) = 1.8873608552483585 " "
absolute error = 2.4424906541753444000000000000000E-15 " "
relative error = 1.29413018574762150000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.2688050761772486 " "
Order of pole = 2.3874235921539366000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7269255727838955 " "
y[1] (analytic) = 1.8924312252929567 " "
y[1] (numeric) = 1.8924312252929598 " "
absolute error = 3.1086244689504383000000000000000E-15 " "
relative error = 1.64266179262034180000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Complex estimate of poles used for equation 1"
Radius of convergence = 0.2038952988677595 " "
Order of pole = 1.3873346915715956000000000000E-12 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7259497897196052 " "
y[1] (analytic) = 1.8975220550402125 " "
y[1] (numeric) = 1.8975220550402165 " "
absolute error = 3.9968028886505635000000000000000E-15 " "
relative error = 2.1063275011925290000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7232906329807065 " "
Order of pole = 225.0549450549454 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.724974006655315 " "
y[1] (analytic) = 1.9026334547156525 " "
y[1] (numeric) = 1.9026334547156576 " "
absolute error = 5.10702591327572000000000000000E-15 " "
relative error = 2.6841880135230580000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7223184242133547 " "
Order of pole = 225.05494505494522 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7239982235910247 " "
y[1] (analytic) = 1.9077655352880991 " "
y[1] (numeric) = 1.907765535288105 " "
absolute error = 5.995204332975845000000000000000E-15 " "
relative error = 3.14252680535529500000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7213462154460032 " "
Order of pole = 225.05494505494525 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7229004676436982 " "
y[1] (analytic) = 1.91356398519833 " "
y[1] (numeric) = 1.9135639851983375 " "
absolute error = 7.549516567451064000000000000000E-15 " "
relative error = 3.94526476556183700000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7202524805827347 " "
Order of pole = 225.05494505494582 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.721924684579408 " "
y[1] (analytic) = 1.9187403845568438 " "
y[1] (numeric) = 1.918740384556852 " "
absolute error = 8.215650382226158000000000000000E-15 " "
relative error = 4.281793643554160000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7192802718153817 " "
Order of pole = 225.05494505494534 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7209489015151177 " "
y[1] (analytic) = 1.923937816447344 " "
y[1] (numeric) = 1.923937816447353 " "
absolute error = 9.103828801926284000000000000000E-15 " "
relative error = 4.7318726853329390000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7183080630480294 " "
Order of pole = 225.05494505494508 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7199731184508275 " "
y[1] (analytic) = 1.929156394969034 " "
y[1] (numeric) = 1.9291563949690445 " "
absolute error = 1.043609643147647100000000000000E-14 " "
relative error = 5.4096684222659860000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7173358542806761 " "
Order of pole = 225.05494505494448 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7189973353865372 " "
y[1] (analytic) = 1.9343962349958879 " "
y[1] (numeric) = 1.934396234995899 " "
absolute error = 1.110223024625156500000000000000E-14 " "
relative error = 5.7393775098384470000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7163636455133253 " "
Order of pole = 225.05494505494474 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7178995794392107 " "
y[1] (analytic) = 1.9403166132036966 " "
y[1] (numeric) = 1.9403166132037089 " "
absolute error = 1.221245327087672200000000000000E-14 " "
relative error = 6.2940517994702370000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7152699106500575 " "
Order of pole = 225.05494505494553 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7169237963749204 " "
y[1] (analytic) = 1.9456020189207326 " "
y[1] (numeric) = 1.945602018920746 " "
absolute error = 1.332267629550187800000000000000E-14 " "
relative error = 6.8475855626898740000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7142977018827076 " "
Order of pole = 225.05494505494602 " "
" "
"TOP MAIN SOLVE Loop"
x[1] = -0.7159480133106302 " "
y[1] (analytic) = 1.9509090501876978 " "
y[1] (numeric) = 1.9509090501877122 " "
absolute error = 1.443289932012703500000000000000E-14 " "
relative error = 7.3980380165535850000000000000E-13 "%"
Correct digits = 15
h = 1.219728830363039900E-4 " "
"Real estimate of pole used for equation 1"
Radius of convergence = 0.7133254931153531 " "
Order of pole = 225.05494505494502 " "
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"
Iterations = 419
"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 0 Minutes 9 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 9 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 3 Minutes 10 Seconds
"Time to Timeout " Unknown
Percent Done = 94.92794132919582 "%"
(%o58) true
(%o58) diffeq.max